| Name | qsiml JSON |
| Version |
0.0.5
JSON |
| download |
| home_page | None |
| Summary | A simulation of quantum circuits in python |
| upload_time | 2024-11-05 11:06:11 |
| maintainer | None |
| docs_url | None |
| author | None |
| requires_python | >=3.12 |
| license | GNU GENERAL PUBLIC LICENSE Version 2, June 1991 Copyright (C) 1989, 1991 Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The licenses for most software are designed to take away your freedom to share and change it. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change free software--to make sure the software is free for all its users. This General Public License applies to most of the Free Software Foundation's software and to any other program whose authors commit to using it. (Some other Free Software Foundation software is covered by the GNU Lesser General Public License instead.) You can apply it to your programs, too. When we speak of free software, we are referring to freedom, not price. Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software (and charge for this service if you wish), that you receive source code or can get it if you want it, that you can change the software or use pieces of it in new free programs; and that you know you can do these things. To protect your rights, we need to make restrictions that forbid anyone to deny you these rights or to ask you to surrender the rights. These restrictions translate to certain responsibilities for you if you distribute copies of the software, or if you modify it. For example, if you distribute copies of such a program, whether gratis or for a fee, you must give the recipients all the rights that you have. You must make sure that they, too, receive or can get the source code. And you must show them these terms so they know their rights. We protect your rights with two steps: (1) copyright the software, and (2) offer you this license which gives you legal permission to copy, distribute and/or modify the software. Also, for each author's protection and ours, we want to make certain that everyone understands that there is no warranty for this free software. If the software is modified by someone else and passed on, we want its recipients to know that what they have is not the original, so that any problems introduced by others will not reflect on the original authors' reputations. Finally, any free program is threatened constantly by software patents. We wish to avoid the danger that redistributors of a free program will individually obtain patent licenses, in effect making the program proprietary. To prevent this, we have made it clear that any patent must be licensed for everyone's free use or not licensed at all. The precise terms and conditions for copying, distribution and modification follow. GNU GENERAL PUBLIC LICENSE TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION 0. This License applies to any program or other work which contains a notice placed by the copyright holder saying it may be distributed under the terms of this General Public License. The "Program", below, refers to any such program or work, and a "work based on the Program" means either the Program or any derivative work under copyright law: that is to say, a work containing the Program or a portion of it, either verbatim or with modifications and/or translated into another language. (Hereinafter, translation is included without limitation in the term "modification".) Each licensee is addressed as "you". Activities other than copying, distribution and modification are not covered by this License; they are outside its scope. The act of running the Program is not restricted, and the output from the Program is covered only if its contents constitute a work based on the Program (independent of having been made by running the Program). Whether that is true depends on what the Program does. 1. You may copy and distribute verbatim copies of the Program's source code as you receive it, in any medium, provided that you conspicuously and appropriately publish on each copy an appropriate copyright notice and disclaimer of warranty; keep intact all the notices that refer to this License and to the absence of any warranty; and give any other recipients of the Program a copy of this License along with the Program. You may charge a fee for the physical act of transferring a copy, and you may at your option offer warranty protection in exchange for a fee. 2. You may modify your copy or copies of the Program or any portion of it, thus forming a work based on the Program, and copy and distribute such modifications or work under the terms of Section 1 above, provided that you also meet all of these conditions: a) You must cause the modified files to carry prominent notices stating that you changed the files and the date of any change. b) You must cause any work that you distribute or publish, that in whole or in part contains or is derived from the Program or any part thereof, to be licensed as a whole at no charge to all third parties under the terms of this License. c) If the modified program normally reads commands interactively when run, you must cause it, when started running for such interactive use in the most ordinary way, to print or display an announcement including an appropriate copyright notice and a notice that there is no warranty (or else, saying that you provide a warranty) and that users may redistribute the program under these conditions, and telling the user how to view a copy of this License. (Exception: if the Program itself is interactive but does not normally print such an announcement, your work based on the Program is not required to print an announcement.) These requirements apply to the modified work as a whole. If identifiable sections of that work are not derived from the Program, and can be reasonably considered independent and separate works in themselves, then this License, and its terms, do not apply to those sections when you distribute them as separate works. But when you distribute the same sections as part of a whole which is a work based on the Program, the distribution of the whole must be on the terms of this License, whose permissions for other licensees extend to the entire whole, and thus to each and every part regardless of who wrote it. Thus, it is not the intent of this section to claim rights or contest your rights to work written entirely by you; rather, the intent is to exercise the right to control the distribution of derivative or collective works based on the Program. In addition, mere aggregation of another work not based on the Program with the Program (or with a work based on the Program) on a volume of a storage or distribution medium does not bring the other work under the scope of this License. 3. You may copy and distribute the Program (or a work based on it, under Section 2) in object code or executable form under the terms of Sections 1 and 2 above provided that you also do one of the following: a) Accompany it with the complete corresponding machine-readable source code, which must be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange; or, b) Accompany it with a written offer, valid for at least three years, to give any third party, for a charge no more than your cost of physically performing source distribution, a complete machine-readable copy of the corresponding source code, to be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange; or, c) Accompany it with the information you received as to the offer to distribute corresponding source code. (This alternative is allowed only for noncommercial distribution and only if you received the program in object code or executable form with such an offer, in accord with Subsection b above.) The source code for a work means the preferred form of the work for making modifications to it. For an executable work, complete source code means all the source code for all modules it contains, plus any associated interface definition files, plus the scripts used to control compilation and installation of the executable. However, as a special exception, the source code distributed need not include anything that is normally distributed (in either source or binary form) with the major components (compiler, kernel, and so on) of the operating system on which the executable runs, unless that component itself accompanies the executable. If distribution of executable or object code is made by offering access to copy from a designated place, then offering equivalent access to copy the source code from the same place counts as distribution of the source code, even though third parties are not compelled to copy the source along with the object code. 4. You may not copy, modify, sublicense, or distribute the Program except as expressly provided under this License. Any attempt otherwise to copy, modify, sublicense or distribute the Program is void, and will automatically terminate your rights under this License. However, parties who have received copies, or rights, from you under this License will not have their licenses terminated so long as such parties remain in full compliance. 5. You are not required to accept this License, since you have not signed it. However, nothing else grants you permission to modify or distribute the Program or its derivative works. These actions are prohibited by law if you do not accept this License. Therefore, by modifying or distributing the Program (or any work based on the Program), you indicate your acceptance of this License to do so, and all its terms and conditions for copying, distributing or modifying the Program or works based on it. 6. Each time you redistribute the Program (or any work based on the Program), the recipient automatically receives a license from the original licensor to copy, distribute or modify the Program subject to these terms and conditions. You may not impose any further restrictions on the recipients' exercise of the rights granted herein. You are not responsible for enforcing compliance by third parties to this License. 7. If, as a consequence of a court judgment or allegation of patent infringement or for any other reason (not limited to patent issues), conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot distribute so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not distribute the Program at all. For example, if a patent license would not permit royalty-free redistribution of the Program by all those who receive copies directly or indirectly through you, then the only way you could satisfy both it and this License would be to refrain entirely from distribution of the Program. If any portion of this section is held invalid or unenforceable under any particular circumstance, the balance of the section is intended to apply and the section as a whole is intended to apply in other circumstances. It is not the purpose of this section to induce you to infringe any patents or other property right claims or to contest validity of any such claims; this section has the sole purpose of protecting the integrity of the free software distribution system, which is implemented by public license practices. Many people have made generous contributions to the wide range of software distributed through that system in reliance on consistent application of that system; it is up to the author/donor to decide if he or she is willing to distribute software through any other system and a licensee cannot impose that choice. This section is intended to make thoroughly clear what is believed to be a consequence of the rest of this License. 8. If the distribution and/or use of the Program is restricted in certain countries either by patents or by copyrighted interfaces, the original copyright holder who places the Program under this License may add an explicit geographical distribution limitation excluding those countries, so that distribution is permitted only in or among countries not thus excluded. In such case, this License incorporates the limitation as if written in the body of this License. 9. The Free Software Foundation may publish revised and/or new versions of the General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies a version number of this License which applies to it and "any later version", you have the option of following the terms and conditions either of that version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of this License, you may choose any version ever published by the Free Software Foundation. 10. If you wish to incorporate parts of the Program into other free programs whose distribution conditions are different, write to the author to ask for permission. For software which is copyrighted by the Free Software Foundation, write to the Free Software Foundation; we sometimes make exceptions for this. Our decision will be guided by the two goals of preserving the free status of all derivatives of our free software and of promoting the sharing and reuse of software generally. NO WARRANTY 11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. END OF TERMS AND CONDITIONS How to Apply These Terms to Your New Programs If you develop a new program, and you want it to be of the greatest possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms. To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively convey the exclusion of warranty; and each file should have at least the "copyright" line and a pointer to where the full notice is found. <one line to give the program's name and a brief idea of what it does.> Copyright (C) <year> <name of author> This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. Also add information on how to contact you by electronic and paper mail. If the program is interactive, make it output a short notice like this when it starts in an interactive mode: Gnomovision version 69, Copyright (C) year name of author Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than `show w' and `show c'; they could even be mouse-clicks or menu items--whatever suits your program. You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the program, if necessary. Here is a sample; alter the names: Yoyodyne, Inc., hereby disclaims all copyright interest in the program `Gnomovision' (which makes passes at compilers) written by James Hacker. <signature of Ty Coon>, 1 April 1989 Ty Coon, President of Vice This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Lesser General Public License instead of this License. |
| keywords |
quantum
quantum computing
simulator
|
| VCS |
 |
| bugtrack_url |
|
| requirements |
No requirements were recorded.
|
| Travis-CI |
No Travis.
|
| coveralls test coverage |
No coveralls.
|
Qsiml is a Python-based quantum computing simulator that provides a minimalist approach to quantum circuit simulation.
## Installation
```bash
pip install qsiml
```
### Quantum Circuit
A quantum circuit is represented by the `QuantumCircuit` class. It manages a collection of qubits and applies quantum gates to manipulate their states.
```python
from qsiml import QuantumCircuit
qc = QuantumCircuit(n) # Creates a circuit with `n` qubits
```
### Gates
### Single-Qubit Gates
1. Hadamard (H): Creates superposition
```python
qc.h(qubit)
```
2. Pauli-X (NOT): Bit flip
```python
qc.px(qubit)
```
3. Pauli-Y: Rotation around Y-axis
```python
qc.py(qubit)
```
4. Pauli-Z: Phase flip
```python
qc.pz(qubit)
```
5. Phase (P): Applies a phase shift
```python
qc.phase(qubit, theta)
```
6. Rotation Gates: Rotate around X, Y, or Z axis
```python
qc.rx(qubit, theta)
qc.ry(qubit, theta)
qc.rz(qubit, theta)
```
where θ is the rotation angle in radians.
### Multi-Qubit Gates
1. CNOT: Controlled-NOT
```python
qc.cnot(control, target)
```
2. SWAP: Swaps two qubits
```python
qc.swap(qubit1, qubit2)
```
3. Toffoli (CCNOT): Controlled-Controlled-NOT
```python
qc.ccnot(control1, control2, target)
```
4. Fredkin (CSWAP): Controlled-SWAP
```python
qc.cswap(control, target1, target2)
```
## Measurement
Measure all qubits, collapsing the state vector:
```python
result = qc.measure_all() # collapses the state vector to a single basis states
# returns a bitstring of the basis state and stores the collapsed state in qc.classical_bits
```
Measure a specific qubit, partially collapsing the state vector.
```python
qc.measure(qubit) # classical state of qn is stored in qc.classical_bits[n]
```
## Circuit Visualization
```python
from qsiml import QuantumCircuit
qc = QuantumCircuit(5)
qc.px(0)
qc.h(1)
qc.h(2)
qc.h(3)
qc.ccnot(1, 2, 3)
qc.ccnot(2, 3, 4)
```
Display the circuit as an ASCII diagram:
```python
qc.draw("Circuit Visualization: ")
```
```
Circuit Visualization
|q0⟩—X————————————————
|q1⟩————H————————●————
│
|q2⟩———————H—————●——●—
│ │
|q3⟩——————————H——⨁——●—
│
|q4⟩————————————————⨁—
```
```python
qc.operations("Operations: ")
```
prints the gates applied with respect to time:
```
Operations:
1. X on qubit 0
2. H on qubit 1
3. H on qubit 2
4. H on qubit 3
5. CCNOT on qubits 1, 2, 3
6. CCNOT on qubits 2, 3, 4
```
```python
print(qc.circuit)
```
```
prints the internal circuit representation
[('X', [0]), ('H', [1]), ('H', [2]), ('H', [3]), ('CCNOT', [1, 2, 3]), ('CCNOT', [2, 3, 4])]
```
## State Inspection
View the circuit's state without collapsing it.
```python
qc.dump("Dump table: ")
```
prints a table which shows the amplitude, probability, and phase of each possible basis state.
```
Dump Table:
+---------------+---------------+----------------------+---------+
| Basis State | Probability | Amplitude | Phase |
+===============+===============+======================+=========+
| |00001⟩ | 12.500000% | 0.353553 + 0.000000i | 0 |
| |00011⟩ | 12.500000% | 0.353553 + 0.000000i | 0 |
| |00101⟩ | 12.500000% | 0.353553 + 0.000000i | 0 |
| |00111⟩ | 12.500000% | 0.353553 + 0.000000i | 0 |
| |01001⟩ | 12.500000% | 0.353553 + 0.000000i | 0 |
| |01011⟩ | 12.500000% | 0.353553 + 0.000000i | 0 |
| |11101⟩ | 12.500000% | 0.353553 + 0.000000i | 0 |
| |11111⟩ | 12.500000% | 0.353553 + 0.000000i | 0 |
+---------------+---------------+----------------------+---------+
```
## Examples
### Bell State Preparation
```python
qc = QuantumCircuit(2)
qc.h(0)
qc.cnot(0, 1)
qc.draw("Bell State diagram: ")
qc.dump("Bell State dump table: ")
```
Output:
```
Bell State diagram:
|q0⟩—H——●—
│
|q1⟩————⨁—
Bell State dump table:
+---------------+---------------+----------------------+---------+
| Basis State | Probability | Amplitude | Phase |
+===============+===============+======================+=========+
| |00⟩ | 50.000000% | 0.707107 + 0.000000i | 0 |
| |11⟩ | 50.000000% | 0.707107 + 0.000000i | 0 |
+---------------+---------------+----------------------+---------+
```
### Quantum Fourier Transform (2 qubits)
```python
qc = QuantumCircuit(2)
qc.h(0)
qc.phase(1, np.pi/2)
qc.cnot(0, 1)
qc.h(1)
qc.swap(0, 1)
qc.draw("Draw: ")
qc.dump("Dump: ")
```
```
Draw:
|q0⟩—H—————————————●—————x—
│ │
|q1⟩————-P(1.5707)—⨁——H——x—
Dump:
+---------------+---------------+-----------------------+---------+
| Basis State | Probability | Amplitude | Phase |
+===============+===============+=======================+=========+
| |00⟩ | 56.250000% | 0.750000 + 0.000000i | 0 |
| |01⟩ | 56.250000% | 0.750000 + 0.000000i | 0 |
| |10⟩ | 31.250000% | 0.250000 + 0.500000i | 1.10715 |
| |11⟩ | 31.250000% | -0.250000 + 0.500000i | 2.03444 |
+---------------+---------------+-----------------------+---------+
```
### Theory for nerds
Quantum computing leverages the principles of quantum mechanics to perform computations. Unlike classical bits, which can be in one of two states (0 or 1), quantum bits (qubits) can exist in a superposition of states, represented as a linear combination of basis states:
`|ψ⟩ = α|0⟩ + β|1⟩`
where `α` and `β` are complex numbers satisfying `|α⟩^2 + |β⟩^2 = 1.0`
A trivial example to illustrate the, albeit niche, advantage of quantum computing over classical computing is the Deutsch-Jozsa algorithm. In the problem, we're given a black box quantum computer known as an oracle that implements some function `f: {0, 1}ⁿ-> {0, 1}`, which takes an n-bit binary value as input and returns either a 0 or a 1 for each input. The function output is either constant, either 1 OR 0 for all inputs, or balanced, 0 for exactly half of the input domain and 1 for the other half. The task is to determine if `f` is constant or balanced using the function.
the deterministic classical approach requires `2^(n - 1) + 1` evaluations to prove that f is either constant or balanced. It needs to map *half + 1* the set of inputs to evaluate, with 100% certainty, the nature of the oracle. If `n := 2`:
|**x (input)** | **f(x) (output)** |
|:--------:|:------------:|
| 00 | 0 |
| 01 | 0 |
| 10 | 1 |
| 00 | 1 |
Only the first 3 calculations are required to determine that the oracle is balanced. Though, the computational complexity increases exponentially, which makes it more expensive to solve for larger values of `n`.
This is where quantum computing shines. The Deutsch-Jozsa algorithm applies the oracle to a superposition of all possible inputs, represented by `n + 1`, where the first `n` qubits are initialized to |0⟩, and the last one is initialized to |1⟩.
```python
n = 10
qc = QuantumCircuit(n + 1) # initialize a circuit with n + 1 qubits
qc.px(n) # initialize the last qubit to |1⟩
```
Apply the Hadamard gate to all qubits to create a superposition of all possible states (try it!)
```python
# applies the hadamard gate to all qubits in the system
for i in range(n + 1):
qc.h(i)
```
The next step is to create an oracle. The oracle essentially acts as a query system, which is easy to represent in classical computing by storing the mapped value in a certain memory register. In quantum computing however, this is impractical. We'll have to create a custom quantum circuit representation of an oracle. We'll use the `n + 1`th qubit as an ancilla qubit that is initialized to a state of |1⟩, and the first `n` qubits as the query. For a balanced function, the oracle should flip the ancilla qubit for exactly half of the input states.
```python
import numpy as np
random_bits = np.random.randint(1, 2**n) # returns a random integer between 1 and 2**n - 1 inclusive.
for i in range(n):
# applies cnot with control bits that lie within the randomly generated binary number. If `random_bit` = `101`, then qubits 0 and 2 would be used as control bits.
if a & (1 << i):
qc.cnot(i, n)
```
Afterwards, we revert the query qubits back to their original state by applying the hadamard gate
```python
for i in range(n):
qc.h(i)
```
Finally, we measure the query qubits individually
```python
for i in range(n):
qc.measure(i)
```
The measured values of the nth qubit are stored in `qc.classical_bits[n]`. If all measured values are 0, i.e. `qc.classical_bits[0..n]`, then the oracle is a constant function. Anything other than that, the oracle is a balanced function.
Now that a balanced oracle function has been implemented, we can implement a constant oracle.
```python
from qsiml import QuantumCircuit
import numpy as np
class DeutschJozsa():
def __init__(self, n: int = 10):
self.qc = QuantumCircuit(n + 1)
self.n = n
def constant_oracle(self, constant_value: int):
if constant_value == 0:
self.qc.i(self.n)
else:
self.qc.px(self.n)
def balanced_oracle(self, random_bits: int):
for i in range(self.n):
if random_bits & (1 << i):
self.qc.cnot(i, self.n)
def deutsch_jozsa(self):
n = self.n
constant_or_balanced = np.random.randint(0, 2)
constant_value = np.random.randint(0, 2)
random_bits = np.random.randint(1, 2**n)
self.qc.px(n)
for i in range(n + 1):
self.qc.h(i)
if constant_or_balanced == 0:
self.constant_oracle(constant_value)
else:
self.balanced_oracle(random_bits)
for i in range(n):
self.qc.h(i)
for i in range(n):
self.qc.measure(i)
self.qc.draw()
print("Classical Bits: ", self.qc.classical_bits[:-1])
dj = DeutschJozsa(10)
dj.deutsch_jozsa()
```
returns this for a constant oracle (Notice how every measured value is 0):
```
|q00⟩—H——————————————————————————————————————H—————————————————————————————M————————————————————————————
0
|q01⟩————H——————————————————————————————————————H—————————————————————————————M—————————————————————————
0
|q02⟩———————H——————————————————————————————————————H—————————————————————————————M——————————————————————
0
|q03⟩——————————H——————————————————————————————————————H—————————————————————————————M———————————————————
0
|q04⟩—————————————H——————————————————————————————————————H—————————————————————————————M————————————————
0
|q05⟩————————————————H——————————————————————————————————————H—————————————————————————————M—————————————
0
|q06⟩———————————————————H——————————————————————————————————————H—————————————————————————————M——————————
0
|q07⟩——————————————————————H——————————————————————————————————————H—————————————————————————————M———————
0
|q08⟩—————————————————————————H——————————————————————————————————————H—————————————————————————————M————
0
|q09⟩————————————————————————————H——————————————————————————————————————H—————————————————————————————M—
0
|q10⟩———————————————————————————————X——H——X—————————————————————————————————————————————————————————————
Classical Bits: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
```
And this for a balanced oracle (The measured values form a non-zero bitstring)
```
|q00⟩—H——————————————————————————————————————————————————H—————————————————————————————M————————————————————————————
0
|q01⟩————H————————————————————————————————●—————————————————H—————————————————————————————M—————————————————————————
│ 1
|q02⟩———————H—————————————————————————————│————————————————————H—————————————————————————————M——————————————————————
│ 0
|q03⟩——————————H——————————————————————————│———————————————————————H—————————————————————————————M———————————————————
│ 0
|q04⟩—————————————H———————————————————————│——————————————————————————H—————————————————————————————M————————————————
│ 0
|q05⟩————————————————H————————————————————│—————————————————————————————H—————————————————————————————M—————————————
│ 0
|q06⟩———————————————————H—————————————————│——●—————————————————————————————H—————————————————————————————M——————————
│ │ 1
|q07⟩——————————————————————H——————————————│——│——●—————————————————————————————H—————————————————————————————M———————
│ │ │ 1
|q08⟩—————————————————————————H———————————│——│——│——●—————————————————————————————H—————————————————————————————M————
│ │ │ │ 1
|q09⟩————————————————————————————H————————│——│——│——│——●—————————————————————————————H—————————————————————————————M—
│ │ │ │ │ 1
|q10⟩———————————————————————————————X——H——⨁——⨁——⨁——⨁——⨁—————————————————————————————————————————————————————————————
Classical Bits: [0, 1, 0, 0, 0, 0, 1, 1, 1, 1]
```
You can import this class using:
```python
from qsiml import DeutschJozsa
```
### State Vector Representation
In Qsiml, an n-qubit system is represented by a 2^n dimensional complex vector, known as the state vector. For example, a two-qubit system is represented by a 4-dimensional vector:
`|ψ⟩ = α|00⟩ + β|01⟩ + γ|10⟩ + δ|11⟩`
where `|α|^2 + |β|^2 + |γ|^2 + |δ|^2 = 1`.
Raw data
{
"_id": null,
"home_page": null,
"name": "qsiml",
"maintainer": null,
"docs_url": null,
"requires_python": ">=3.12",
"maintainer_email": null,
"keywords": "quantum, quantum computing, simulator",
"author": null,
"author_email": "Mustafa Aamir <mustafa.290101@gmail.com>, Yusuf Sabuwala <yusuff.0279@gmail.com>",
"download_url": "https://files.pythonhosted.org/packages/62/ae/18fe893f63ba833b2f2e99402e562aab4977b45a88cd62b3ab1e217ef58e/qsiml-0.0.5.tar.gz",
"platform": null,
"description": "\n\nQsiml is a Python-based quantum computing simulator that provides a minimalist approach to quantum circuit simulation.\n\n## Installation\n\n```bash\npip install qsiml\n```\n\n### Quantum Circuit\n\nA quantum circuit is represented by the `QuantumCircuit` class. It manages a collection of qubits and applies quantum gates to manipulate their states.\n\n```python\nfrom qsiml import QuantumCircuit\n\nqc = QuantumCircuit(n) # Creates a circuit with `n` qubits\n```\n\n### Gates\n\n### Single-Qubit Gates\n\n1. Hadamard (H): Creates superposition\n ```python\n qc.h(qubit)\n ```\n\n2. Pauli-X (NOT): Bit flip\n ```python\n qc.px(qubit)\n ```\n\n3. Pauli-Y: Rotation around Y-axis\n ```python\n qc.py(qubit)\n ```\n\n4. Pauli-Z: Phase flip\n ```python\n qc.pz(qubit)\n ```\n\n5. Phase (P): Applies a phase shift\n ```python\n qc.phase(qubit, theta)\n ```\n\n6. Rotation Gates: Rotate around X, Y, or Z axis\n ```python\n qc.rx(qubit, theta)\n qc.ry(qubit, theta)\n qc.rz(qubit, theta)\n ```\n where \u03b8 is the rotation angle in radians.\n\n### Multi-Qubit Gates\n\n1. CNOT: Controlled-NOT\n ```python\n qc.cnot(control, target)\n ```\n\n2. SWAP: Swaps two qubits\n ```python\n qc.swap(qubit1, qubit2)\n ```\n\n3. Toffoli (CCNOT): Controlled-Controlled-NOT\n ```python\n qc.ccnot(control1, control2, target)\n ```\n\n4. Fredkin (CSWAP): Controlled-SWAP\n ```python\n qc.cswap(control, target1, target2)\n ```\n\n## Measurement\n\nMeasure all qubits, collapsing the state vector:\n\n```python\nresult = qc.measure_all() # collapses the state vector to a single basis states\n# returns a bitstring of the basis state and stores the collapsed state in qc.classical_bits\n```\n\nMeasure a specific qubit, partially collapsing the state vector.\n\n```python\nqc.measure(qubit) # classical state of qn is stored in qc.classical_bits[n]\n```\n\n## Circuit Visualization\n\n```python\nfrom qsiml import QuantumCircuit\n\nqc = QuantumCircuit(5)\nqc.px(0)\nqc.h(1)\nqc.h(2)\nqc.h(3)\nqc.ccnot(1, 2, 3)\nqc.ccnot(2, 3, 4)\n```\n\nDisplay the circuit as an ASCII diagram:\n\n```python\nqc.draw(\"Circuit Visualization: \")\n```\n```\nCircuit Visualization\n\n|q0\u27e9\u2014X\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n\n|q1\u27e9\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u25cf\u2014\u2014\u2014\u2014\n \u2502\n|q2\u27e9\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u25cf\u2014\u2014\u25cf\u2014\n \u2502 \u2502\n|q3\u27e9\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2a01\u2014\u2014\u25cf\u2014\n \u2502\n|q4\u27e9\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2a01\u2014\n```\n\n```python\nqc.operations(\"Operations: \")\n```\nprints the gates applied with respect to time:\n```\n Operations:\n 1. X on qubit 0\n 2. H on qubit 1\n 3. H on qubit 2\n 4. H on qubit 3\n 5. CCNOT on qubits 1, 2, 3\n 6. CCNOT on qubits 2, 3, 4\n```\n\n```python\nprint(qc.circuit)\n```\n```\nprints the internal circuit representation\n\n[('X', [0]), ('H', [1]), ('H', [2]), ('H', [3]), ('CCNOT', [1, 2, 3]), ('CCNOT', [2, 3, 4])]\n```\n\n## State Inspection\n\nView the circuit's state without collapsing it.\n\n```python\nqc.dump(\"Dump table: \")\n```\n\nprints a table which shows the amplitude, probability, and phase of each possible basis state.\n```\nDump Table:\n+---------------+---------------+----------------------+---------+\n| Basis State | Probability | Amplitude | Phase |\n+===============+===============+======================+=========+\n| |00001\u27e9 | 12.500000% | 0.353553 + 0.000000i | 0 |\n| |00011\u27e9 | 12.500000% | 0.353553 + 0.000000i | 0 |\n| |00101\u27e9 | 12.500000% | 0.353553 + 0.000000i | 0 |\n| |00111\u27e9 | 12.500000% | 0.353553 + 0.000000i | 0 |\n| |01001\u27e9 | 12.500000% | 0.353553 + 0.000000i | 0 |\n| |01011\u27e9 | 12.500000% | 0.353553 + 0.000000i | 0 |\n| |11101\u27e9 | 12.500000% | 0.353553 + 0.000000i | 0 |\n| |11111\u27e9 | 12.500000% | 0.353553 + 0.000000i | 0 |\n+---------------+---------------+----------------------+---------+\n```\n\n## Examples\n\n### Bell State Preparation\n\n```python\nqc = QuantumCircuit(2)\nqc.h(0)\nqc.cnot(0, 1)\nqc.draw(\"Bell State diagram: \")\nqc.dump(\"Bell State dump table: \")\n```\n\nOutput:\n```\nBell State diagram:\n|q0\u27e9\u2014H\u2014\u2014\u25cf\u2014\n \u2502\n|q1\u27e9\u2014\u2014\u2014\u2014\u2a01\u2014\n\nBell State dump table:\n+---------------+---------------+----------------------+---------+\n| Basis State | Probability | Amplitude | Phase |\n+===============+===============+======================+=========+\n| |00\u27e9 | 50.000000% | 0.707107 + 0.000000i | 0 |\n| |11\u27e9 | 50.000000% | 0.707107 + 0.000000i | 0 |\n+---------------+---------------+----------------------+---------+\n```\n\n### Quantum Fourier Transform (2 qubits)\n\n```python\nqc = QuantumCircuit(2)\nqc.h(0)\nqc.phase(1, np.pi/2)\nqc.cnot(0, 1)\nqc.h(1)\nqc.swap(0, 1)\nqc.draw(\"Draw: \")\nqc.dump(\"Dump: \")\n```\n\n```\nDraw:\n\n|q0\u27e9\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u25cf\u2014\u2014\u2014\u2014\u2014x\u2014\n \u2502 \u2502\n|q1\u27e9\u2014\u2014\u2014\u2014-P(1.5707)\u2014\u2a01\u2014\u2014H\u2014\u2014x\u2014\n\nDump:\n\n+---------------+---------------+-----------------------+---------+\n| Basis State | Probability | Amplitude | Phase |\n+===============+===============+=======================+=========+\n| |00\u27e9 | 56.250000% | 0.750000 + 0.000000i | 0 |\n| |01\u27e9 | 56.250000% | 0.750000 + 0.000000i | 0 |\n| |10\u27e9 | 31.250000% | 0.250000 + 0.500000i | 1.10715 |\n| |11\u27e9 | 31.250000% | -0.250000 + 0.500000i | 2.03444 |\n+---------------+---------------+-----------------------+---------+\n```\n\n### Theory for nerds\n\nQuantum computing leverages the principles of quantum mechanics to perform computations. Unlike classical bits, which can be in one of two states (0 or 1), quantum bits (qubits) can exist in a superposition of states, represented as a linear combination of basis states:\n\n`|\u03c8\u27e9 = \u03b1|0\u27e9 + \u03b2|1\u27e9`\n\nwhere `\u03b1` and `\u03b2` are complex numbers satisfying `|\u03b1\u27e9^2 + |\u03b2\u27e9^2 = 1.0`\n\nA trivial example to illustrate the, albeit niche, advantage of quantum computing over classical computing is the Deutsch-Jozsa algorithm. In the problem, we're given a black box quantum computer known as an oracle that implements some function `f: {0, 1}\u207f-> {0, 1}`, which takes an n-bit binary value as input and returns either a 0 or a 1 for each input. The function output is either constant, either 1 OR 0 for all inputs, or balanced, 0 for exactly half of the input domain and 1 for the other half. The task is to determine if `f` is constant or balanced using the function.\n\nthe deterministic classical approach requires `2^(n - 1) + 1` evaluations to prove that f is either constant or balanced. It needs to map *half + 1* the set of inputs to evaluate, with 100% certainty, the nature of the oracle. If `n := 2`:\n\n|**x (input)** | **f(x) (output)** |\n|:--------:|:------------:|\n| 00 | 0 |\n| 01 | 0 |\n| 10 | 1 |\n| 00 | 1 |\n\nOnly the first 3 calculations are required to determine that the oracle is balanced. Though, the computational complexity increases exponentially, which makes it more expensive to solve for larger values of `n`.\nThis is where quantum computing shines. The Deutsch-Jozsa algorithm applies the oracle to a superposition of all possible inputs, represented by `n + 1`, where the first `n` qubits are initialized to |0\u27e9, and the last one is initialized to |1\u27e9.\n\n```python\nn = 10\nqc = QuantumCircuit(n + 1) # initialize a circuit with n + 1 qubits\nqc.px(n) # initialize the last qubit to |1\u27e9\n```\nApply the Hadamard gate to all qubits to create a superposition of all possible states (try it!)\n```python\n# applies the hadamard gate to all qubits in the system\nfor i in range(n + 1):\n qc.h(i)\n```\nThe next step is to create an oracle. The oracle essentially acts as a query system, which is easy to represent in classical computing by storing the mapped value in a certain memory register. In quantum computing however, this is impractical. We'll have to create a custom quantum circuit representation of an oracle. We'll use the `n + 1`th qubit as an ancilla qubit that is initialized to a state of |1\u27e9, and the first `n` qubits as the query. For a balanced function, the oracle should flip the ancilla qubit for exactly half of the input states.\n\n```python\nimport numpy as np\nrandom_bits = np.random.randint(1, 2**n) # returns a random integer between 1 and 2**n - 1 inclusive.\nfor i in range(n):\n # applies cnot with control bits that lie within the randomly generated binary number. If `random_bit` = `101`, then qubits 0 and 2 would be used as control bits.\n if a & (1 << i):\n qc.cnot(i, n)\n```\n\nAfterwards, we revert the query qubits back to their original state by applying the hadamard gate\n\n```python\nfor i in range(n):\n qc.h(i)\n```\n\nFinally, we measure the query qubits individually\n```python\nfor i in range(n):\n qc.measure(i)\n```\nThe measured values of the nth qubit are stored in `qc.classical_bits[n]`. If all measured values are 0, i.e. `qc.classical_bits[0..n]`, then the oracle is a constant function. Anything other than that, the oracle is a balanced function.\n\nNow that a balanced oracle function has been implemented, we can implement a constant oracle.\n\n```python\nfrom qsiml import QuantumCircuit\nimport numpy as np\n\nclass DeutschJozsa():\n def __init__(self, n: int = 10):\n self.qc = QuantumCircuit(n + 1)\n self.n = n\n\n def constant_oracle(self, constant_value: int):\n if constant_value == 0:\n self.qc.i(self.n)\n else:\n self.qc.px(self.n)\n\n def balanced_oracle(self, random_bits: int):\n for i in range(self.n):\n if random_bits & (1 << i):\n self.qc.cnot(i, self.n)\n\n def deutsch_jozsa(self):\n n = self.n\n constant_or_balanced = np.random.randint(0, 2)\n constant_value = np.random.randint(0, 2)\n random_bits = np.random.randint(1, 2**n)\n\n self.qc.px(n)\n for i in range(n + 1):\n self.qc.h(i)\n\n if constant_or_balanced == 0:\n self.constant_oracle(constant_value)\n else:\n self.balanced_oracle(random_bits)\n\n for i in range(n):\n self.qc.h(i)\n\n for i in range(n):\n self.qc.measure(i)\n\n\n self.qc.draw()\n print(\"Classical Bits: \", self.qc.classical_bits[:-1])\n\ndj = DeutschJozsa(10)\ndj.deutsch_jozsa()\n```\n\nreturns this for a constant oracle (Notice how every measured value is 0):\n```\n|q00\u27e9\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014M\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n 0\n|q01\u27e9\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014M\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n 0\n|q02\u27e9\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014M\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n 0\n|q03\u27e9\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014M\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n 0\n|q04\u27e9\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014M\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n 0\n|q05\u27e9\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014M\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n 0\n|q06\u27e9\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014M\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n 0\n|q07\u27e9\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014M\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n 0\n|q08\u27e9\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014M\u2014\u2014\u2014\u2014\n 0\n|q09\u27e9\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014M\u2014\n 0\n|q10\u27e9\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014X\u2014\u2014H\u2014\u2014X\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n\nClassical Bits: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n```\n\nAnd this for a balanced oracle (The measured values form a non-zero bitstring)\n```\n|q00\u27e9\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014M\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n 0\n|q01\u27e9\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u25cf\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014M\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n \u2502 1\n|q02\u27e9\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2502\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014M\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n \u2502 0\n|q03\u27e9\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2502\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014M\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n \u2502 0\n|q04\u27e9\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2502\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014M\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n \u2502 0\n|q05\u27e9\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2502\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014M\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n \u2502 0\n|q06\u27e9\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2502\u2014\u2014\u25cf\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014M\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n \u2502 \u2502 1\n|q07\u27e9\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2502\u2014\u2014\u2502\u2014\u2014\u25cf\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014M\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n \u2502 \u2502 \u2502 1\n|q08\u27e9\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2502\u2014\u2014\u2502\u2014\u2014\u2502\u2014\u2014\u25cf\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014M\u2014\u2014\u2014\u2014\n \u2502 \u2502 \u2502 \u2502 1\n|q09\u27e9\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2502\u2014\u2014\u2502\u2014\u2014\u2502\u2014\u2014\u2502\u2014\u2014\u25cf\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014H\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014M\u2014\n \u2502 \u2502 \u2502 \u2502 \u2502 1\n|q10\u27e9\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014X\u2014\u2014H\u2014\u2014\u2a01\u2014\u2014\u2a01\u2014\u2014\u2a01\u2014\u2014\u2a01\u2014\u2014\u2a01\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n\nClassical Bits: [0, 1, 0, 0, 0, 0, 1, 1, 1, 1]\n```\nYou can import this class using:\n\n```python\nfrom qsiml import DeutschJozsa\n```\n\n### State Vector Representation\n\nIn Qsiml, an n-qubit system is represented by a 2^n dimensional complex vector, known as the state vector. For example, a two-qubit system is represented by a 4-dimensional vector:\n\n`|\u03c8\u27e9 = \u03b1|00\u27e9 + \u03b2|01\u27e9 + \u03b3|10\u27e9 + \u03b4|11\u27e9`\n\nwhere `|\u03b1|^2 + |\u03b2|^2 + |\u03b3|^2 + |\u03b4|^2 = 1`.\n\n",
"bugtrack_url": null,
"license": "GNU GENERAL PUBLIC LICENSE Version 2, June 1991 Copyright (C) 1989, 1991 Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The licenses for most software are designed to take away your freedom to share and change it. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change free software--to make sure the software is free for all its users. This General Public License applies to most of the Free Software Foundation's software and to any other program whose authors commit to using it. (Some other Free Software Foundation software is covered by the GNU Lesser General Public License instead.) You can apply it to your programs, too. When we speak of free software, we are referring to freedom, not price. Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software (and charge for this service if you wish), that you receive source code or can get it if you want it, that you can change the software or use pieces of it in new free programs; and that you know you can do these things. To protect your rights, we need to make restrictions that forbid anyone to deny you these rights or to ask you to surrender the rights. These restrictions translate to certain responsibilities for you if you distribute copies of the software, or if you modify it. For example, if you distribute copies of such a program, whether gratis or for a fee, you must give the recipients all the rights that you have. You must make sure that they, too, receive or can get the source code. And you must show them these terms so they know their rights. We protect your rights with two steps: (1) copyright the software, and (2) offer you this license which gives you legal permission to copy, distribute and/or modify the software. Also, for each author's protection and ours, we want to make certain that everyone understands that there is no warranty for this free software. If the software is modified by someone else and passed on, we want its recipients to know that what they have is not the original, so that any problems introduced by others will not reflect on the original authors' reputations. Finally, any free program is threatened constantly by software patents. We wish to avoid the danger that redistributors of a free program will individually obtain patent licenses, in effect making the program proprietary. To prevent this, we have made it clear that any patent must be licensed for everyone's free use or not licensed at all. The precise terms and conditions for copying, distribution and modification follow. GNU GENERAL PUBLIC LICENSE TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION 0. This License applies to any program or other work which contains a notice placed by the copyright holder saying it may be distributed under the terms of this General Public License. The \"Program\", below, refers to any such program or work, and a \"work based on the Program\" means either the Program or any derivative work under copyright law: that is to say, a work containing the Program or a portion of it, either verbatim or with modifications and/or translated into another language. (Hereinafter, translation is included without limitation in the term \"modification\".) Each licensee is addressed as \"you\". Activities other than copying, distribution and modification are not covered by this License; they are outside its scope. The act of running the Program is not restricted, and the output from the Program is covered only if its contents constitute a work based on the Program (independent of having been made by running the Program). Whether that is true depends on what the Program does. 1. You may copy and distribute verbatim copies of the Program's source code as you receive it, in any medium, provided that you conspicuously and appropriately publish on each copy an appropriate copyright notice and disclaimer of warranty; keep intact all the notices that refer to this License and to the absence of any warranty; and give any other recipients of the Program a copy of this License along with the Program. You may charge a fee for the physical act of transferring a copy, and you may at your option offer warranty protection in exchange for a fee. 2. You may modify your copy or copies of the Program or any portion of it, thus forming a work based on the Program, and copy and distribute such modifications or work under the terms of Section 1 above, provided that you also meet all of these conditions: a) You must cause the modified files to carry prominent notices stating that you changed the files and the date of any change. b) You must cause any work that you distribute or publish, that in whole or in part contains or is derived from the Program or any part thereof, to be licensed as a whole at no charge to all third parties under the terms of this License. c) If the modified program normally reads commands interactively when run, you must cause it, when started running for such interactive use in the most ordinary way, to print or display an announcement including an appropriate copyright notice and a notice that there is no warranty (or else, saying that you provide a warranty) and that users may redistribute the program under these conditions, and telling the user how to view a copy of this License. (Exception: if the Program itself is interactive but does not normally print such an announcement, your work based on the Program is not required to print an announcement.) These requirements apply to the modified work as a whole. If identifiable sections of that work are not derived from the Program, and can be reasonably considered independent and separate works in themselves, then this License, and its terms, do not apply to those sections when you distribute them as separate works. But when you distribute the same sections as part of a whole which is a work based on the Program, the distribution of the whole must be on the terms of this License, whose permissions for other licensees extend to the entire whole, and thus to each and every part regardless of who wrote it. Thus, it is not the intent of this section to claim rights or contest your rights to work written entirely by you; rather, the intent is to exercise the right to control the distribution of derivative or collective works based on the Program. In addition, mere aggregation of another work not based on the Program with the Program (or with a work based on the Program) on a volume of a storage or distribution medium does not bring the other work under the scope of this License. 3. You may copy and distribute the Program (or a work based on it, under Section 2) in object code or executable form under the terms of Sections 1 and 2 above provided that you also do one of the following: a) Accompany it with the complete corresponding machine-readable source code, which must be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange; or, b) Accompany it with a written offer, valid for at least three years, to give any third party, for a charge no more than your cost of physically performing source distribution, a complete machine-readable copy of the corresponding source code, to be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange; or, c) Accompany it with the information you received as to the offer to distribute corresponding source code. (This alternative is allowed only for noncommercial distribution and only if you received the program in object code or executable form with such an offer, in accord with Subsection b above.) The source code for a work means the preferred form of the work for making modifications to it. For an executable work, complete source code means all the source code for all modules it contains, plus any associated interface definition files, plus the scripts used to control compilation and installation of the executable. However, as a special exception, the source code distributed need not include anything that is normally distributed (in either source or binary form) with the major components (compiler, kernel, and so on) of the operating system on which the executable runs, unless that component itself accompanies the executable. If distribution of executable or object code is made by offering access to copy from a designated place, then offering equivalent access to copy the source code from the same place counts as distribution of the source code, even though third parties are not compelled to copy the source along with the object code. 4. You may not copy, modify, sublicense, or distribute the Program except as expressly provided under this License. Any attempt otherwise to copy, modify, sublicense or distribute the Program is void, and will automatically terminate your rights under this License. However, parties who have received copies, or rights, from you under this License will not have their licenses terminated so long as such parties remain in full compliance. 5. You are not required to accept this License, since you have not signed it. However, nothing else grants you permission to modify or distribute the Program or its derivative works. These actions are prohibited by law if you do not accept this License. Therefore, by modifying or distributing the Program (or any work based on the Program), you indicate your acceptance of this License to do so, and all its terms and conditions for copying, distributing or modifying the Program or works based on it. 6. Each time you redistribute the Program (or any work based on the Program), the recipient automatically receives a license from the original licensor to copy, distribute or modify the Program subject to these terms and conditions. You may not impose any further restrictions on the recipients' exercise of the rights granted herein. You are not responsible for enforcing compliance by third parties to this License. 7. If, as a consequence of a court judgment or allegation of patent infringement or for any other reason (not limited to patent issues), conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot distribute so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not distribute the Program at all. For example, if a patent license would not permit royalty-free redistribution of the Program by all those who receive copies directly or indirectly through you, then the only way you could satisfy both it and this License would be to refrain entirely from distribution of the Program. If any portion of this section is held invalid or unenforceable under any particular circumstance, the balance of the section is intended to apply and the section as a whole is intended to apply in other circumstances. It is not the purpose of this section to induce you to infringe any patents or other property right claims or to contest validity of any such claims; this section has the sole purpose of protecting the integrity of the free software distribution system, which is implemented by public license practices. Many people have made generous contributions to the wide range of software distributed through that system in reliance on consistent application of that system; it is up to the author/donor to decide if he or she is willing to distribute software through any other system and a licensee cannot impose that choice. This section is intended to make thoroughly clear what is believed to be a consequence of the rest of this License. 8. If the distribution and/or use of the Program is restricted in certain countries either by patents or by copyrighted interfaces, the original copyright holder who places the Program under this License may add an explicit geographical distribution limitation excluding those countries, so that distribution is permitted only in or among countries not thus excluded. In such case, this License incorporates the limitation as if written in the body of this License. 9. The Free Software Foundation may publish revised and/or new versions of the General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies a version number of this License which applies to it and \"any later version\", you have the option of following the terms and conditions either of that version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of this License, you may choose any version ever published by the Free Software Foundation. 10. If you wish to incorporate parts of the Program into other free programs whose distribution conditions are different, write to the author to ask for permission. For software which is copyrighted by the Free Software Foundation, write to the Free Software Foundation; we sometimes make exceptions for this. Our decision will be guided by the two goals of preserving the free status of all derivatives of our free software and of promoting the sharing and reuse of software generally. NO WARRANTY 11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM \"AS IS\" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. END OF TERMS AND CONDITIONS How to Apply These Terms to Your New Programs If you develop a new program, and you want it to be of the greatest possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms. To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively convey the exclusion of warranty; and each file should have at least the \"copyright\" line and a pointer to where the full notice is found. <one line to give the program's name and a brief idea of what it does.> Copyright (C) <year> <name of author> This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. Also add information on how to contact you by electronic and paper mail. If the program is interactive, make it output a short notice like this when it starts in an interactive mode: Gnomovision version 69, Copyright (C) year name of author Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than `show w' and `show c'; they could even be mouse-clicks or menu items--whatever suits your program. You should also get your employer (if you work as a programmer) or your school, if any, to sign a \"copyright disclaimer\" for the program, if necessary. Here is a sample; alter the names: Yoyodyne, Inc., hereby disclaims all copyright interest in the program `Gnomovision' (which makes passes at compilers) written by James Hacker. <signature of Ty Coon>, 1 April 1989 Ty Coon, President of Vice This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Lesser General Public License instead of this License.",
"summary": "A simulation of quantum circuits in python",
"version": "0.0.5",
"project_urls": {
"Homepage": "https://github.com/MustafaAamir/qsiml"
},
"split_keywords": [
"quantum",
" quantum computing",
" simulator"
],
"urls": [
{
"comment_text": "",
"digests": {
"blake2b_256": "b7a52af32c9c5ab426726955c1063c246565808f057e9b57f01079c176da7911",
"md5": "502c91d970b8445cad2260b96b3914c8",
"sha256": "3884aed3af3836a67a4524bc908c7ba42575d5a2b6db23844904176262bb6c75"
},
"downloads": -1,
"filename": "qsiml-0.0.5-py3-none-any.whl",
"has_sig": false,
"md5_digest": "502c91d970b8445cad2260b96b3914c8",
"packagetype": "bdist_wheel",
"python_version": "py3",
"requires_python": ">=3.12",
"size": 24581,
"upload_time": "2024-11-05T11:06:09",
"upload_time_iso_8601": "2024-11-05T11:06:09.839290Z",
"url": "https://files.pythonhosted.org/packages/b7/a5/2af32c9c5ab426726955c1063c246565808f057e9b57f01079c176da7911/qsiml-0.0.5-py3-none-any.whl",
"yanked": false,
"yanked_reason": null
},
{
"comment_text": "",
"digests": {
"blake2b_256": "62ae18fe893f63ba833b2f2e99402e562aab4977b45a88cd62b3ab1e217ef58e",
"md5": "462771834334e6ae39e9d8e9d772d797",
"sha256": "ae3dc014d4298b0571fe0a0edc8968b3df9292f2f3f17f84fdfcf9faedd72e0d"
},
"downloads": -1,
"filename": "qsiml-0.0.5.tar.gz",
"has_sig": false,
"md5_digest": "462771834334e6ae39e9d8e9d772d797",
"packagetype": "sdist",
"python_version": "source",
"requires_python": ">=3.12",
"size": 27279,
"upload_time": "2024-11-05T11:06:11",
"upload_time_iso_8601": "2024-11-05T11:06:11.496407Z",
"url": "https://files.pythonhosted.org/packages/62/ae/18fe893f63ba833b2f2e99402e562aab4977b45a88cd62b3ab1e217ef58e/qsiml-0.0.5.tar.gz",
"yanked": false,
"yanked_reason": null
}
],
"upload_time": "2024-11-05 11:06:11",
"github": true,
"gitlab": false,
"bitbucket": false,
"codeberg": false,
"github_user": "MustafaAamir",
"github_project": "qsiml",
"travis_ci": false,
"coveralls": false,
"github_actions": false,
"requirements": [],
"lcname": "qsiml"
}
