# sdim
## Project Overview
Despite the growing research interest in qudits as an alternative way to scale certain quantum architectures, no publicly available stabilizer circuit simulators for **qudits** (multi-level quantum systems) are available. The two most prominent ones are [Cirq](https://quantumai.google/cirq/build/qudits) which is a statevector simulation and [True-Q™](https://trueq.quantumbenchmark.com/index.html) which is a licensed program.
The following are relevant details for the project:
- Supports **only Clifford** operations.
- **Prime** dimensions are strongly tested while the "fast" solver for composite dimensions is known to have possible errors
- The issue lies in math implementation details that can be found inside the [markdown](sdim/tableau/COMPOSITE.md) located in `sdim/tableau`
- Does not currently `.stim` circuit notation, only a variant based on Scott Aaronson's original `.chp`
## Project Installation
You can install the `sdim` Python module directly from PyPI using `pip install sdim`
## How to use sdim?
Take a look at the Python notebooks for an in-depth examples.
```python
from sdim import Circuit, Program
# Create a new quantum circuit
circuit = Circuit(4, 2) # Create a circuit with 4 qubits and dimension 2
# Add gates to the circuit
circuit.add_gate('H', 0) # Hadamard gate on qubit 0
circuit.add_gate('CNOT', 0, 1) # CNOT gate with control on qubit 0 and target on qubit 1
circuit.add_gate('CNOT', 0, [2, 3]) # Short-hand for multiple target qubits, applies CNOT between 0 -> 2 and 0 -> 3
circuit.add_gate('MEASURE', [0, 1, 2, 3]) # Short-hand for multiple single-qubit gates
# Create a program and add the circuit
program = Program(circuit) # Must be given an initial circuit as a constructor argument
# Execute the program
result = program.simulate(show_measurement=True) # Runs the program and prints the measurement results. Also returns the results as a list of MeasurementResult objects.
```
## Primary References
<a id="1">[1]
</a> Aaronson, Scott, and Daniel Gottesman. “Improved Simulation of Stabilizer Circuits.” Physical Review A, vol. 70, no. 5, Nov. 2004, p. 052328. arXiv.org, https://doi.org/10.1103/PhysRevA.70.052328.
<a id="2">[2]
</a>de Beaudrap, Niel. “A Linearized Stabilizer Formalism for Systems of Finite Dimension.” Quantum Information and Computation, vol. 13, no. 1 & 2, Jan. 2013, pp. 73–115. arXiv.org, https://doi.org/10.26421/QIC13.1-2-6.
<a id="3">[3]
</a>Gottesman, Daniel. “Fault-Tolerant Quantum Computation with Higher-Dimensional Systems.” Chaos, Solitons & Fractals, vol. 10, no. 10, Sept. 1999, pp. 1749–58. arXiv.org, https://doi.org/10.1016/S0960-0779(98)00218-5.
## Secondary References
<a id="1a">[4]
</a>Farinholt, J. M. “An Ideal Characterization of the Clifford Operators.” Journal of Physics A: Mathematical and Theoretical, vol. 47, no. 30, Aug. 2014, p. 305303. arXiv.org, https://doi.org/10.1088/1751-8113/47/30/305303.
<a id="2a">[5]
</a>Greenberg, H. (1971). *Integer Programming*. Academic Press. Chapter 6, Sections 2 and 3.
<a id="3a">[6]
</a>Extended gcd and Hermite normal form algorithms via lattice basis reduction, G. Havas, B.S. Majewski, K.R. Matthews, Experimental Mathematics, Vol 7 (1998) 125-136
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"description": "# sdim\n\n## Project Overview\n\nDespite the growing research interest in qudits as an alternative way to scale certain quantum architectures, no publicly available stabilizer circuit simulators for **qudits** (multi-level quantum systems) are available. The two most prominent ones are [Cirq](https://quantumai.google/cirq/build/qudits) which is a statevector simulation and [True-Q\u2122](https://trueq.quantumbenchmark.com/index.html) which is a licensed program.\n\nThe following are relevant details for the project:\n- Supports **only Clifford** operations. \n- **Prime** dimensions are strongly tested while the \"fast\" solver for composite dimensions is known to have possible errors\n - The issue lies in math implementation details that can be found inside the [markdown](sdim/tableau/COMPOSITE.md) located in `sdim/tableau`\n- Does not currently `.stim` circuit notation, only a variant based on Scott Aaronson's original `.chp`\n\n## Project Installation\nYou can install the `sdim` Python module directly from PyPI using `pip install sdim`\n\n## How to use sdim?\nTake a look at the Python notebooks for an in-depth examples.\n```python\nfrom sdim import Circuit, Program\n\n# Create a new quantum circuit\ncircuit = Circuit(4, 2) # Create a circuit with 4 qubits and dimension 2\n\n# Add gates to the circuit\ncircuit.add_gate('H', 0) # Hadamard gate on qubit 0\ncircuit.add_gate('CNOT', 0, 1) # CNOT gate with control on qubit 0 and target on qubit 1\ncircuit.add_gate('CNOT', 0, [2, 3]) # Short-hand for multiple target qubits, applies CNOT between 0 -> 2 and 0 -> 3\ncircuit.add_gate('MEASURE', [0, 1, 2, 3]) # Short-hand for multiple single-qubit gates\n\n# Create a program and add the circuit\nprogram = Program(circuit) # Must be given an initial circuit as a constructor argument\n\n# Execute the program\nresult = program.simulate(show_measurement=True) # Runs the program and prints the measurement results. Also returns the results as a list of MeasurementResult objects.\n```\n\n## Primary References\n<a id=\"1\">[1]\n</a> Aaronson, Scott, and Daniel Gottesman. \u201cImproved Simulation of Stabilizer Circuits.\u201d Physical Review A, vol. 70, no. 5, Nov. 2004, p. 052328. arXiv.org, https://doi.org/10.1103/PhysRevA.70.052328.\n\n<a id=\"2\">[2]\n</a>de Beaudrap, Niel. \u201cA Linearized Stabilizer Formalism for Systems of Finite Dimension.\u201d Quantum Information and Computation, vol. 13, no. 1 & 2, Jan. 2013, pp. 73\u2013115. arXiv.org, https://doi.org/10.26421/QIC13.1-2-6.\n\n<a id=\"3\">[3]\n</a>Gottesman, Daniel. \u201cFault-Tolerant Quantum Computation with Higher-Dimensional Systems.\u201d Chaos, Solitons & Fractals, vol. 10, no. 10, Sept. 1999, pp. 1749\u201358. arXiv.org, https://doi.org/10.1016/S0960-0779(98)00218-5.\n\n## Secondary References\n\n<a id=\"1a\">[4]\n</a>Farinholt, J. M. \u201cAn Ideal Characterization of the Clifford Operators.\u201d Journal of Physics A: Mathematical and Theoretical, vol. 47, no. 30, Aug. 2014, p. 305303. arXiv.org, https://doi.org/10.1088/1751-8113/47/30/305303.\n\n<a id=\"2a\">[5]\n</a>Greenberg, H. (1971). *Integer Programming*. Academic Press. Chapter 6, Sections 2 and 3.\n\n<a id=\"3a\">[6]\n</a>Extended gcd and Hermite normal form algorithms via lattice basis reduction, G. Havas, B.S. Majewski, K.R. Matthews, Experimental Mathematics, Vol 7 (1998) 125-136\n\n\n",
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