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 which is a statevector simulation and True-Q™ 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 located in
sdim/tableau
- The issue lies in math implementation details that can be found inside the markdown located in
- Does not currently
.stimcircuit notation, only a variant based on Scott Aaronson's original.chp
You can install the sdim Python module directly from PyPI using pip install sdim
Take a look at the Python notebooks for an in-depth examples.
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.[1] 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.
[2] 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.
[3] 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.
[4] 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.
[5] Greenberg, H. (1971). Integer Programming. Academic Press. Chapter 6, Sections 2 and 3.
[6] 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