trasyn: tensor-based arbitrary unitary synthesis

trasyn is a gate synthesis algorithm for early fault-tolerant quantum computing. trasyn natively synthesizes arbitrary single-qubit unitaries to reduce the resulting non-Clifford gate count. For details, check out our paper Reducing T Gates with Unitary Synthesis. For the original code and data for the paper, please refer to the paper branch.

Install

Minimum Installation

pip install trasyn

GPU Acceleration

It is highly recommended to install cupy for GPU acceleration, which significantly speeds up the computation:

pip install trasyn[cupy-cuda12] # or [cupy-cuda11] depending on CUDA version

The CUDA Toolkit version can be found using nvcc --version.

Qiskit Integration

Optionally, qiskit may be installed to support features like full-circuit transpilation and synthesis.

pip install trasyn[qiskit]

Usage

Synthesize a single-qubit unitary

trasyn.synthesize(target, nonclifford_budget) takes a target unitary matrix (in the form of a numpy array, three angles for U(theta, phi, lam), or a single Rz angle) and a non-Clifford gate count budget and outputs a gate sequence string of the target gate set, the corresponding matrix, and the distance to the target.

>>> seq, mat, err = trasyn.synthesize(trasyn.gates.t(), nonclifford_budget=10)
>>> print(seq, err)
t 0.0

>>> seq, mat, err = trasyn.synthesize([0.1, 0.2, 0.3], nonclifford_budget=20) # U(0.1, 0.2, 0.3)
>>> print(seq, err, seq.count("t"))
yththyththththxthththythththxththxththxththxthsz 0.0018002056473114445 19

>>> seq, mat, err = trasyn.synthesize(pi / 16, 30, error_threshold=0.001) # Rz(pi/16)
>>> print(seq, err, seq.count("t"))
hththththxththththththxthththxththththththxththths 0.0005551347294707683 22

>>> seq, mat, err = trasyn.synthesize(pi / 16, 30, logical_error_rates={"t": 1e-5}) # execution-error-aware synthesis
>>> print(seq, err, seq.count("t"))
hththxthythththythththththythththxthythth 0.006293156923603058 17

Full list of synthesize() arguments

• target_unitary : NDArray | Sequence[float] | float

  The target unitary matrix, three angles for U(theta, phi, lam), or a single Rz angle.

• nonclifford_budget : int | Sequence[int]

  The budget for non-Clifford gates (e.g. T gates). Can be a single integer representing the total budget or a sequence of integers specifying the budget for each tensor.

• error_threshold : float, optional

  The synthesis error threshold for the method to return once it is met. Note that this is not a hard constraint; the method will return the best solution found after all attempts if the error threshold is not met or it is not specified. Default is None.

• gate_set : "tsh" or "tshxyz", optional

  The target gate set. Gates are listed in the order of cost. Additional gate sets can be added with the unique_matrices.py script. This process will be made more user-friendly in the future. Default is "tshxyz".

• num_attempts : int, optional

  The number of sampling attempts per budget configuration. Default is 5.

• num_samples : int, optional

  The number of samples to in the sampling process. If None, it is calculated based on available memory. Default is None.

• logical_error_rates : dict[str, float], optional

  A dictionary mapping gate names to their logical error rates. If provided, the synthesis will minimize the overall process infidelity, which consists of the synthesis error and the execution error for performing the gates. Default is None.

• gpu : bool, optional

  Whether to use GPU for synthesis. Default is True.

• rng : numpy.random.Generator | int, optional

  Random number generator or seed for reproducibility. Default is None.

• verbose : bool, optional

  Whether to print verbose output during synthesis. Default is False.

Synthesize a Qiskit circuit

Given a Qiskit circuit, trasyn.synthesize_qiskit_circuit(circuit, u3_transpile=True) transpiles it to CNOT+U3 and synthesizes each U3 gate to bring the full circuit to Clifford+T. The transpilation step attempts various configurations to minimize the nontrivial U3 count and thus, the total T count.

Use in Command-line

Synthesize a single-qubit unitary:

$ trasyn 'rz(pi/16)' 30
Sequence: hththththxththththththxthththxththththththxththths, Error: 0.0005551347294707683, T-count: 22

Synthesize a qasm circuit (Qiskit needs to be installed):

$ trasyn circuit.qasm 20 -s synthesized.qasm

Full list of flags

usage: trasyn [-h] [-e ERROR_THRESHOLD] [-g GATE_SET] [--num-attempts NUM_ATTEMPTS] [--num-samples NUM_SAMPLES] [-c] [--seed SEED] [-v] [-s SAVE_PATH] [--skip-transpile] target budget

Synthesize a single-qubit unitary or a qasm circuit to Clifford+T.

positional arguments:
  target                An expression of the target unitary or a filename, e.g. 'Rz(3*pi/8)', 'u(0.1, pi+0.2, 0.3**0.5)', 'unitary.npy', or 'circuit.qasm'.
  budget                The non-Clifford gate budget for synthesis.

options:
  -h, --help            show this help message and exit
  -e ERROR_THRESHOLD, --error-threshold ERROR_THRESHOLD
                        The synthesis error threshold for the method to return once it is met. Note that this is not a hard constraint; the method will return the best solution found after all attempts if the error threshold is not
                        met or it is not specified. Default is None.
  -g GATE_SET, --gate-set GATE_SET
                        The target gate set. Gates are listed in the order of cost. Additional gate sets can be added with the unique_matrices.py script. This process will be made more user-friendly in the future. Default is
                        'tshxyz'.
  --num-attempts NUM_ATTEMPTS, --na NUM_ATTEMPTS
                        The number of sampling attempts per budget configuration. Default is 5.
  --num-samples NUM_SAMPLES, --ns NUM_SAMPLES
                        The number of samples in the sampling process. If None, it is calculated based on available memory. Default is None.
  -c, --cpu-only        Do not use GPU for synthesis.
  --seed SEED           Random seed for reproducibility.
  -v, --verbose         Enable verbose output.
  -s SAVE_PATH, --save-path SAVE_PATH
                        Path to save the synthesized circuit. Default is '<target>_synthesized.qasm' if target is a QASM circuit.
  --skip-transpile, --st
                        Skip the transpilation step for circuit synthesis.