Quellcode fΓΌr qiskit.transpiler.passes.synthesis.solovay_kitaev_synthesis

# This code is part of Qiskit.
# (C) Copyright IBM 2021.
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
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A Solovay-Kitaev synthesis plugin to Qiskit's transpiler.

from __future__ import annotations

import numpy as np

from qiskit.converters import circuit_to_dag
from qiskit.circuit.gate import Gate
from qiskit.dagcircuit import DAGCircuit
from qiskit.synthesis.discrete_basis.solovay_kitaev import SolovayKitaevDecomposition
from qiskit.synthesis.discrete_basis.generate_basis_approximations import (
from qiskit.transpiler.basepasses import TransformationPass
from qiskit.transpiler.exceptions import TranspilerError

from .plugin import UnitarySynthesisPlugin

[Doku]class SolovayKitaev(TransformationPass): r"""Approximately decompose 1q gates to a discrete basis using the Solovay-Kitaev algorithm. The Solovay-Kitaev theorem [1] states that any single qubit gate can be approximated to arbitrary precision by a set of fixed single-qubit gates, if the set generates a dense subset in :math:`SU(2)`. This is an important result, since it means that any single-qubit gate can be expressed in terms of a discrete, universal gate set that we know how to implement fault-tolerantly. Therefore, the Solovay-Kitaev algorithm allows us to take any non-fault tolerant circuit and rephrase it in a fault-tolerant manner. This implementation of the Solovay-Kitaev algorithm is based on [2]. For example, the following circuit .. parsed-literal:: β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β” q_0: ─ RX(0.8) β”œ β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜ can be decomposed into .. parsed-literal:: global phase: 7Ο€/8 β”Œβ”€β”€β”€β”β”Œβ”€β”€β”€β”β”Œβ”€β”€β”€β” q_0: ─ H β”œβ”€ T β”œβ”€ H β”œ β””β”€β”€β”€β”˜β””β”€β”€β”€β”˜β””β”€β”€β”€β”˜ with an L2-error of approximately 0.01. Examples: Per default, the basis gate set is ``["t", "tdg", "h"]``: .. code-block:: import numpy as np from qiskit.circuit import QuantumCircuit from qiskit.transpiler.passes.synthesis import SolovayKitaev from qiskit.quantum_info import Operator circuit = QuantumCircuit(1) circuit.rx(0.8, 0) print("Original circuit:") print(circuit.draw()) skd = SolovayKitaev(recursion_degree=2) discretized = skd(circuit) print("Discretized circuit:") print(discretized.draw()) print("Error:", np.linalg.norm(Operator(circuit).data - Operator(discretized).data)) .. parsed-literal:: Original circuit: β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β” q: ─ Rx(0.8) β”œ β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜ Discretized circuit: global phase: 7Ο€/8 β”Œβ”€β”€β”€β”β”Œβ”€β”€β”€β”β”Œβ”€β”€β”€β” q: ─ H β”œβ”€ T β”œβ”€ H β”œ β””β”€β”€β”€β”˜β””β”€β”€β”€β”˜β””β”€β”€β”€β”˜ Error: 2.828408279166474 For individual basis gate sets, the ``generate_basic_approximations`` function can be used: .. code-block:: from qiskit.synthesis import generate_basic_approximations from qiskit.transpiler.passes import SolovayKitaev basis = ["s", "sdg", "t", "tdg", "z", "h"] approx = generate_basic_approximations(basis, depth=3) skd = SolovayKitaev(recursion_degree=2, basic_approximations=approx) References: [1]: Kitaev, A Yu (1997). Quantum computations: algorithms and error correction. Russian Mathematical Surveys. 52 (6): 1191–1249. `Online <https://iopscience.iop.org/article/10.1070/RM1997v052n06ABEH002155>`_. [2]: Dawson, Christopher M.; Nielsen, Michael A. (2005) The Solovay-Kitaev Algorithm. `arXiv:quant-ph/0505030 <https://arxiv.org/abs/quant-ph/0505030>`_. """ def __init__( self, recursion_degree: int = 3, basic_approximations: str | dict[str, np.ndarray] | None = None, ) -> None: """ Args: recursion_degree: The recursion depth for the Solovay-Kitaev algorithm. A larger recursion depth increases the accuracy and length of the decomposition. basic_approximations: The basic approximations for the finding the best discrete decomposition at the root of the recursion. If a string, it specifies the ``.npy`` file to load the approximations from. If a dictionary, it contains ``{label: SO(3)-matrix}`` pairs. If None, a default based on the H, T and Tdg gates up to combinations of depth 10 is generated. """ super().__init__() self.recursion_degree = recursion_degree self._sk = SolovayKitaevDecomposition(basic_approximations)
[Doku] def run(self, dag: DAGCircuit) -> DAGCircuit: """Run the ``SolovayKitaev`` pass on `dag`. Args: dag: The input dag. Returns: Output dag with 1q gates synthesized in the discrete target basis. Raises: TranspilerError: if a gates does not have to_matrix """ for node in dag.op_nodes(): if not node.op.num_qubits == 1: continue # ignore all non-single qubit gates # we do not check the input matrix as we know it comes from a Qiskit gate, as this # we know it will generate a valid SU(2) matrix check_input = not isinstance(node.op, Gate) if not hasattr(node.op, "to_matrix"): raise TranspilerError( f"SolovayKitaev does not support gate without to_matrix method: {node.op.name}" ) matrix = node.op.to_matrix() # call solovay kitaev approximation = self._sk.run( matrix, self.recursion_degree, return_dag=True, check_input=check_input ) # convert to a dag and replace the gate by the approximation dag.substitute_node_with_dag(node, approximation) return dag
[Doku]class SolovayKitaevSynthesis(UnitarySynthesisPlugin): """A Solovay-Kitaev Qiskit unitary synthesis plugin. This plugin is invoked by :func:`~.compiler.transpile` when the ``unitary_synthesis_method`` parameter is set to ``"sk"``. This plugin supports customization and additional parameters can be passed to the plugin by passing a dictionary as the ``unitary_synthesis_plugin_config`` parameter of the :func:`~qiskit.compiler.transpile` function. Supported parameters in the dictionary: basis_approximations (str | dict): The basic approximations for the finding the best discrete decomposition at the root of the recursion. If a string, it specifies the ``.npy`` file to load the approximations from. If a dictionary, it contains ``{label: SO(3)-matrix}`` pairs. If None, a default based on the specified ``basis_gates`` and ``depth`` is generated. basis_gates (list): A list of strings specifying the discrete basis gates to decompose to. If None, defaults to ``["h", "t", "tdg"]``. depth (int): The gate-depth of the basic approximations. All possible, unique combinations of the basis gates up to length ``depth`` are considered. If None, defaults to 10. recursion_degree (int): The number of times the decomposition is recursively improved. If None, defaults to 3. """ # we cache an instance of the Solovay-Kitaev class to generate the # computationally expensive basis approximation of single qubit gates only once _sk = None @property def max_qubits(self): """Maximum number of supported qubits is ``1``.""" return 1 @property def min_qubits(self): """Minimum number of supported qubits is ``1``.""" return 1 @property def supports_natural_direction(self): """The plugin does not support natural direction, it does not assume bidirectional two qubit gates.""" return True @property def supports_pulse_optimize(self): """The plugin does not support optimization of pulses.""" return False @property def supports_gate_lengths(self): """The plugin does not support gate lengths.""" return False @property def supports_gate_errors(self): """The plugin does not support gate errors.""" return False @property def supported_bases(self): """The plugin does not support bases for synthesis.""" return None @property def supports_basis_gates(self): """The plugin does not support basis gates. By default it synthesis to the ``["h", "t", "tdg"]`` gate basis.""" return True @property def supports_coupling_map(self): """The plugin does not support coupling maps.""" return False
[Doku] def run(self, unitary, **options): # Runtime imports to avoid the overhead of these imports for # plugin discovery and only use them if the plugin is run/used config = options.get("config") or {} recursion_degree = config.get("recursion_degree", 3) # if we didn't yet construct the Solovay-Kitaev instance, which contains # the basic approximations, do it now if SolovayKitaevSynthesis._sk is None: basic_approximations = config.get("basic_approximations", None) basis_gates = options.get("basis_gates", ["h", "t", "tdg"]) # if the basic approximations are not generated and not given, # try to generate them if the basis set is specified if basic_approximations is None: depth = config.get("depth", 10) basic_approximations = generate_basic_approximations(basis_gates, depth) SolovayKitaevSynthesis._sk = SolovayKitaevDecomposition(basic_approximations) approximate_circuit = SolovayKitaevSynthesis._sk.run(unitary, recursion_degree) dag_circuit = circuit_to_dag(approximate_circuit) return dag_circuit