Simulating quantum circuit expectation values by Clifford perturbation theory
Abstract: The classical simulation of quantum circuits is of central importance for benchmarking near-term quantum devices. The fact that gates belonging to the Clifford group can be simulated efficiently on classical computers has motivated a range of methods that scale exponentially only in the number of non-Clifford gates. Here, we consider the expectation value problem for circuits composed of Clifford gates and non-Clifford Pauli rotations, and introduce a heuristic perturbative approach based on the truncation of the exponentially growing sum of Pauli terms in the Heisenberg picture. Numerical results are shown on a Quantum Approximate Optimization Algorithm (QAOA) benchmark for the E3LIN2 problem and we also demonstrate how this method can be used to quantify coherent and incoherent errors of local observables in Clifford circuits. Our results indicate that this systematically improvable perturbative method offers a viable alternative to exact methods for approximating expectation values of large near-Clifford circuits.
- “Validating quantum computers using randomized model circuits”. Phys. Rev. A 100, 032328 (2019).
- Daniel Gottesman. “The Heisenberg Representation of Quantum Computers” (1998). arXiv:9807006.
- “Improved simulation of stabilizer circuits”. Phys. Rev. A 70, 052328 (2004).
- Maarten Van Den Nest. “Classical Simulation of Quantum Computation, the Gottesman-Knill Theorem, and Slightly Beyond”. Quantum Info. Comput. 10, 258–271 (2010).
- “Improved Classical Simulation of Quantum Circuits Dominated by Clifford Gates”. Phys. Rev. Lett. 116, 250501 (2016).
- “Unbiased simulation of near-Clifford quantum circuits”. Phys. Rev. A 95, 062337 (2017).
- “Clifford recompilation for faster classical simulation of quantum circuits”. Quantum 3, 170 (2019).
- “Simulation of quantum circuits by low-rank stabilizer decompositions”. Quantum 3, 181 (2019).
- “Feynman-path-type simulation using stabilizer projector decomposition of unitaries”. Phys. Rev. A 103, 022428 (2021).
- Aleks Kissinger and John van de Wetering. “Simulating quantum circuits with zx-calculus reduced stabiliser decompositions”. Quantum Sci. Technol. 7, 044001 (2022).
- “Classical algorithms for quantum mean values”. Nat. Phys. 17, 337–341 (2021).
- “Variational quantum algorithms”. Nat. Rev. Phys. 3, 625–644 (2021).
- “A variational eigenvalue solver on a photonic quantum processor”. Nat. Commun. 5, 4213 (2014).
- “A quantum approximate optimization algorithm” (2014). arXiv:1411.4028.
- “Quantum Supremacy through the Quantum Approximate Optimization Algorithm” (2016). arXiv:1602.07674.
- “Fourier expansion in variational quantum algorithms” (2023). arXiv:2304.03787.
- “Quadratic Clifford expansion for efficient benchmarking and initialization of variational quantum algorithms”. Phys. Rev. Res. 4, 033012 (2022).
- Qiskit contributors. “Qiskit: An open-source framework for quantum computing” (2023).
- “A Quantum Approximate Optimization Algorithm Applied to a Bounded Occurrence Constraint Problem” (2015). arXiv:1412.6062.
- Yingkai Ouyang. “Avoiding coherent errors with rotated concatenated stabilizer codes”. npj Quantum Inf. 7, 87 (2021).
- “Simulation of qubit quantum circuits via Pauli propagation”. Phys. Rev. A 99, 062337 (2019). arXiv:1901.09070.
- “Efficient Classical Computation of Quantum Mean Values for Shallow QAOA Circuits” (2021). arXiv:2112.11151.
- “6-qubit optimal Clifford circuits”. npj Quantum Inf. 8, 79 (2022).
- “Quantum computation and quantum information”. Cambridge University Press. Cambridge (2010).
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