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Simulating quantum circuit expectation values by Clifford perturbation theory.

Tomislav Begušić¹, Kasra Hejazi¹, Garnet Kin-Lic Chan¹

¹Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA.

The Journal of Chemical Physics

|April 15, 2025

Summary

We developed a new perturbative method to efficiently simulate near-Clifford quantum circuits. This approach approximates expectation values for complex quantum computations, offering a viable alternative to exact simulation methods.

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Area of Science:

Quantum computing
Computational physics

Background:

Classical simulation of quantum circuits is crucial for benchmarking near-term quantum devices.
Efficient simulation methods exist for Clifford gates, but non-Clifford gates pose a challenge.
Existing methods scale exponentially with the number of non-Clifford gates.

Purpose of the Study:

To introduce a heuristic perturbative approach for simulating quantum circuits with Clifford and non-Clifford Pauli rotation gates.
To address the expectation value problem in near-Clifford quantum circuits.
To provide a systematically improvable method for approximating expectation values.

Main Methods:

A heuristic perturbative approach based on truncating the exponentially growing sum of Pauli terms in the Heisenberg picture.
Application to the expectation value problem for circuits with Clifford and non-Clifford Pauli rotations.
Numerical validation on a Quantum Approximate Optimization Algorithm (QAOA) benchmark for the E3LIN2 problem.

Main Results:

The perturbative method effectively approximates expectation values for near-Clifford circuits.
Demonstrated quantification of coherent and incoherent errors in Clifford circuits.
Numerical results show viability on a QAOA benchmark.

Conclusions:

The proposed perturbative method is a viable alternative to exact simulation for large near-Clifford circuits.
This approach offers systematic improvability.
The method aids in understanding and quantifying errors in quantum computations.