Simulating quantum circuit expectation values by Clifford perturbation theory.

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.