Simulation of quantum circuits by low-rank stabilizer decompositions

Author:

Bravyi Sergey1,Browne Dan2,Calpin Padraic2,Campbell Earl3,Gosset David14,Howard Mark3

Affiliation:

1. IBM T.J. Watson Research Center, Yorktown Heights NY 10598

2. Department of Physics and Astronomy, University College London, London, UK

3. Department of Physics and Astronomy, University of Sheffield, Sheffield, UK

4. Department of Combinatorics & Optimization and Institute for Quantum Computing, University of Waterloo, Waterloo, Canada

Abstract

Recent work has explored using the stabilizer formalism to classically simulate quantum circuits containing a few non-Clifford gates. The computational cost of such methods is directly related to the notion of stabilizerrank, which for a pure state ψ is defined to be the smallest integer χ such that ψ is a superposition of χ stabilizer states. Here we develop a comprehensive mathematical theory of the stabilizer rank and the related approximate stabilizer rank. We also present a suite of classical simulation algorithms with broader applicability and significantly improved performance over the previous state-of-the-art. A new feature is the capability to simulate circuits composed of Clifford gates and arbitrary diagonal gates, extending the reach of a previous algorithm specialized to the Clifford+T gate set. We implemented the new simulation methods and used them to simulate quantum algorithms with 40-50 qubits and over 60 non-Clifford gates, without resorting to high-performance computers. We report a simulation of the Quantum Approximate Optimization Algorithm in which we process superpositions of χ106 stabilizer states and sample from the full n-bit output distribution, improving on previous simulations which used 103 stabilizer states and sampled only from single-qubit marginals. We also simulated instances of the Hidden Shift algorithm with circuits including up to 64 T gates or 16 CCZ gates; these simulations showcase the performance gains available by optimizing the decomposition of a circuit's non-Clifford components.

Publisher

Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften

Subject

Physics and Astronomy (miscellaneous),Atomic and Molecular Physics, and Optics

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