Quasiprobability representations are important tools for analyzing a quantum system, such as a quantum state or a quantum circuit. In this work, we propose classical algorithms specialized for approximating outcome probabilities of a linear optical circuit using quasiprobability distributions. Notably, we can reduce the negativity bound of a circuit from exponential to at most polynomial for specific cases by modulating the shapes of quasiprobability distributions thanks to the symmetry of the linear optical transformation in the phase space. Consequently, our scheme provides an efficient estimation of outcome probabilities within an additive-error whose precision depends on the classicality of the input state. When the classicality is high enough, we reach a polynomial-time estimation algorithm of a probability within a multiplicative-error by an efficient sampling from a log-concave function. By choosing appropriate input states and measurements, our results provide plenty of quantum-inspired classical algorithms for approximating various matrix functions beating best-known results. Moreover, we give sufficient conditions for the classical simulability of Gaussian Boson sampling using our approximating algorithm for any (marginal) outcome probability under the poly-sparse condition.
Simulating Markovian Open Quantum Systems Using Higher-Order Series Expansion
We present an efficient quantum algorithm for simulating the dynamics of Markovian open quantum systems. The performance of our algorithm is similar to the previous state-of-the-art quantum algorithm, i.e., it scales linearly in evolution time and poly-logarithmically in inverse precision. However, our algorithm is conceptually cleaner, and it only uses simple quantum primitives without compressed encoding. Our approach is based on a novel mathematical treatment of the evolution map, which involves a higher-order series expansion based on Duhamel’s principle and approximating multiple integrals using scaled Gaussian quadrature. Our method easily generalizes to simulating quantum dynamics with time-dependent Lindbladians. Furthermore, our method of approximating multiple integrals using scaled Gaussian quadrature could potentially be used to produce a more efficient approximation of time-ordered integrals, and therefore can simplify existing quantum algorithms for simulating time-dependent Hamiltonians based on a truncated Dyson series.
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- Award ID(s):
- 2238766
- NSF-PAR ID:
- 10487911
- Editor(s):
- Etessami, Kousha; Feige, Uriel; Puppis, Gabriele
- Publisher / Repository:
- Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- Date Published:
- Journal Name:
- Leibniz International Proceedings in Informatics (LIPIcs):50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)
- Page Range / eLocation ID:
- 87:1--87:20
- Subject(s) / Keyword(s):
- Quantum algorithms open quantum systems Lindblad simulation Theory of computation → Quantum computation theory
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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