Classical simulation of non-Gaussian bosonic circuits (2403.19059v1)
Abstract: We propose efficient classical algorithms which (strongly) simulate the action of bosonic linear optics circuits applied to superpositions of Gaussian states. Our approach relies on an augmented covariance matrix formalism to keep track of relative phases between individual terms in a linear combination. This yields an exact simulation algorithm whose runtime is polynomial in the number of modes and the size of the circuit, and quadratic in the number of terms in the superposition. We also present a faster approximate randomized algorithm whose runtime is linear in this number. Our main building blocks are a formula for the triple overlap of three Gaussian states and a fast algorithm for estimating the norm of a superposition of Gaussian states up to a multiplicative error. Our construction borrows from earlier work on simulating quantum circuits in finite-dimensional settings, including, in particular, fermionic linear optics with non-Gaussian initial states and Clifford computations with non-stabilizer initial states. It provides algorithmic access to a practically relevant family of non-Gaussian bosonic circuits.
- Richard P. Feynman. Simulating physics with computers. International Journal of Theoretical Physics, 21(6):467–488, Jun 1982.
- Leslie G. Valiant. Quantum computers that can be simulated classically in polynomial time. In Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing, STOC ’01, page 114–123, New York, USA, 2001.
- Matchgates and classical simulation of quantum circuits. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 464(2100):3089–3106, Jul 2008.
- Classical simulation of noninteracting-fermion quantum circuits. Phys. Rev. A, 65:032325, Mar 2002.
- Emanuel Knill. Fermionic linear optics and matchgates. Technical Report LAUR-01-4472, Los Alamos National Laboratory, 2001.
- Improved simulation of stabilizer circuits. Phys. Rev. A, 70:052328, Nov 2004.
- No-go theorem for Gaussian quantum error correction. Phys. Rev. Lett., 102:120501, Mar 2009.
- Quantum error correction with the toric Gottesman-Kitaev-Preskill code. Phys. Rev. A, 99:032344, Mar 2019.
- Encoding a qubit in an oscillator. Physical Review A, 64(1), Jun 2001.
- Encoding an oscillator into many oscillators. Phys. Rev. Lett., 125:080503, Aug 2020.
- Marcel Bergmann and Peter van Loock. Quantum error correction against photon loss using multicomponent cat states. Phys. Rev. A, 94:042332, Oct 2016.
- Cat codes with optimal decoherence suppression for a lossy bosonic channel. Phys. Rev. Lett., 119:030502, Jul 2017.
- Hardware-efficient autonomous quantum memory protection. Phys. Rev. Lett., 111:120501, Sep 2013.
- All-optical cat-code quantum error correction. Phys. Rev. Res., 4:043065, Oct 2022.
- Efficient simulation scheme for a class of quantum optics experiments with non-negative Wigner representation. New Journal of Physics, 15(1):013037, Jan 2013.
- Positive Wigner functions render classical simulation of quantum computation efficient. Phys. Rev. Lett., 109:230503, Dec 2012.
- Negative quasi-probability as a resource for quantum computation. New Journal of Physics, 14(11):113011, Nov 2012.
- Classical simulation of Gaussian quantum circuits with non-Gaussian input states. Phys. Rev. Res., 3:033018, Jul 2021.
- Performance and structure of single-mode bosonic codes. Phys. Rev. A, 97:032346, Mar 2018.
- Improved classical simulation of quantum circuits dominated by Clifford gates. Physical Review Letters, 116(25):250501, Jun 2016.
- Classical simulation of non-gaussian fermionic circuits. arXiv:2307.12912, 2023.
- Gaussian decomposition of magic states for matchgate computations. arXiv:2307.12654, 2023.
- Simulation of quantum circuits by low-rank stabilizer decompositions. Quantum, 3:181, Sep 2019.
- Improved simulation of quantum circuits dominated by free fermionic operations. arXiv:2307.12702, Jul 2023.
- From estimation of quantum probabilities to simulation of quantum circuits. Quantum, 4:223, Jan 2020.
- Fast estimation of outcome probabilities for quantum circuits. PRX Quantum, 3(2):020361, Jun 2022.
- Fidelity for multimode thermal squeezed states. Phys. Rev. A, 61:022306, Jan 2000.
- John Williamson. On the algebraic problem concerning the normal forms of linear dynamical systems. American Journal of Mathematics, 58(1):141–163, 1936.
- Vladimir I. Arnold. Mathematical methods of classical mechanics, volume 60. Springer Science & Business Media, 2013.
- The real symplectic groups in quantum mechanics and optics. Pramana, 45(6):471–497, Dec 1995.
- Raul Garcia-Patron Sanchez. Quantum information with optical continuous variables: from Bell tests to key distribution. Université libre de Bruxelles, 2007.
- Quantum fidelity for arbitrary Gaussian states. Phys. Rev. Lett., 115:260501, Dec 2015.
- Complexity of quantum impurity problems. Communications in Mathematical Physics, 356(2):451–500, Dec 2017.
- Andreas Winter. Energy-constrained diamond norm with applications to the uniform continuity of continuous variable channel capacities. arXiv:1712.10267, 2017.
- Maksim E. Shirokov. On extension of quantum channels and operations to the space of relatively bounded operators. Lobachevskii Journal of Mathematics, 41(4):714–727, Apr 2020.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.