Simulation of quantum optics by coherent state decomposition

Abstract

We introduce a framework for simulating quantum optics by decomposing the system into a finite rank (number of terms) superposition of coherent states. This allows us to define a resource theory, where linear optical operations are 'free' (i.e., do not increase the rank), and the simulation complexity for an $m$-mode system scales quadratically in $m$, in stark contrast to the Hilbert space dimension. We outline this approach explicitly in the Fock basis, relevant in particular for Boson sampling, where the simulation time (space) complexity for computing output amplitudes, to arbitrary accuracy, scales as $O(m^2{2}^n)$ ($O(m{2}^n)$), for $n$ photons distributed amongst $m$ modes. We additionally demonstrate that linear optical simulations with the $n$ photons initially in the same mode scales efficiently, as $O(m^{2}n)$. This paradigm provides a practical notion of 'non-classicality', i.e., the classical resources required for simulation. Moreover, by making connections to the stellar rank formalism, we show this comes from two independent contributions, the number of single-photon additions, and the amount of squeezing.

arXiv comment25+9 pages. 6 figures. V2: Improvements to main text and additional references. V3: Updated to published version; additional discussion in Sect. 3.5, and other minor changes

References in corpus (52)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Gaussian Quantum Information
• Review article: Linear optical quantum computing
• Efficient classical simulation of slightly entangled quantum computations
• Circuit Quantum Electrodynamics
• Quantum Coherence as a Resource
• Improved Simulation of Stabilizer Circuits
• Quantum Resource Theories
• Quantum Optical Metrology -- The Lowdown on High-N00N States
• Boson sampling with 20 input photons in 60-mode interferometers at $10^{14}$ state spaces
• Gaussian Boson Sampling
• The Resource Theory of Stabilizer Computation
• Simulating quantum computation by contracting tensor networks
• Positive Wigner functions render classical simulation of quantum computation efficient
• Phase-Programmable Gaussian Boson Sampling Using Stimulated Squeezed Light
• Efficient Classical Simulation of Continuous Variable Quantum Information Processes
• Negative Quasi-Probability as a Resource for Quantum Computation
• Improved classical simulation of quantum circuits dominated by Clifford gates
• Information Scrambling in Computationally Complex Quantum Circuits
• Stabilizer Rényi entropy
• Simulation of quantum circuits by low-rank stabilizer decompositions
• Resource theory of quantum non-Gaussianity and Wigner negativity
• Hyper-optimized tensor network contraction
• Universal Control of an Oscillator with Dispersive Coupling to a Qubit
• Unified quantification of nonclassicality and entanglement
• Quantum computing with rotation-symmetric bosonic codes
• A flexible high-performance simulator for verifying and benchmarking quantum circuits implemented on real hardware
• Sufficient Conditions for Efficient Classical Simulation of Quantum Optics
• A resource theory of superposition
• Wigner function negativity and contextuality in quantum computation on rebits
• Leveraging Secondary Storage to Simulate Deep 54-qubit Sycamore Circuits
• Quantifying coherence of Gaussian states
• Quantifying quantum speedups: improved classical simulation from tighter magic monotones
• Quantifying Coherence in Infinite Dimensional Systems
• Stellar representation of non-Gaussian quantum states
• Operational resource theory of continuous-variable nonclassicality
• Efficient simulation scheme for a class of quantum optics experiments with non-negative Wigner representation
• Quantifying the Coherence Between Coherent States
• Phase space simulation method for quantum computation with magic states on qubits
• Contracting Arbitrary Tensor Networks: General Approximate Algorithm and Applications in Graphical Models and Quantum Circuit Simulations
• Resources for bosonic quantum computational advantage
• Large Deviation Bounds for k-designs
• Quantum Supremacy Is Both Closer and Farther than It Appears
• Extremal quantum states
• Classical simulation of Gaussian quantum circuits with non-Gaussian input states
• Strong Simulation of Linear Optical Processes
• The curious nonexistence of Gaussian 2-designs
• Quantum-inspired permanent identities
• Faster classical Boson Sampling
• Sample caching Markov chain Monte Carlo approach to boson sampling simulation
• BQP and the Polynomial Hierarchy
• Simulating Gaussian Boson Sampling with Tensor Networks in the Heisenberg picture

Cited by in corpus (14)

• Assessing and Advancing the Potential of Quantum Computing: A NASA Case Study
• Riemannian optimization of photonic quantum circuits in phase and Fock space
• Classical simulation of non-Gaussian bosonic circuits
• Seeding Gaussian boson samplers with single photons for enhanced state generation
• Open quantum dynamics with variational non-Gaussian states and the truncated Wigner approximation
• Classical simulation and quantum resource theory of non-Gaussian optics
• General protocols for the efficient distillation of indistinguishable photons
• Quadrature Coherence Scale of Linear Combinations of Gaussian Functions in Phase Space
• What's my phase again? Computing the vacuum-to-vacuum amplitude of quadratic bosonic evolution
• Adaptive Non-Gaussian Quantum State Engineering
• Advancing Quantum Networking: Some Tools and Protocols for Ideal and Noisy Photonic Systems
• Bosonic randomized benchmarking with passive transformations
• Classical algorithms for measurement-adaptive Gaussian circuits
• Non-Gaussianity from superselection rules