Classical simulation of Gaussian quantum circuits with non-Gaussian input states

Abstract

We consider Gaussian quantum circuits supplemented with non-Gaussian input states and derive sufficient conditions for efficient classical strong simulation of these circuits. In particular, we generalise the stellar representation of continuous-variable quantum states to the multimode setting and relate the stellar rank of the input non-Gaussian states, a recently introduced measure of non-Gaussianity, to the cost of evaluating classically the output probability densities of these circuits. Our results have consequences for the strong simulability of a large class of near-term continuous-variable quantum circuits.

arXiv comment8+6 pages, 3 figures. Comments welcome!

References in corpus (32)

• Gaussian Quantum Information
• Encoding a qubit in an oscillator
• Universal Quantum Computation with Continuous-Variable Cluster States
• Ultra-Large-Scale Continuous-Variable Cluster States Multiplexed in the Time Domain
• The characterization of Gaussian operations and Distillation of Gaussian States
• Gaussian Boson Sampling
• Positive Wigner functions render classical simulation of quantum computation efficient
• Efficient Classical Simulation of Continuous Variable Quantum Information Processes
• Application of a resource theory for magic states to fault-tolerant quantum computing
• Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States
• Classical simulation of noninteracting-fermion quantum circuits
• Improved classical simulation of quantum circuits dominated by Clifford gates
• Resource theory of quantum non-Gaussianity and Wigner negativity
• Generation of one-million-mode continuous-variable cluster state by unlimited time-domain multiplexing
• Estimating outcome probabilities of quantum circuits using quasiprobabilities
• A detailed study of Gaussian Boson Sampling
• All-Gaussian universality and fault tolerance with the Gottesman-Kitaev-Preskill code
• Gaussian Boson Sampling using threshold detectors
• Stellar representation of non-Gaussian quantum states
• Non-Gaussian states for continuous variable quantum computation via Gaussian maps
• Efficient simulation scheme for a class of quantum optics experiments with non-negative Wigner representation
• Continuous-Variable Instantaneous Quantum Computing is hard to sample
• Boson sampling with Gaussian measurements
• From estimation of quantum probabilities to simulation of quantum circuits
• ON states as resource units for universal quantum computation with photonic architectures
• Efficient classical simulation of Clifford circuits with nonstabilizer input states
• Franck-Condon factors by counting perfect matchings of graphs with loops
• Continuous-Variable Sampling from Photon-Added or Photon-Subtracted Squeezed States
• Efficient simulatability of continuous-variable circuits with large Wigner negativity
• Further extensions of Clifford circuits and their classical simulation complexities
• Probabilistic Fault-Tolerant Universal Quantum Computation and Sampling Problems in Continuous Variables
• Approximate stabilizer rank and improved weak simulation of Clifford-dominated circuits for qudits

Cited by in corpus (24)

• Non-Gaussian Quantum States and Where to Find Them
• Computational advantage of quantum random sampling
• Resources for bosonic quantum computational advantage
• Fast simulation of bosonic qubits via Gaussian functions in phase space
• Measurement-based generation and preservation of cat and grid states within a continuous-variable cluster state
• Efficient verification of Boson Sampling
• Holomorphic representation of quantum computations
• Correlation-pattern-based Continuous-variable Entanglement Detection through Neural Networks
• Simulation of quantum optics by coherent state decomposition
• Classical simulation of non-Gaussian bosonic circuits
• Hierarchical Verification of Non-Gaussian Coherence in Bosonic Quantum States
• Quantum Kernel Machine Learning With Continuous Variables
• Multicopy observables for the detection of optically nonclassical states
• Classical simulation and quantum resource theory of non-Gaussian optics
• Boson Sampling for Generalized Bosons
• Superselection rules and bosonic quantum computational resources
• Characterizing the Multipartite Entanglement Structure of Non-Gaussian Continuous-Variable States with a Single Evolution Operator
• Continuous Variable Quantum Advantages and Applications in Quantum Optics
• Classical simulation of circuits with realistic odd-dimensional Gottesman-Kitaev-Preskill states
• Non-Gaussianity from superselection rules
• Variational Tensor Network Simulation of Gaussian Boson Sampling and Beyond
• The symplectic rank of non-Gaussian quantum states
• Classical algorithms for measurement-adaptive Gaussian circuits
• Sequential information theoretic protocols in continuous variable systems