Classical simulation of non-Gaussian fermionic circuits

Abstract

We propose efficient algorithms for classically simulating fermionic linear optics operations applied to non-Gaussian initial states. By gadget constructions, this provides algorithms for fermionic linear optics with non-Gaussian operations. We argue that this problem is analogous to that of simulating Clifford circuits with non-stabilizer initial states: Algorithms for the latter problem immediately translate to the fermionic setting. Our construction is based on an extension of the covariance matrix formalism which permits to efficiently track relative phases in superpositions of Gaussian states. It yields simulation algorithms with polynomial complexity in the number of fermions, the desired accuracy, and certain quantities capturing the degree of non-Gaussianity of the initial state. We study one such quantity, the fermionic Gaussian extent, and show that it is multiplicative on tensor products when the so-called fermionic Gaussian fidelity is. We establish this property for the tensor product of two arbitrary pure states of four fermions with positive parity.

68 pages and 15 figures; updated to match published version

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Cited by in corpus (15)

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• Lie-algebraic classical simulations for quantum computing
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• Efficient learning of quantum states prepared with few fermionic non-Gaussian gates
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• Stability and Loop Models from Decohering Non-Abelian Topological Order
• The non-stabilizerness of fermionic Gaussian states
• Fermionic Magic Resources of Quantum Many-Body Systems
• Classical simulation and quantum resource theory of non-Gaussian optics
• Matchgate circuits deeply thermalize
• Simulation of quantum computation with magic states via Jordan-Wigner transformations
• Characterization of non-adaptive Clifford channels
• Classifying fermionic states via many-body correlation measures
• Complexity of Quantum Trajectories
• Classical simulation of noisy quantum circuits via locally entanglement-optimal unravelings