Fermionic Linear Optics Revisited

Abstract

We provide an alternative view of the efficient classical simulatibility of fermionic linear optics in terms of Slater determinants. We investigate the generic effects of two-mode measurements on the Slater number of fermionic states. We argue that most such measurements are not capable (in conjunction with fermion linear optics) of an efficient exact implementation of universal quantum computation. Our arguments do not apply to the two-mode parity measurement, for which exact quantum computation becomes possible, see quant-ph/0401066.

16 pages, submitted to the special issue of Foundation of Physics in honor of Asher Peres' 70th birthday

References in corpus (9)

• Conditional Quantum Dynamics and Logic Gates
• Quantum Correlations in Systems of Indistinguishable Particles
• Quantum Correlations in Two-Fermion Systems
• Zeeman energy and spin relaxation in a one-electron quantum dot
• Classical simulation of noninteracting-fermion quantum circuits
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Cited by in corpus (27)

• Gaussian Quantum Information
• Matchgates and classical simulation of quantum circuits
• Fermionic partial tomography via classical shadows
• Efficient classical simulation of matchgate circuits with generalized inputs and measurements
• Matchgate benchmarking: Scalable benchmarking of a continuous family of many-qubit gates
• Quantum algorithms for spin models and simulable gate sets for quantum computation
• Concatenated tensor network states
• Universal extensions of restricted classes of quantum operations
• Entanglement dynamics with string measurement operators
• Error-mitigated fermionic classical shadows on noisy quantum devices
• Complexity of quantum circuits via sensitivity, magic, and coherence
• Group-theoretic error mitigation enabled by classical shadows and symmetries
• One-body entanglement as a quantum resource in fermionic systems
• Solving search problems by strongly simulating quantum circuits
• Mode-entanglement of Gaussian fermionic states
• Classical Ising model test for quantum circuits
• Diagnosing Topological Edge States via Entanglement Monogamy
• The impact of different unravelings in a monitored system of free fermions
• Stabilizer Testing and Magic Entropy via Quantum Fourier Analysis
• Degradability of Fermionic Gaussian Channels
• A classification of Markovian fermionic Gaussian master equations
• The matrix permanent and determinant from a spin system
• Analyzing the free states of one quantum resource theory as resource states of another
• Fermionic anyons: entanglement and quantum computation from a resource-theoretic perspective
• Permanents, Bosons and Linear Optics
• Generalized Interference of Fermions and Bosons
• Two-particle scattering on general graphs