Fermionic Linear Optics and Matchgates
read the original abstract
Fermionic linear optics is efficiently classically simulatable. Here it is shown that the set of states achievable with fermionic linear optics and particle measurements is the closure of a low dimensional Lie group. The weakness of fermionic linear optics and measurements can therefore be explained and contrasted with the strength of bosonic linear optics with particle measurements. An analysis of fermionic linear optics is used to show that the two-qubit matchgates and the simulatable matchcircuits introduced by Valiant generate a monoid of extended fermionic linear optics operators. A useful interpretation of efficient classical simulations such as this one is as a simulation of a model of non-deterministic quantum computation. Problem areas for future investigations are suggested.
This paper has not been read by Pith yet.
Forward citations
Cited by 9 Pith papers
-
Enabling Lie-Algebraic Classical Simulation beyond Free Fermions
New Pauli orbit and modified Gell-Mann bases enable polynomial-cost Lie-algebraic simulation for permutation-equivariant and bounded-excitation quantum dynamics.
-
Classical simulation of free-fermionic dynamics and quantum chemistry with magic input
Block-product paired non-Gaussian fermionic states allow efficient classical additive-error approximation of transition amplitudes, overlaps, and high-weight correlators under free-fermionic dynamics using multivariat...
-
Fermionic mean-field dynamics for spin systems beyond free fermions
fTDHF is a mean-field dynamics method for spin systems that is formally exact for free fermions and reproduces qualitative features of exact evolution in benchmarks for adiabatic preparation, many-body localization, a...
-
Fermionic mean-field dynamics for spin systems beyond free fermions
fTDHF extends time-dependent Hartree-Fock to fermionized spin-1/2 Hamiltonians, remaining exact for free fermions while handling non-local strings via non-orthogonal Slater determinant transitions and reproducing qual...
-
Holographic Representation of One-Dimensional Many-Body Quantum States via Isometric Tensor Networks
Holographic isoTNS represent volume-law entangled states including arbitrary fermionic Gaussian states, Clifford states, and certain short-time evolved states using an extra network dimension with isometric constraints.
-
Disentangling strategies and entanglement transitions in unitary circuit games with matchgates
Introduces a minimal matchgate circuit representation for fermionic Gaussian states together with a Yang-Baxter update algorithm, then maps out entanglement transitions in unitary circuit games under braiding and gene...
-
Free-Fermion Subsystem Codes
Constructs free-fermion subsystem codes with a 2D topological example, graph-based solvability algorithm, and gap analysis via skew energy and median eigenvalues.
-
Classical simulation of free-fermionic dynamics and quantum chemistry with magic input
Paired non-Gaussian fermionic states under free-fermionic dynamics admit efficient classical additive-error approximations for amplitudes, overlaps, and high-weight correlators via reduction to multivariate Pfaffian c...
-
Mitigating the barren plateau problem in linear optics
A dual-valued phase shifter in linear optics creates variational cost landscapes with fewer local minima and outperforms prior linear-optical variational algorithms by mitigating barren plateaus.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.