Related papers: Efficient classical simulation of matchgate circui…
We study the classical simulation complexity in both the weak and strong senses, of matchgate (MG) computations supplemented with all combinations of settings involving inclusion of intermediate adaptive or nonadaptive computational basis…
Let G(A,B) denote the 2-qubit gate which acts as the 1-qubit SU(2) gates A and B in the even and odd parity subspaces respectively, of two qubits. Using a Clifford algebra formalism we show that arbitrary uniform families of circuits of…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
Matchgates are an especially multiflorous class of two-qubit nearest neighbour quantum gates, defined by a set of algebraic constraints. They occur for example in the theory of perfect matchings of graphs, non-interacting fermions, and…
Matchgates are a restricted set of two-qubit gates known to be classically simulable when acting on nearest-neighbor qubits on a path, but universal for quantum computation when the qubits are arranged on certain other graphs. Here we…
Though Cliffords and matchgates are both examples of classically simulable circuits, they are considered simulable for different reasons. The celebrated Gottesman-Knill explains the simulability Cliffords, and the efficient simulability of…
Fermionic Gaussian states (FGSs) and the associated matchgate circuits play a central role in quantum information theory and condensed matter physics. Despite being possibly highly entangled, they can still be efficiently simulated on…
We describe a simple formalism for generating classes of quantum circuits that are classically efficiently simulatable and show that the efficient simulation of Clifford circuits (Gottesman-Knill theorem) and of matchgate circuits…
Quantum circuits consisting of Clifford and matchgates are two classes of circuits that are known to be efficiently simulatable on a classical computer. We introduce a unified framework that shows in a transparent way the special structure…
In the circuit model, quantum computers rely on the availability of a universal quantum gate set. A particularly intriguing example is a set of two-qubit only gates: matchgates, along with SWAP (the exchange of two qubits). In this paper,…
Concordant computation is a circuit-based model of quantum computation for mixed states, that assumes that all correlations within the register are discord-free (i.e. the correlations are essentially classical) at every step of the…
We present verification protocols to gain confidence in the correct performance of the realization of an arbitrary universal quantum computation. The derivation of the protocols is based on the fact that matchgate computations, which are…
The theory of matchgates is of interest in various areas in physics and computer science. Matchgates occur in e.g. the study of fermions and spin chains, in the theory of holographic algorithms and in several recent works in quantum…
Random quantum circuits are commonly viewed as hard to simulate classically. In some regimes this has been formally conjectured, and there had been no evidence against the more general possibility that for circuits with uniformly random…
Clifford gates are a winsome class of quantum operations combining mathematical elegance with physical significance. The Gottesman-Knill theorem asserts that Clifford computations can be classically efficiently simulated but this is true…
The study of quantum circuits composed of commuting gates is particularly useful to understand the delicate boundary between quantum and classical computation. Indeed, while being a restricted class, commuting circuits exhibit genuine…
Matchgates are a family of parity-preserving two-qubit gates, nearest-neighbour circuits of which are known to be classically simulable in polynomial time. In this work, we present a simulation method to classically simulate an…
We present elementary mappings between classical lattice models and quantum circuits. These mappings provide a general framework to obtain efficiently simulable quantum gate sets from exactly solvable classical models. For example, we…
We identify a broad class of physical processes in an optical quantum circuit that can be efficiently simulated on a classical computer: this class includes unitary transformations, amplification, noise, and measurements. This…
We propose a method to reliably and efficiently extract the fidelity of many-qubit quantum circuits composed of continuously parametrized two-qubit gates called matchgates. This method, which we call matchgate benchmarking, relies on…