Related papers: Classical simulation complexity of extended Cliffo…
We present conditions for the efficient simulation of a broad class of optical quantum circuits on a classical machine: this class includes unitary transformations, amplification, noise, and measurements. Various proposed schemes for…
We present a comprehensive study of quantum simulation methods and quantum simulators for classical computers. We first study an exhaustive set of 150+ simulators and quantum libraries. Then, we short-list the simulators that are actively…
We consider quantum computations comprising only commuting gates, known as IQP computations, and provide compelling evidence that the task of sampling their output probability distributions is unlikely to be achievable by any efficient…
Quantum information science strives to leverage the quantum-mechanical nature of our universe in order to achieve large improvements in certain information processing tasks. In deep-space optical communications, current receivers for the…
We show that a separation between the class of all problems that can efficiently be solved on a quantum computer and those solvable using probabilistic classical algorithms in polynomial time implies the generalized contextuality of quantum…
Clifford algebras are important structures in Geometric Algebra and Quantum Mechanics. They have allowed a formalization of the primitive operators in Quantum Theory. The algebras are built over vector spaces with dimension a power of 2…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
The goal of benchmarking is to determine how far the output of a noisy system is from its ideal behavior; this becomes exceedingly difficult for large quantum systems where classical simulations become intractable. A common approach is to…
It is believed that random quantum circuits are difficult to simulate classically. These have been used to demonstrate quantum supremacy: the execution of a computational task on a quantum computer that is infeasible for any classical…
Nonequilibrium time evolution of large quantum systems is a strong candidate for quantum advantage. Variational quantum algorithms have been put forward for this task, but their quantum optimization routines suffer from trainability and…
Given any quantum error correcting code permitting universal fault-tolerant quantum computation and transversal measurement of logical X and Z, we describe how to perform time-optimal quantum computation, meaning the execution of an…
A unitary operator that satisfies the constant Yang-Baxter equation immediately yields a unitary representation of the braid group B n for every $n \ge 2$. If we view such an operator as a quantum-computational gate, then topological…
As quantum devices scale up, many-body quantum gates and algorithms begin to surpass what is possible to simulate classically. Validation methods which rely on such classical simulation, such as process tomography and randomized…
We show that a class of quantum computations that was recently shown to be efficiently simulatable on a classical computer by Valiant corresponds to a physical model of noninteracting fermions in one dimension. We give an alternative proof…
A strong analog classical simulation of general quantum evolution is proposed, which serves as a novel scheme in quantum computation and simulation. The scheme employs the approach of geometric quantum mechanics and quantum informational…
We consider the possibility of adding noise to a quantum circuit to make it efficiently simulatable classically. In previous works this approach has been used to derive upper bounds to fault tolerance thresholds - usually by identifying a…
It is one of the most fundamental objectives in quantum information science to understand the boundary between the computational power of classical and quantum computers. One possible avenue to explore this boundary is to identify classes…
We discuss classical and quantum computations in terms of corresponding Hamiltonian dynamics. This allows us to introduce quantum computations which involve parallel processing of both: the data and programme instructions. Using mixed…
Gaussian quantum systems exhibit many explicitly quantum effects but can be simulated classically. Using both the Hilbert space (Koopman) and the phase-space (Moyal) formalisms we investigate how robust this classicality is. We find…
We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from…