Related papers: Classical simulation of quantum circuits by half G…
We study the quantum simulation of mixed quantum-semiclassical (MQS) systems, of fundamental interest in many areas of physics, such as molecular scattering and gravitational backreaction. A basic question for these systems is whether…
Hamiltonian quantum simulation of bosons on digital quantum computers requires truncating the Hilbert space to finite dimensions. The method of truncation and the choice of basis states can significantly impact the complexity of the quantum…
We define a quantum model for multiparty communication complexity and prove a simulation theorem between the classical and quantum models. As a result of our simulation, we show that if the quantum k-party communication complexity of a…
It is imperative that useful quantum computers be very difficult to simulate classically; otherwise classical computers could be used for the applications envisioned for the quantum ones. Perfect quantum computers are unarguably…
We investigate the simulation of fermionic systems on a quantum computer. We show in detail how quantum computers avoid the dynamical sign problem present in classical simulations of these systems, therefore reducing a problem believed to…
We estimate short exponential sums weighted by the Fourier coefficients of a Maass form. This requires working out a certain transformation formula for non-linear exponential sums, which is of independent interest. We also discuss how the…
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 consider Gaussian quantum circuits supplemented with non-Gaussian input states and derive sufficient conditions for efficient classical strong simulation of these circuits. In particular, we generalise the stellar representation of…
Quantum simulation advantage over classical memory limitations would allow compact quantum circuits to yield insight into intractable quantum many-body problems, but the interrelated obstacles of large circuit depth in quantum time…
Many quantum algorithms make use of oracles which evaluate classical functions on a superposition of inputs. In order to facilitate implementation, testing, and resource estimation of such algorithms, we present quantum circuits for…
Investigating the classical simulability of quantum circuits provides a promising avenue towards understanding the computational power of quantum systems. Whether a class of quantum circuits can be efficiently simulated with a probabilistic…
We construct a classical algorithm that designs quantum circuits for algorithmic quantum simulation of arbitrary qudit channels on fault-tolerant quantum computers within a pre-specified error tolerance with respect to diamond-norm…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
We introduce a distributed classical simulation algorithm for general quantum circuits, and present numerical results for calculating the output probabilities of universal random circuits. We find that we can simulate more qubits to greater…
For many quantum systems of interest, the classical computational cost of simulating their time evolution scales exponentially in the system size. At the same time, quantum computers have been shown to allow for simulations of some of these…
Simulating quantum circuits using classical computers lets us analyse the inner workings of quantum algorithms. The most complete type of simulation, strong simulation, is believed to be generally inefficient. Nevertheless, several…
The computational complexity of simulating quantum many-body systems generally scales exponentially with the number of particles. This enormous computational cost prohibits first principles simulations of many important problems throughout…
We illustrate the application of Quantum Computing techniques to the investigation of the thermodynamical properties of a simple system, made up of three quantum spins with frustrated pair interactions and affected by a hard sign problem…
By the Gottesman-Knill Theorem, the outcome probabilities of Clifford circuits can be computed efficiently. We present an alternative proof of this result for quopit Clifford circuits (i.e., Clifford circuits on collections of $p$-level…
In this note we describe a simple and intriguing observation: the quantum Fourier transform (QFT) over $Z_q$, which is considered the most ``quantum'' part of Shor's algorithm, can in fact be simulated efficiently by classical computers.…