Related papers: Hamiltonian simulation with nearly optimal depende…

Here we explore which heuristic quantum algorithms for combinatorial optimization might be most practical to try out on a small fault-tolerant quantum computer. We compile circuits for several variants of quantum accelerated simulated…

Hamiltonian simulations are key subroutines in adiabatic quantum computation, quantum control, and quantum many-body physics, where quantum dynamics often happen in the low-energy sector. In contrast to time-independent Hamiltonian…

We show how to efficiently simulate continuous-time quantum query algorithms that run in time T in a manner that preserves the query complexity (within a polylogarithmic factor) while also incurring a small overhead cost in the total number…

We use complexity theory to rigorously investigate the difficulty of classically simulating evolution under many-body localized (MBL) Hamiltonians. Using the defining feature that MBL systems have a complete set of quasilocal integrals of…

We discuss classical algorithms for approximating the largest eigenvalue of quantum spin and fermionic Hamiltonians based on semidefinite programming relaxation methods. First, we consider traceless $2$-local Hamiltonians $H$ describing a…

Principal component analysis is an important dimension reduction technique in machine learning. In [S. Lloyd, M. Mohseni and P. Rebentrost, Nature Physics 10, 631-633, (2014)], a quantum algorithm to implement principal component analysis…

In fault-tolerant quantum computing, the cost of calculating Hamiltonian eigenvalues using the quantum phase estimation algorithm is proportional to the constant scaling the Hamiltonian matrix block-encoded in a unitary circuit. We present…

We present a universal quantum Monte Carlo algorithm for simulating arbitrary high-spin (spin greater than 1/2) Hamiltonians, based on the recently developed permutation matrix representation (PMR) framework. Our approach extends a…

Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…

Approximate Bayesian inference methods that scale to very large datasets are crucial in leveraging probabilistic models for real-world time series. Sparse Markovian Gaussian processes combine the use of inducing variables with efficient…

Digital quantum simulation has broad applications in approximating unitary evolution of Hamiltonians. In practice, many simulation tasks for quantum systems focus on quantum states in the low-energy subspace instead of the entire Hilbert…

Hamiltonian simulation is known to be one of the fundamental building blocks of a variety of quantum algorithms such as its most immediate application, that of simulating many-body systems to extract their physical properties. In this work,…

In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…

Two cluster algorithms, based on constructing and flipping loops, are presented for worldline quantum Monte Carlo simulations of fermions and are tested on the one-dimensional repulsive Hubbard model. We call these algorithms the loop-flip…

With the increasing crossover between quantum information and machine learning, quantum simulation of neural networks has drawn unprecedentedly strong attention, especially for the simulation of associative memory in Hopfield neural…

Random walks describe diffusion processes, where movement at every time step is restricted to only the neighbouring locations. We construct a quantum random walk algorithm, based on discretisation of the Dirac evolution operator inspired by…

We make the case for studying the complexity of approximately simulating (sampling) quantum systems for reasons beyond that of quantum computational supremacy, such as diagnosing phase transitions. We consider the sampling complexity as a…

We propose a novel combinatorial algorithm for efficient generation of Hamiltonian walks and cycles on a cubic lattice, modeling the conformations of lattice toy proteins. Through extensive tests on small lattices (allowing complete…

We present a unified view of likelihood based Gaussian progress regression for simulation experiments exhibiting input-dependent noise. Replication plays an important role in that context, however previous methods leveraging replicates have…

Quantum signal processing (QSP) is a powerful toolbox for the design of quantum algorithms and can lead to asymptotically optimal computational costs. Its realization on noisy quantum computers without fault tolerance, however, is…