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Quantum computers solve intractable problems which classically require an exponentially long time to compute. With the development of large-scale experiments that claim quantum advantage, a vital issue has now emerged. What are the errors,…
Estimating thermal expectation values of observables is a fundamental task in quantum physics, quantum chemistry, and materials science. While recent quantum algorithms have enabled efficient quantum preparation of thermal states,…
We present a method for approximating the many-body density of states of a system of quantum identical particles, with a reduction of the computational cost by a combinatorial factor compared to the full calculation. This is carried out by…
We show how to efficiently simulate a quantum many-body system with tree structure when its entanglement is bounded for any bipartite split along an edge of the tree. This is achieved by expanding the {\em time-evolving block decimation}…
Perturbation theory is an important technique for reducing computational cost and providing physical insights in simulating quantum systems with classical computers. Here, we provide a quantum algorithm to obtain perturbative energies on…
A major motivation for building a quantum computer is that it provides a tool to efficiently simulate strongly correlated quantum systems. In this work, we present a detailed roadmap on how to simulate a two-dimensional electron…
We introduce a unified Gaussian quantum operator representation for fermions and bosons. The representation extends existing phase-space methods to Fermi systems as well as the important case of Fermi-Bose mixtures. It enables simulations…
Here we describe an approach for simulating electronic structure on quantum computers with significantly lower asymptotic complexity than prior work. The approach uses a real-space first-quantised representation of the molecular Hamiltonian…
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…
Efficient sampling from ensembles of Hamiltonian cycles is critical for predicting the thermodynamic properties of compact polymers, with applications including modeling protein and RNA folding and designing soft materials. Although…
Preparing the ground state of a system of interacting classical particles is an NP-hard problem. Thus, there is in general no better algorithm to solve this problem than exhaustively going through all N configurations of the system to…
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…
Recently, there have been several advancements in quantum algorithms for Gibbs sampling. These algorithms simulate the dynamics generated by an artificial Lindbladian, which is meticulously constructed to obey a detailed-balance condition…
Preparing thermal and ground states is an essential quantum algorithmic task for quantum simulation. In this work, we construct the first efficiently implementable and exactly detailed-balanced Lindbladian for Gibbs states of arbitrary…
We investigate the problem of simulating classical stochastic processes through quantum dynamics, and present three scenarios where memory or time quantum advantages arise. First, by introducing and analysing a quantum version of the…
Quantum computing raises the possibility of solving a variety of problems in physics that are presently intractable. A number of such problems involves the physics of systems in or near thermal equilibrium. There are two main ways to…
We suggest that quantum computers can solve quantum many-body problems that are impracticable to solve on a classical computer.
A measurement-based quantum computer could consist of a local-gapped Hamiltonian system, whose thermal states --at sufficiently low temperature-- are universal resources for the computation. Initialization of the computer would correspond…
Preparing the Gibbs state of an interacting quantum many-body system on noisy intermediate-scale quantum (NISQ) devices is a crucial task for exploring the thermodynamic properties in the quantum regime. It encompasses understanding…
The preparation and computation of many properties of quantum Gibbs states is essential for algorithms such as quantum semidefinite programming and quantum Boltzmann machines. We propose a quantum algorithm that can predict $M$ linear…