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We revisit quantum phase estimation algorithms for the purpose of obtaining the energy levels of many-body Hamiltonians and pay particular attention to the statistical analysis of their outputs. We introduce the mean phase direction of the…
The preparation of quantum Gibbs state is an essential part of quantum computation and has wide-ranging applications in various areas, including quantum simulation, quantum optimization, and quantum machine learning. In this paper, we…
In a recent work [10], Poulin and one of us presented a quantum algorithm for preparing thermal Gibbs states of interacting quantum systems. This algorithm is based on Grovers's technique for quantum state engineering, and its running time…
The problem of simulating the thermal behavior of quantum systems remains a central open challenge in quantum computing. Unlike well-established quantum algorithms for unitary dynamics, \emph{provably efficient} algorithms for preparing…
Solving the electronic structure problem via unitary evolution of the electronic Hamiltonian is one of the promising applications of digital quantum computers. One of the practical strategies to implement the unitary evolution is via…
We implement a variational quantum algorithm for Gibbs state preparation of a transverse-field Ising model on IonQ's quantum computers. To this end, we train the variational parameters via classical simulation and perform state tomography…
We provide practical simulation methods for scalar field theories on a quantum computer that yield improved asymptotics as well as concrete gate estimates for the simulation and physical qubit estimates using the surface code. We achieve…
Trotterization is the most common and convenient approximation method for Hamiltonian simulations on digital quantum computers, but estimating its error accurately is computationally difficult for large quantum systems. Here, we develop a…
It is of great interest to understand the thermalization of open quantum many-body systems, and how quantum computers are able to efficiently simulate that process. A recently introduced disispative evolution, inspired by existing models of…
As first proposed for the adiabatic quantum information processing by Wu, Byrd and Lidar [ Phys. Rev. Lett. 89, 057904 (2002)], the Trotterization technique is a very useful tool for universal quantum computing, and in particular, the…
Trotter approximation in conjunction with Quantum Phase Estimation can be used to extract eigen-energies of a many-body Hamiltonian on a quantum computer. There were several ways proposed to assess the quality of this approximation based on…
Imaginary-time evolution plays an important role in algorithms for computing ground-state and thermal equilibrium properties of quantum systems, but can be challenging to simulate on classical computers. Many quantum algorithms for…
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…
Accurate simulations of vibrational molecular spectra are expensive on conventional computers. Compared to the electronic structure problem, the vibrational structure problem with quantum computers is less investigated. In this work we…
We present two scalable and entanglement-free methods for estimating the collective state of an n-qubit quantum computer. The first method consists of a fixed set of five quantum circuits-regardless of the number of qubits-that avoid the…
We introduce an inductive $n$-qubit pure-state estimation method. This is based on projective measurements on states of $2n+1$ separable bases or $2$ entangled bases plus the computational basis. Thus, the total number of measurement bases…
We present a novel quantum algorithm for estimating Gibbs partition functions in sublinear time with respect to the logarithm of the size of the state space. This is the first speed-up of this type to be obtained over the seminal…
The preparation of quantum Gibbs states at finite temperatures is a cornerstone of quantum computation, enabling applications in quantum simulation of many-body systems, machine learning via quantum Boltzmann machines, and optimization…
The notion of entanglement has been useful for characterizing universal properties of quantum phases of matter. From the perspective of quantum information theory, it is tempting to ask whether their entanglement structures possess any…
The extent to which quantum computers can simulate physical phenomena and solve the partial differential equations (PDEs) that govern them remains a central open question. In this work, one of the most fundamental PDEs is addressed: the…