Related papers: Partition function estimation with a quantum coin …
Phase estimation is a quantum algorithm for measuring the eigenvalues of a Hamiltonian. We propose and rigorously analyse a randomized phase estimation algorithm with two distinctive features. First, our algorithm has complexity independent…
The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly…
We present a quantum algorithm for estimating the matrix determinant based on quantum spectral sampling. The algorithm estimates the logarithm of the determinant of an $n \times n$ positive sparse matrix to an accuracy $\epsilon$ in time…
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…
Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its…
Block-encodings have become one of the most common oracle assumptions in the circuit model. I present an algorithm that uses von Neumann's measurement procedure to measure a phase, using time evolution on a block-encoded Hamiltonian as a…
For a large class of variational quantum circuits, we show how arbitrary-order derivatives can be analytically evaluated in terms of simple parameter-shift rules, i.e., by running the same circuit with different shifts of the parameters. As…
We present a quantum algorithm to prepare the thermal Gibbs state of interacting quantum systems. This algorithm sets a universal upper bound D^alpha on the thermalization time of a quantum system, where D is the system's Hilbert space…
Sampling noisy intermediate-scale quantum devices is a fundamental step that converts coherent quantum-circuit outputs to measurement data for running variational quantum algorithms that utilize gradient and Hessian methods in cost-function…
A potential approach for demonstrating quantum advantage is using quantum computers to simulate fermionic systems. Quantum algorithms for fermionic system simulation usually involve the Hamiltonian evolution and measurements. However, in…
We develop several algorithms for performing quantum phase estimation based on basic measurements and classical post-processing. We present a pedagogical review of quantum phase estimation and simulate the algorithm to numerically determine…
We present quantum algorithms for the estimation of n-time correlation functions, the local and non-local density of states, and dynamical linear response functions. These algorithms are all based on block-encodings - a versatile technique…
We present a quantum algorithm to estimate parameters at the quantum metrology limit using deterministic quantum computation with one bit. When the interactions occurring in a quantum system are described by a Hamiltonian $H= \theta H_0$,…
Consider a family of distributions $\{\pi_{\beta}\}$ where $X\sim\pi_{\beta}$ means that $\mathbb{P}(X=x)=\exp(-\beta H(x))/Z(\beta)$. Here $Z(\beta)$ is the proper normalizing constant, equal to $\sum_x\exp(-\beta H(x))$. Then…
This paper discusses a classical simulation to compute the partition function (or free energy) of generic one-dimensional quantum many-body systems. Many numerical methods have previously been developed to approximately solve…
Variational quantum algorithms are promising applications of noisy intermediate-scale quantum (NISQ) computers. These algorithms consist of a number of separate prepare-and-measure experiments that estimate terms in a Hamiltonian. The…
Expectation value estimation is ubiquitous in quantum algorithms. The expectation value of a Hamiltonian, which is essential in various practical applications, is often estimated by measuring a large number of Pauli strings on quantum…
We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…
In this work we propose an approach for implementing time-evolution of a quantum system using product formulas. The quantum algorithms we develop have provably better scaling (in terms of gate complexity and circuit depth) than a naive…
We numerically investigate quantum circuit elementary-gate level instantiations of the standard Quantum Phase Estimation (QPE) algorithm for the task of computing the ground-state energy of a quantum magnet; the disordered fully-connected…