Related papers: The quantum super-Krylov method
Quantum computers have been widely speculated to offer significant advantages in obtaining the ground state of difficult Hamiltonian in chemistry and physics. In this work, we first propose a Lyapunov control-inspired strategy to accelerate…
In the current noisy intermediate scale quantum era of quantum computation, available hardware is severely limited by both qubit count and noise levels, precluding the application of many current hybrid quantum-classical algorithms to…
We propose a new quantum computational way of obtaining a ground-state energy and expectation values of observables of interacting Hamiltonians. It is based on the combination of the adiabatic quantum evolution to project a ground state of…
We present an iterative method to solve the multipartite quantum state estimation problem. We demonstrate convergence for any informationally complete set of generalized quantum measurements in every finite dimension. Our method exhibits…
In this paper, we explore an efficient online algorithm for quantum state estimation based on a matrix-exponentiated gradient method previously used in the context of machine learning. The state update is governed by a learning rate that…
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…
While most work on the quantum simulation of chemistry has focused on computing energy surfaces, a similarly important application requiring subtly different algorithms is the computation of energy derivatives. Almost all molecular…
The rapid progress of noisy intermediate-scale quantum (NISQ) computing underscores the need to test and evaluate new devices and applications. Quantum chemistry is a key application area for these devices, and therefore serves as an…
We present a hybrid quantum algorithm for estimating gaps in many-body energy spectra, supported by an analytic proof of its inherent resilience to state preparation and measurement errors, as well as mid-circuit multi-qubit depolarizing…
Quantum phase estimation is the flagship algorithm for quantum simulation on fault-tolerant quantum computers. We demonstrate that an \emph{off-grid} compressed sensing protocol, combined with a state-of-the-art signal classification…
Quantum computing shows promise for addressing computationally intensive problems but is constrained by the exponential resource requirements of general quantum state tomography (QST), which fully characterizes quantum states through…
Quantum tomography is a crucial tool for characterizing quantum states and devices and estimating nonlinear properties of the systems. Performing full quantum state tomography on an $N_\mathrm{q}$ qubit system requires an exponentially…
Considering recent advancements and successes in the development of efficient quantum algorithms for electronic structure calculations --- alongside impressive results using machine learning techniques for computation --- hybridizing…
Quantum computing holds immense promise for simulating quantum systems, a critical task for advancing our understanding of complex quantum phenomena. One of the primary goals in this domain is to accurately approximate the ground state of…
Sample-based quantum diagonalization (SQD) offers a powerful route to accurate quantum chemistry on noisy intermediate-scale quantum (NISQ) devices by combining quantum sampling with classical diagonalization. Here we introduce HSQD, a…
The DMRG method is very effective at finding ground states of 1D quantum systems in practice, but it is a heuristic method, and there is no known proof for when it works. In this paper we describe an efficient classical algorithm which…
In this paper, we explore accelerating Hamiltonian ground state energy calculation on NISQ devices. We suggest using search-based methods together with machine learning to accelerate quantum algorithms, exemplified in the Quantum…
Calculating the energy spectrum of a quantum system is an important task, for example to analyse reaction rates in drug discovery and catalysis. There has been significant progress in developing algorithms to calculate the ground state…
A major thrust in quantum algorithm development over the past decade has been the search for the quantum algorithms that will deliver practical quantum advantage first. Today's quantum computers - and even early fault-tolerant quantum…
Variational quantum algorithms, optimized using gradient-based methods, often exhibit sub-optimal convergence performance due to their dependence on Euclidean geometry. Quantum natural gradient descent (QNGD) is a more efficient method that…