Related papers: Variational Quantum Time Evolution without the Qua…
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…
The quantum imaginary time evolution (QITE) methodology was developed to overcome a critical issue as regards non-unitarity in the implementation of imaginary time evolution on a quantum computer. QITE has since been used to approximate…
Many current and near-future applications of quantum computing utilise parametric families of quantum circuits and variational methods to find optimal values for these parameters. Solving a quantum computational problem with such…
We develop a framework for simulating measure-preserving, ergodic dynamical systems on a quantum computer. Our approach provides a new operator-theoretic representation of classical dynamics by combining ergodic theory with quantum…
We introduce a variational wavefunction for many-body ground states that involves imaginary time evolution with two different Hamiltonians in an alternating fashion with variable time intervals. We successfully apply the ansatz on the one-…
Variational quantum algorithms offer a promising new paradigm for solving partial differential equations on near-term quantum computers. Here, we propose a variational quantum algorithm for solving a general evolution equation through…
Quantum circuits make it possible to simulate the continuous-time dynamics of a many-body Hamiltonian by implementing discrete Trotter steps of duration $\tau$. However, when $\tau$ is sufficiently large, the discrete dynamics exhibit…
A novel scheme to simulate the evolution of a restricted set of observables of a quantum system is proposed. The set comprises the spectrum-generating algebra of the Hamiltonian. The idea is to consider a certain open-system evolution,…
The classical and quantum dynamics of simple time-reparametrization- invariant models containing two degrees of freedom are studied in detail. Elimination of one ``clock'' variable through the Hamiltonian constraint leads to a description…
In light of recent exciting progress in building up quantum computing facilities based on both optical and cold-atom techniques, the algorithms for quantum simulations of particle-physics systems are in rapid progress. In this paper, we…
In the Hamiltonian formulation, Quantum Field Theory calculations scale exponentially with spatial volume, making real-time simulations intractable on classical computers and motivating quantum computation approaches. In Hamiltonian…
The capacity for solving eigenstates with a quantum computer is key for ultimately simulating physical systems. Here we propose inverse iteration quantum eigensolvers, which exploit the power of quantum computing for the classical inverse…
Compared with time independent Hamiltonians, the dynamics of generic quantum Hamiltonians $H(t)$ are complicated by the presence of time ordering in the evolution operator. In the context of digital quantum simulation, this difficulty…
Quantum simulation has begun to penetrate the field of quantum chemistry in hopes of efficiently calculating ground state energies and approximating real-time evolution. With modern research highlighting nonadiabatic dynamics, tunably…
Variational quantum algorithms are promising tools whose efficacy depends on their optimisation method. For noise-free unitary circuits, the quantum generalisation of natural gradient descent has been introduced and shown to be equivalent…
We adapt a recent advance in resource-frugal quantum signal processing - the Quantum Eigenvalue Transform with Unitary matrices (QET-U) - to explore non-unitary imaginary time evolution on early fault-tolerant quantum computers using…
Finding the ground state of a Hamiltonian system is of great significance in many-body quantum physics and quantum chemistry. We propose an improved iterative quantum algorithm to prepare the ground state of a Hamiltonian. The crucial point…
Analog quantum simulation is emerging as a powerful tool for uncovering classically unreachable physics such as many-body real-time dynamics. A complete quantification of uncertainties is necessary in order to make precise predictions using…
We introduce a new class of generative quantum-neural-network-based models called Quantum Hamiltonian-Based Models (QHBMs). In doing so, we establish a paradigmatic approach for quantum-probabilistic hybrid variational learning, where we…
The use of quantum computing to solve a problem in quantum mechanics is illustrated, step by step, by calculating energies and transition amplitudes in a nonrelativistic quark model. The quantum computations feature the use of variational…