Related papers: Equating quantum imaginary time evolution, Riemann…
We propose in this paper a gradient-type dynamical system to solve the problem of maximizing quantum observables for finite dimensional closed quantum ensembles governed by the controlled Liouville-von Neumann equation. The asymptotic…
Simulation of quantum matters is a significant application of quantum computers. In contrast to the unitary operation which can be realized naturally on a quantum computer, the implementation of nonunitary operation, widely used in…
Calculations at finite temperatures are fundamental in different scientific fields, from nuclear physics to condensed matter. Evolution in imaginary time is a prominent classical technique for preparing thermal states of quantum systems. We…
Quantum Annealing, or Quantum Stochastic Optimization, is a classical randomized algorithm which provides good heuristics for the solution of hard optimization problems. The algorithm, suggested by the behaviour of quantum systems, is an…
The efficient simulation of quantum dynamics and ground states is a central challenge in physics and a key frontier for quantum advantage. While short-time evolution in one-dimensional systems can often be simulated classically, extending…
We give a quantum algorithm for solving instances of the satisfiability problem, based on adiabatic evolution. The evolution of the quantum state is governed by a time-dependent Hamiltonian that interpolates between an initial Hamiltonian,…
For addressing optimisation tasks on finite dimensional quantum systems, we give a comprehensive account of the foundations of gradient flows on Riemannian manifolds including new developments: we extend former results from Lie groups such…
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 consider the approximation of the ground state of the one-dimensional cubic nonlinear Schr{\"o}dinger equation by a normalized gradient algorithm combined with linearly implicit time integrator, and finite difference space approximation.…
In recent years there has been substantial development in algorithms for quantum phase estimation. In this work we provide a new approach to online Bayesian phase estimation that achieves Heisenberg limited scaling that requires…
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…
We calculate the energy levels and corresponding eigenstates of an interacting scalar quantum field theory on a lattice using a continuous-variable version of the quantum imaginary time evolution algorithm. Only a single qumode is needed…
Hamiltonian simulation, i.e., simulating the real time evolution of a target quantum system, is a natural application of quantum computing. Trotter-Suzuki splitting methods can generate corresponding quantum circuits; however, a faithful…
We perform a convergence analysis of a discrete-in-time minimization scheme approximating a finite dimensional singularly perturbed gradient flow. We allow for different scalings between the viscosity parameter $\varepsilon$ and the time…
In this paper, we propose an implicit gradient descent algorithm for the classic $k$-means problem. The implicit gradient step or backward Euler is solved via stochastic fixed-point iteration, in which we randomly sample a mini-batch…
Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is "designed" by its level…
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…
Efficiently preparing approximate ground-states of large, strongly correlated systems on quantum hardware is challenging and yet nature is innately adept at this. This has motivated the study of thermodynamically inspired approaches to…
The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation…
Random quantum processes play a central role both in the study of fundamental mixing processes in quantum mechanics related to equilibration, thermalisation and fast scrambling by black holes, as well as in quantum process design and…