Related papers: How to discretize a quantum bath for real-time evo…
Recently, quantized versions of random walks have been explored as effective elements for quantum algorithms. In the simplest case of one dimension, the theory has remained divided into the discrete-time quantum walk and the continuous-time…
The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems…
This paper is part of a program to combine a staggered time and staggered spatial discretization of continuum wave equations so that important properties of the continuum that are proved using vector calculus can be proven in an analogous…
Understanding the dynamics of dissipative quantum systems, particularly beyond the weak coupling approximation, is central to various quantum applications. While numerically exact methods provide accurate solutions, they often lack the…
Quantum simulation is widely regarded as one of the most promising routes to genuine quantum advantage, yet most existing approaches to quantum chemistry are formulated in terms of closed-system, unitary dynamics and ground-state…
In this paper we design discrete port-Hamiltonian systems systematically in two different ways, by applying discrete gradient methods and splitting methods respectively. The discrete port-Hamiltonian systems we get satisfy a discrete notion…
While it seems possible that quantum computers may allow for algorithms offering a computational speed-up over classical algorithms for some problems, the issue is poorly understood. We explore this computational speed-up by investigating…
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…
We present rigorous bounds on the thermalization time of the family of quantum mechanical spin systems known as stabilizer Hamiltonians. The thermalizing dynamics are modeled by a Davies master equation that arises from a weak local…
Characterizing the interactions and dynamics of quantum mechanical systems is an essential task in the development of quantum technologies. We propose an efficient protocol based on the estimation of the time derivatives of few qubit…
Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using…
We investigate discretization strategies for a recently introduced class of energy-based models. The model class encompasses classical port-Hamiltonian systems, generalized gradient flows, and certain systems with algebraic constraints. Our…
We describe a method to simulate Hamiltonian evolution on a quantum computer by repeatedly using a superposition of steps of a quantum walk, then applying a correction to the weightings for the numbers of steps of the quantum walk. This…
I introduce an innovative methodology for deriving numerical models of systems of partial differential equations which exhibit the evolution of spatial patterns. The new approach directly produces a discretisation for the evolution of the…
In quantum adiabatic evolution algorithms, the quantum computer follows the ground state of a slowly varying Hamiltonian. The ground state of the initial Hamiltonian is easy to construct; the ground state of the final Hamiltonian encodes…
Annealing machines specialized for combinatorial optimization problems have been developed, and some companies offer services to use those machines. Such specialized machines can only handle binary variables, and their input format is the…
This paper extends the previously reported theory of dissipation pathways [J. Chem. Phys. 160, 214111 (2024)] to incorporate off-diagonal subsystem-bath coupling, which is often required to model molecular systems where the environment…
We present a quantum computational framework using Hamiltonian Truncation (HT) for simulating real-time scattering processes in $(1+1)$-dimensional scalar $\phi^4$ theory. Unlike traditional lattice discretisation methods, HT approximates…
We prove fundamental rigorous bounds on the speed of quantum evolution for a quantum system coupled to a thermal bath. The bounds are formulated in terms of expectation values of few-body observables derived from the system-bath…