Related papers: A quantum algorithm for the direct estimation of t…
Imaginary-time evolution is fundamental for analyzing quantum many-body systems, yet classical simulation requires exponentially growing resources in both system size and evolution time. While quantum approaches reduce the system-size…
Quantum dynamics can be analyzed via the structure of energy eigenstates. However, in the many-body setting, preparing eigenstates associated with finite temperatures requires time scaling exponentially with system size. In this work we…
Emerging quantum hardware provides new possibilities for quantum simulation. While much of the research has focused on simulating closed quantum systems, the real-world quantum systems are mostly open. Therefore, it is essential to develop…
Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work we consider time-periodically modulated quantum systems which are in contact with a stationary…
We present an algorithm for measurement of $k$-local operators in a quantum state, which scales logarithmically both in the system size and the output accuracy. The key ingredients of the algorithm are a digital representation of the…
The dynamics of a quantum system coupled to a classical environment and subject to constraints that drive it out of equilibrium is described. The evolution of the system is governed by the quantum-classical Liouville equation. Rather than…
Predicting observables in equilibrium states is a central yet notoriously hard question in quantum many-body systems. In the physically relevant thermodynamic limit, certain mathematical formulations of this task have even been shown to…
Quantum-phase-estimation algorithms are critical subroutines in many applications for quantum computers and in quantum-metrology protocols. These algorithms estimate the unknown strength of a unitary evolution. By using coherence or…
The theoretical investigation of non-adiabatic processes is hampered by the complexity of the coupled electron-nuclear dynamics beyond the Born-Oppenheimer approximation. Classically, the simulation of such reactions is limited by the…
We present a general non-perturbative method to determine the exact steady state of open quantum systems under perturbation. The method works for systems with a unique steady state and the perturbation may be time-independent or periodic,…
We present an end-to-end quantum algorithm for simulating nonlinear dynamics described by a system of stochastic dissipative differential equations with a quadratic nonlinearity. The stochastic part of the system is modeled by a Gaussian…
Simulating nonlinear classical dynamics on a quantum computer is an inherently challenging task due to the linear operator formulation of quantum mechanics. In this work, we provide a systematic approach to alleviate this difficulty by…
We describe a numerical algorithm for approximating the equilibrium-reduced density matrix and the effective (mean force) Hamiltonian for a set of system spins coupled strongly to a set of bath spins when the total system (system+bath) is…
In this work, we consider the problem of online (real-time, single-shot) estimation of static or slow-varying parameters along quantum trajectories in quantum dynamical systems. Based on the measurement signal of a continuously-monitored…
Non-Markovian open quantum systems represent the most general dynamics when the quantum system is coupled with a bath environment. The quantum dynamics arising from many important applications are non-Markovian. Although for special cases,…
Measuring expectation values of observables is an essential ingredient in variational quantum algorithms. A practical obstacle is the necessity of a large number of measurements for statistical convergence to meet requirements of precision,…
Quantum simulation using time evolution in phase estimation-based quantum algorithms can yield unbiased solutions of classically intractable models. However, long runtimes open such algorithms to decoherence. We show how measurement-based…
In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…
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…
Solving linear ordinary differential equations (ODE) is one of the most promising applications for quantum computers to demonstrate exponential advantages. The challenge of designing a quantum ODE algorithm is how to embed non-unitary…