相关论文: Generalising quantum imaginary time evolution to s…
A quantum algorithm that solves the time-dependent Dirac equation on a digital quantum computer is developed and analyzed. The time evolution is performed by an operator splitting decomposition technique that allows for a mapping of the…
Approximate combinatorial optimization is a promising use case for quantum computers. The quantum optimization algorithms often employ a fixed ansatz that evolves an unbiased initial state towards states with better values of the optimand,…
Quantum computers promise a highly efficient approach to investigate quantum phase transitions, which describe abrupt changes between different ground states of many-body systems. At quantum critical points, the divergent correlation length…
As fully fault-tolerant quantum computers capable of solving useful problems remain a distant goal, we anticipate an era of "early fault tolerance" where limited error correction is available. We propose a framework for designing early…
We propose quantum methods for solving differential equations that are based on a gradual improvement of the solution via an iterative process, and are targeted at applications in fluid dynamics. First, we implement the Jacobi iteration on…
The role of differential equations (DEs) in science and engineering is of paramount importance, as they provide the mathematical framework for a multitude of natural phenomena. Since quantum computers promise significant advantages over…
The Hubbard model has occupied the minds of condensed matter physicists for most part of the last century. This model provides insight into a range of phenomena in correlated electron systems. We wish to examine the paradigm of quantum…
It is proposed that the ability for a quantum circuit to thermalize under time evolution is a valid way to compute linear algebra problems. The algorithm makes use of the eigenstate thermalization hypothesis and full ergodicity in quantum…
The extent to which quantum computers can simulate physical phenomena and solve the partial differential equations (PDEs) that govern them remains a central open question. In this work, one of the most fundamental PDEs is addressed: the…
Many researchers have been heavily investigated on quantum phase estimation (QPE) algorithms to find the unknown phase, since QPE is the core building block of the most quantum algorithms such as the Shor's factoring algorithm, quantum…
Quantum computers provide new avenues to access ground and excited state properties of systems otherwise difficult to simulate on classical hardware. New approaches using subspaces generated by real-time evolution have shown efficiency in…
We present a quantum algorithm that analyzes time series data simulated by a quantum differential equation solver. The proposed algorithm is a quantum version of the dynamic mode decomposition algorithm used in diverse fields such as fluid…
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…
Hamiltonian diagonalization is at the heart of understanding physical properties and practical applications of quantum systems. It is highly desired to design quantum algorithms that can speedup Hamiltonian diagonalization, especially those…
We present a hybrid quantum-classical framework for solving general time-dependent parabolic partial differential equations (PDEs) using quantum variational circuits. Building on the QPINN approach, this method applies broadly to parabolic…
Topology and symmetry play critical roles in characterizing quantum phases of matter. Recent advancements have unveiled symmetry-protected topological (SPT) phases in many-body systems as a unique class of short-range entangled states,…
Identifying computational tasks suitable for (future) quantum computers is an active field of research. Here we explore utilizing quantum computers for the purpose of solving differential equations. We consider two approaches: (i) basis…
Loosely speaking, the concept of quantum typicality refers to the fact that a single pure state can imitate the full statistical ensemble. This fact has given rise to a rather simple but remarkably useful numerical approach to simulate the…
The description of quantum many-body dynamics is extremely challenging on classical computers, as it can involve many degrees of freedom. On the other hand, the time evolution of quantum states is a natural application for quantum computers…
We present an efficient method to prepare states of a many-body system on quantum hardware, first isolating individual quantum numbers and then using time evolution to isolate the energy. Our method in its simplest form requires only one…