Related papers: Quantum Algorithm for Simulating Hamiltonian Dynam…
We propose a Monte Carlo algorithm designed to simulate quantum as well as classical systems at equilibrium, bridging the algorithmic gap between quantum and classical thermal simulation algorithms. The method is based on a novel…
Simulating physical systems has been an important application of classical and quantum computers. In this article we present an efficient classical algorithm for simulating time-dependent quantum mechanical Hamiltonians over constant…
We address the problem of simulating pair-interaction Hamiltonians in n node quantum networks where the subsystems have arbitrary, possibly different, dimensions. We show that any pair-interaction can be used to simulate any other by…
The simulation of quantum dynamics calls for quantum algorithms working in first quantized grid encodings. Here, we propose a variational quantum algorithm for performing quantum dynamics in first quantization. In addition to the usual…
We introduce a Hamiltonian-based quantum feature extraction method that generates complex features via the dynamics of $k$-local many-body spins Hamiltonians, enhancing machine learning performance. Classical feature vectors are embedded…
We propose an effective and flexible scheme for reverse engineering of a Hamiltonian by designing the evolution operators to eliminate the terms of Hamiltonian which are hard to be realized in practice. Different from transitionless quantum…
Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the…
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 exploration of potential energy operators in quantum systems holds paramount significance, offering profound insights into atomic behaviour, defining interactions, and enabling precise prediction of molecular dynamics. By embracing the…
Principal component analysis is an important dimension reduction technique in machine learning. In [S. Lloyd, M. Mohseni and P. Rebentrost, Nature Physics 10, 631-633, (2014)], a quantum algorithm to implement principal component analysis…
Analog quantum simulation offers a hardware-specific approach to studying quantum dynamics, but mapping a model Hamiltonian onto the available device parameters requires matching the hardware dynamics. We introduce a paradigm for quantum…
This paper presents a useful compact formula for deriving an effective Hamiltonian describing the time-averaged dynamics of detuned quantum systems. The formalism also works for ensemble-averaged dynamics of stochastic systems. To…
We present a quantum algorithm for simulating the wave equation under Dirichlet and Neumann boundary conditions. The algorithm uses Hamiltonian simulation and quantum linear system algorithms as subroutines. It relies on factorizations of…
We propose a new variational quantum algorithm, which we refer to as TIMES-ADAPT, that prepares time-evolved states in a low-energy or symmetric subspace of a time-independent Hamiltonian on a quantum computer. Using a specially trained…
Quantum Hamiltonian identification is important for characterizing the dynamics of quantum systems, calibrating quantum devices and achieving precise quantum control. In this paper, an effective two-step optimization (TSO) quantum…
Quantum computation offers potential exponential speedups for simulating certain physical systems, but its application to nonlinear dynamics is inherently constrained by the requirement of unitary evolution. We propose the quantum Koopman…
Parity-time ($PT$)-symmetric Hamiltonians exhibit non-unitary dynamical evolution while maintaining real spectra, and offer unique approaches to quantum sensing and entanglement generation. Here we present a method for simulating the…
We introduce a constructive method for mapping non-unitary dynamics to a weighted set of unitary operations. We utilize this construction to derive a new correspondence between real and imaginary time, which we term Imaginary Time Quantum…
We present an efficient quantum algorithm for simulating the evolution of a sparse Hamiltonian H for a given time t in terms of a procedure for computing the matrix entries of H. In particular, when H acts on n qubits, has at most a…
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points. A choice among these…