Related papers: Permutation Matrix Representation for Quantum Simu…
Simulating the time-evolution of a Hamiltonian is one of the most promising applications of quantum computers. Multi-Product Formulas (MPFs) are well suited to replace standard product formulas since they scale better with respect to time…
Protein folding processes are a vital aspect of molecular biology that is hard to simulate with conventional computers. Quantum algorithms have been proven superior for certain problems and may help tackle this complex life science…
Parity-time ($PT$) symmetric Hamiltonians are generally non-Hermitian and give rise to exotic behaviour in quantum systems at exceptional points, where eigenvectors coalesce. The recent realisation of $PT$-symmetric Hamiltonians in quantum…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
Recent advances in quantum computing have demonstrated its potential to significantly enhance the analysis and forecasting of complex classical data. Among these, quantum reservoir computing has emerged as a particularly powerful approach,…
We investigate the quantum algorithm of Babbush et al. (arXiv:2303.13012v3) for simulating coupled harmonic oscillators, which promises exponential speedups over classical methods. Focusing on linearly connected oscillator chains, we bridge…
A potential approach for demonstrating quantum advantage is using quantum computers to simulate fermionic systems. Quantum algorithms for fermionic system simulation usually involve the Hamiltonian evolution and measurements. However, in…
We study quantum maps displaying spectral statistics intermediate between Poisson and Wigner-Dyson. It is shown that they can be simulated on a quantum computer with a small number of gates, and efficiently yield information about fidelity…
We investigate the power of quantum systems for the simulation of Hamiltonian time evolutions on a cubic lattice under the constraint of translational invariance. Given a set of translationally invariant local Hamiltonians and short range…
We present a general method to efficiently design optimal control sequences for non-Markovian open quantum systems, and illustrate it by optimizing the shape of a laser pulse to prepare a quantum dot in a specific state. The optimization of…
Classical simulation of quantum systems plays an important role in the study of many-body phenomena and in the benchmarking and verification of quantum technologies. Exact simulation is often limited to small systems because the dimension…
Non-Hermitian quantum systems have recently attracted considerable attention due to their exotic properties. Though many experimental realizations of non-Hermitian systems have been reported, the non-Hermiticity usually resorts to the…
Quantum algorithms are promising candidates for the enhancement of computational efficiency for a variety of computational tasks, allowing for the numerical study of physical systems intractable to classical computers. In the Noisy…
The possibility of using a quantum system to simulate another one has been recognized for a long time as an important research direction in quantum information and quantum computing. In Ref. [J. Li et. al, Nat. Commun. 4, 1420 (2013)], a…
Quantum algorithms for selecting a subspace of Hamiltonians to diagonalize have emerged as a promising alternative to variational algorithms in the NISQ era. So far, such algorithms, which include the quantum selected configuration…
Quantum particle simulations have largely been based on time-independent, split-operator schemes in which kinetic and potential operators are interwoven to provide accurate approximations to system dynamics. These simulations can be very…
Numerical methods for developing port-Hamiltonian representations of general linear time-invariant systems are studied. The approach extends previous port-Hamiltonian characterizations to include the general non-minimal case and the case…
In the age of noisy quantum processors, the exploitation of quantum symmetries can be quite beneficial in the efficient preparation of trial states, an important part of the variational quantum eigensolver algorithm. The benefits include…
The controls enacting logical operations on quantum systems are described by time-dependent Hamiltonians that often include rapid oscillations. In order to accurately capture the resulting time dynamics in numerical simulations, a very…
Linear dissipative differential equation is a fundamental model for a large number of physical systems, such as quantum dynamics with non-Hermitian Hamiltonian, open quantum system dynamics, diffusion process and damped system. In this…