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We present a quantum algorithm for simulating the time evolution generated by any bounded, time-dependent operator $-A$ with non-positive logarithmic norm, thereby serving as a natural generalization of the Hamiltonian simulation problem.…

Quantum Physics · Physics 2025-09-15 Guang Hao Low , Rolando D. Somma

The accuracy of quantum dynamics simulation is usually measured by the error of the unitary evolution operator in the operator norm, which in turn depends on certain norm of the Hamiltonian. For unbounded operators, after suitable…

Quantum Physics · Physics 2021-05-26 Dong An , Di Fang , Lin Lin

Classical optimization is a cornerstone of the success of variational quantum algorithms, which often require determining the derivatives of the cost function relative to variational parameters. The computation of the cost function and its…

Quantum Physics · Physics 2025-07-15 Muhammad Umer , Eleftherios Mastorakis , Dimitris G. Angelakis

The resolution of dynamics in out of equilibrium quantum spin systems lies at the heart of fundamental questions among Quantum Information Processing, Statistical Mechanics and Nano-Technologies. Efficient computational simulations of…

Computational Physics · Physics 2013-12-09 Axel D. Dente , Carlos S. Bederián , Pablo R. Zangara , Horacio M. Pastawski

Standard quantum mechanics relies on two distinct dynamical principles: unitary evolution and collapse. A mathematically self-contained variational framework is presented that replaces this dualism with a single principle, in which…

Quantum Physics · Physics 2026-03-18 Lance H. Carter

In variational quantum algorithms, parameterization is typically applied to single-qubit gates.In this study, we instead parameterize a generalized controlled gate and propose an algorithm to locally minimize the cost function by maximally…

Recent work has shown that it can be advantageous to implement a composite channel that partitions the Hamiltonian $H$ for a given simulation problem into subsets $A$ and $B$ such that $H=A+B$, where the terms in $A$ are simulated with a…

Quantum Physics · Physics 2023-06-30 Matthew Pocrnic , Matthew Hagan , Juan Carrasquilla , Dvira Segal , Nathan Wiebe

The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation…

Quantum Physics · Physics 2020-04-21 Dominic W. Berry , Andrew M. Childs , Yuan Su , Xin Wang , Nathan Wiebe

Variational quantum algorithms are a class of techniques intended to be used on near-term quantum computers. The goal of these algorithms is to perform large quantum computations by breaking the problem down into a large number of shallow…

Quantum Physics · Physics 2023-03-24 Ryan Shaffer , Lucas Kocia , Mohan Sarovar

Here we show how universal quantum computers based on the quantum circuit model can handle mathematical analysis calculations for functions with continuous domains, without any digitalization, and with remarkably few qubits. The basic…

Quantum Physics · Physics 2022-10-10 Pablo Bermejo , Roman Orus

Variational quantum algorithms involve training parameterized quantum circuits using a classical co-processor. An important variational algorithm, designed for combinatorial optimization, is the quantum approximate optimization algorithm.…

By exploiting the invariance of the molecular Hamiltonian by a unitary transformation of the orbitals it is possible to significantly shorter the depth of the variational circuit in the Variational Quantum Eigensolver (VQE) algorithm by…

Quantum Physics · Physics 2025-09-03 Leonardo Ratini , Chiara Capecci , Leonardo Guidoni

The advection-diffusion equation is simulated on a superconducting quantum computer via several quantum algorithms. Three formulations are considered: (1) Trotterization, (2) variational quantum time evolution (VarQTE), and (3) adaptive…

A variational framework for structural topology optimization is developed, integrating quantum and classical latent encoding strategies within a coordinate-based neural decoding architecture. In this approach, a low-dimensional latent…

Computational Engineering, Finance, and Science · Computer Science 2025-06-24 Alireza Tabarraei

We develop a variational principle to determine the quantum controls and initial state which optimizes the quantum Fisher information, the quantity characterizing the precision in quantum metrology. When the set of available controls is…

Quantum Physics · Physics 2022-04-27 Jing Yang , Shengshi Pang , Zekai Chen , Andrew N. Jordan , Adolfo del Campo

Suzuki-Trotter decompositions of exponential operators like $\exp(Ht)$ are required in almost every branch of numerical physics. Often the exponent under consideration has to be split into more than two operators $H=\sum_k A_k$, for…

Quantum Physics · Physics 2023-06-19 Johann Ostmeyer

The Lie-Trotter formula, together with its higher-order generalizations, provides a direct approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly…

Quantum Physics · Physics 2021-02-05 Andrew M. Childs , Yuan Su , Minh C. Tran , Nathan Wiebe , Shuchen Zhu

Hybrid quantum-classical optimization algorithms represent one of the most promising application for near-term quantum computers. In these algorithms the goal is to optimize an observable quantity with respect to some classical parameters,…

Quantum Physics · Physics 2021-01-27 Leonardo Banchi , Gavin E. Crooks

Suzuki-Trotter decomposition is a well-known technique used to calculate the partition function of quantum spin systems, in which the imaginary-time dependence of the partition function occurs inevitably. Since it is very difficult to…

Statistical Mechanics · Physics 2018-08-30 Manaka Okuyama , Masayuki Ohzeki

The adaptive variational quantum dynamics simulation (AVQDS) method performs real-time evolution of quantum states using automatically generated parameterized quantum circuits that often contain substantially fewer gates than Trotter…

Quantum Physics · Physics 2025-06-23 Feng Zhang , Cai-Zhuang Wang , Thomas Iadecola , Peter P. Orth , Yong-Xin Yao