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Imaginary time evolution is a powerful tool for studying quantum systems. While it is possible to simulate with a classical computer, the time and memory requirements generally scale exponentially with the system size. Conversely, quantum…

Quantum Physics · Physics 2019-09-17 Sam McArdle , Tyson Jones , Suguru Endo , Ying Li , Simon Benjamin , Xiao Yuan

Imaginary-time evolution plays an important role in algorithms for computing ground-state and thermal equilibrium properties of quantum systems, but can be challenging to simulate on classical computers. Many quantum algorithms for…

Quantum Physics · Physics 2025-07-22 Annie Ray , Esha Swaroop , Ningping Cao , Michael Vasmer , Anirban Chowdhury

We reveal the power of Grover's algorithm from thermodynamic and geometric perspectives by showing that it is a product formula approximation of imaginary-time evolution (ITE), a Riemannian gradient flow on the special unitary group. This…

Quantum Physics · Physics 2026-02-13 Yudai Suzuki , Marek Gluza , Jeongrak Son , Bi Hong Tiang , Nelly H. Y. Ng , Zoë Holmes

Quantum confinement is studied by numerically solving time-dependent Schr\"odinger equation. An imaginary-time evolution technique is employed in conjunction with the minimization of an expectation value, to reach the global minimum.…

Quantum Physics · Physics 2018-01-31 Amlan K. Roy

Imaginary-time evolution (ITE) on a quantum computer is a promising formalism for obtaining the ground state of a quantum system. As a kind of it, the probabilistic ITE (PITE) takes advantage of measurements to implement the nonunitary…

Quantum Physics · Physics 2022-08-15 Taichi Kosugi , Yusuke Nishiya , Hirofumi Nishi , Yu-ichiro Matsushita

Starting from a time-dependent Schr\"odinger equation, stationary states of 3D central potentials are obtained. An imaginary-time evolution technique coupled with the minimization of energy expectation value, subject to the orthogonality…

Quantum Physics · Physics 2018-01-18 Amlan K. Roy

Several methods exist for finding ground (as well as excited) states of nonlinear waves equations. In this paper we first introduce two modifications of the so-called accelerated imaginary-time evolution method (AITEM). In our first…

Pattern Formation and Solitons · Physics 2017-10-17 C. B. Ward , N. Whitaker , I. G. Kevrekidis , P. G. Kevrekidis

The eigenvalue-function pair of the 3D Schr\"odinger equation can be efficiently computed by use of high order, imaginary time propagators. Due to the diffusion character of the kinetic energy operator in imaginary time, algorithms…

Materials Science · Physics 2009-11-13 Siu A. Chin , S. Janecek , E. Krotscheck

Quantum phase estimation (QPE) plays a pivotal role in many quantum algorithms, offering provable speedups in applications such as Shor's factoring algorithm. While fault-tolerant quantum algorithms for combinatorial and Hamiltonian…

Quantum Physics · Physics 2025-04-17 Nora Bauer , George Siopsis

We present a code for solving the single-particle, time-independent Schr\"odinger equation in two dimensions. Our program utilizes the imaginary time propagation (ITP) algorithm, and it includes the most recent developments in the ITP…

Computational Physics · Physics 2015-11-23 P. J. J. Luukko , E. Räsänen

We examine the recently proposed imaginary-time formulation for strongly correlated steady-state nonequilibrium for its range of validity and discuss significant improvements in the analytic continuation of the Matsubara voltage as well as…

Strongly Correlated Electrons · Physics 2013-05-29 J. E. Han

A new numerical treatment in the Crank-Nicholson method with the imaginary time evolution operator is presented in order to solve the Schr\"{o}dinger equation. The original time evolution technique is extended to a new operator that…

Computational Physics · Physics 2008-11-26 Daekyoung Kang , E. Won

We introduce a method to solve the MaxCut problem efficiently based on quantum imaginary time evolution (QITE). We employ a linear Ansatz for unitary updates and an initial state involving no entanglement, as well as an…

We propose a general algebraic analytic scheme for the spectral transform of solutions of nonlinear evolution equations. This allows us to give the general integrable evolution corresponding to an arbitrary time and space dependence of the…

solv-int · Physics 2009-10-28 Jerome Leon

Various methods have been developed for the quantum computation of the ground and excited states of physical and chemical systems, but many of them require either large numbers of ancilla qubits or high-dimensional optimization. The quantum…

Quantum Physics · Physics 2019-12-16 Kübra Yeter-Aydeniz , Raphael C. Pooser , George Siopsis

This article deals with the numerical integration in time of nonlinear Schr\"odinger equations. The main application is the numerical simulation of rotating Bose-Einstein condensates. The authors perform a change of unknown so that the…

Analysis of PDEs · Mathematics 2017-01-31 Christophe Besse , Guillaume Dujardin , Ingrid Lacroix-Violet

A novel class of high-order linearly implicit energy-preserving integrating factor Runge-Kutta methods are proposed for the nonlinear Schr\"odinger equation. Based on the idea of the scalar auxiliary variable approach, the original equation…

Numerical Analysis · Mathematics 2021-12-07 Chaolong Jiang , Jin Cui , Xu Qian , Songhe Song

Developing scalable quantum algorithms to study finite-temperature physics of quantum many-body systems has attracted considerable interest due to recent advancements in quantum hardware. However, such algorithms in their present form…

The current generation of noisy intermediate scale quantum computers introduces new opportunities to study quantum many-body systems. In this paper, we show that quantum circuits can provide a dramatically more efficient representation than…

Quantum Physics · Physics 2021-03-24 Sheng-Hsuan Lin , Rohit Dilip , Andrew G. Green , Adam Smith , Frank Pollmann

A fast implementation of the quantum imaginary time evolution (QITE) algorithm called Fast QITE is proposed. The algorithmic cost of QITE typically scales exponentially with the number of particles it nontrivially acts on in each Trotter…

Quantum Physics · Physics 2020-09-28 Kok Chuan Tan