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We present an iterative generalisation of the quantum subspace expansion algorithm used with a Krylov basis. The iterative construction connects a sequence of subspaces via their lowest energy states. Diagonalising a Hamiltonian in a given…

Quantum Physics · Physics 2025-05-07 Tom O'Leary , Lewis W. Anderson , Dieter Jaksch , Martin Kiffner

This work provides a nonasymptotic error analysis of quantum Krylov algorithms based on real-time evolutions, subject to generic errors in the outputs of the quantum circuits. We prove upper and lower bounds on the resulting ground state…

Quantum Physics · Physics 2024-09-04 William Kirby

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…

For large scale electronic structure calculation, the Krylov subspace method is introduced to calculate the one-body density matrix instead of the eigenstates of given Hamiltonian. This method provides an efficient way to extract the…

Materials Science · Physics 2009-11-10 Ryu Takayama , Takeo Hoshi , Takeo Fujiwara

Quantum subspace diagonalization (QSD) methods are quantum-classical hybrid methods, commonly used to find ground and excited state energies by projecting the Hamiltonian to a smaller subspace. In applying these, the choice of subspace…

Quantum Physics · Physics 2022-09-23 Akhil Francis , Anjali A. Agrawal , Jack H. Howard , Efekan Kökcü , A. F. Kemper

Krylov subspace methods are among the most extensively studied early fault-tolerant quantum algorithms for estimating ground-state energies of quantum systems. However, the rapid onset of ill-conditioning might make accurate energies…

Quantum Physics · Physics 2026-04-14 Maria Gabriela Jordão Oliveira , Karl Michael Ziems , Nina Glaser

Krylov quantum diagonalization methods have emerged as a promising use case for quantum computers. However, many existing implementations rely on controlled operations, which pose challenges to near-term quantum hardware. We introduce a…

Quantum Physics · Physics 2025-10-15 Nicola Mariella , Enrique Rico , Adam Byrne , Sergiy Zhuk

We evaluate the Sample-based Krylov Quantum Diagonalization (SKQD) algorithm on one- and two-dimensional Heisenberg models, including strongly correlated regimes in which the ground state is dense. Using problem-informed initial states and…

We present a hybrid quantum-classical framework for simulating generic matrix functions more amenable to early fault-tolerant quantum hardware than standard quantum singular-value transformations. The method is based on randomization over…

Quantum Physics · Physics 2024-11-28 Allan Tosta , Thais de Lima Silva , Giancarlo Camilo , Leandro Aolita

A milestone in the field of quantum computing will be solving problems in quantum chemistry and materials faster than state-of-the-art classical methods. The current understanding is that achieving quantum advantage in this area will…

Quantum Physics · Physics 2023-11-08 Guoming Wang , Daniel Stilck França , Ruizhe Zhang , Shuchen Zhu , Peter D. Johnson

We propose quantum-selected configuration interaction (QSCI), a class of hybrid quantum-classical algorithms for calculating the ground- and excited-state energies of many-electron Hamiltonians on noisy quantum devices. Suppose that an…

Quantum Physics · Physics 2023-02-23 Keita Kanno , Masaya Kohda , Ryosuke Imai , Sho Koh , Kosuke Mitarai , Wataru Mizukami , Yuya O. Nakagawa

We apply the recently proposed Sample-based Krylov Quantum Diagonalization (SKQD) method to lattice gauge theories, using the Schwinger model with a $\theta$-term as a benchmark. SKQD approximates the ground state of a Hamiltonian,…

Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…

Quantum Physics · Physics 2023-01-12 Karen J. Morenz Korol , Kenny Choo , Antonio Mezzacapo

Computing electronic structures of quantum systems is a key task underpinning many applications in photonics, solid-state physics, and quantum technologies. This task is typically performed through iterative algorithms to find the energy…

Quantum Physics · Physics 2026-02-03 Shaobo Zhang , Akib Karim , Harry M. Quiney , Muhammad Usman

Calculating the energy spectrum of a quantum system is an important task, for example to analyse reaction rates in drug discovery and catalysis. There has been significant progress in developing algorithms to calculate the ground state…

Quantum Physics · Physics 2019-06-12 Suguru Endo , Tyson Jones , Sam McArdle , Xiao Yuan , Simon Benjamin

Quantum phase estimation is one of the most powerful quantum primitives. This work proposes a new approach for the problem of multiple eigenvalue estimation: Quantum Multiple Eigenvalue Gaussian filtered Search (QMEGS). QMEGS leverages the…

Quantum Physics · Physics 2024-10-02 Zhiyan Ding , Haoya Li , Lin Lin , HongKang Ni , Lexing Ying , Ruizhe Zhang

Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to…

Quantum Physics · Physics 2026-05-22 Grzegorz Rajchel-Mieldzioć , Szymon Pliś , Emil Zak

Many quantum algorithms rely on the measurement of complex quantum amplitudes. Standard approaches to obtain the phase information, such as the Hadamard test, give rise to large overheads due to the need for global controlled-unitary…

Quantum Physics · Physics 2024-05-29 Yilun Yang , Arthur Christianen , Mari Carmen Bañuls , Dominik S. Wild , J. Ignacio Cirac

Quantum phase estimation is the flagship algorithm for quantum simulation on fault-tolerant quantum computers. We demonstrate that an \emph{off-grid} compressed sensing protocol, combined with a state-of-the-art signal classification…

Quantum Physics · Physics 2025-07-17 Davide Castaldo , Stefano Corni

Finding the ground state of a Hamiltonian system is of great significance in many-body quantum physics and quantum chemistry. We propose an improved iterative quantum algorithm to prepare the ground state of a Hamiltonian. The crucial point…

Quantum Physics · Physics 2022-10-25 Jin-Min Liang , Qiao-Qiao Lv , Shu-Qian Shen , Ming Li , Zhi-Xi Wang , Shao-Ming Fei