Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2108.12378 · PRX Quantum

Probing Infinite Many-Body Quantum Systems with Finite-Size Quantum Simulators

Viacheslav Kuzmin, Torsten V. Zache, Christian Kokail, Lorenzo Pastori, Alessio Celi, Mikhail Baranov, P. Zoller

Published Apr 6, 2022• 8 citations
arXivHTMLPDF

Abstract

Experimental studies of synthetic quantum matter are necessarily restricted to approximate ground states prepared on finite-size quantum simulators.In general, this limits their reliability for strongly correlated systems, for instance, in the vicinity of a quantum phase transition (QPT).Here, we propose a protocol that makes optimal use of a given finite-size simulator by directly preparing, on its bulk region, a mixed state representing the reduced density operator of the translation-invariant infinite-sized system of interest.This protocol is based on coherent evolution with a local deformation of the system Hamiltonian.For systems of free fermions in one and two spatial dimensions, we illustrate and explain the underlying physics, which consists of quasiparticle transport towards the system's boundaries while retaining the bulk "vacuum."For the example of a nonintegrable extended Su-Schrieffer-Heeger model, we demonstrate that our protocol enables a more accurate study of QPTs.In addition, we demonstrate the protocol for an interacting spinful Fermi-Hubbard model with doping for one-dimensional chains and a small two-leg ladder, where the initial state is a random superposition of energetically low-lying states.

DOI
10.1103/prxquantum.3.020304

Related papers

Efficient quantum simulation for thermodynamics of infinite-size many-body systems in arbitrary dimensions

Shi-Ju Ran, Bin Xi, Cheng Peng +2 more

In this work we propose to simulate many-body thermodynamics of infinite-size quantum lattice models in one, two, and three dimensions, in terms of few-body models of only O(10) sites, which we coin as quantum entanglement simulators (QES's). The QES is described by a temperature-independent Hamiltonian, with the boundary interactions optimized by the tensor network methods to mimic the entanglement between the bulk and environment in a finite-size canonical ensemble. The reduced density matrix of the physical bulk then gives that of the infinite-size canonical ensemble under interest. We show that the QES can, for instance, accurately simulate varieties of many-body phenomena, including finite-temperature crossover and algebraic excitations of the one-dimensional spin liquid, the phase transitions and low-temperature physics of the two- and three-dimensional antiferromagnets, and the crossovers of the two-dimensional topological system. Our work provides an efficient way to explore the thermodynamics of intractable quantum many-body systems with easily accessible systems.

arXiv:1810.01612•Physical review. B./Physical review. B•May 20, 2019•16 citations

Infinite boundary conditions for matrix product state calculations

Ho N. Phien, Guifré Vidal, Ian P. McCulloch

We propose a formalism to study dynamical properties of a quantum many-body system in the thermodynamic limit by studying a finite system with ``infinite boundary conditions'' where both finite-size effects and boundary effects have been eliminated. For one-dimensional systems, infinite boundary conditions are obtained by attaching two boundary sites to a finite system, where each of these two sites effectively represents a semi-infinite extension of the system. One can then use standard finite-size matrix product state techniques to study a region of the system while avoiding many of the complications normally associated with finite-size calculations such as boundary Friedel oscillations. We illustrate the technique with an example of time evolution of a local perturbation applied to an infinite (translationally invariant) ground state, and use this to calculate the spectral function of the $S=1$ Heisenberg spin chain. This approach is more efficient and more accurate than conventional simulations based on finite-size matrix product state and density-matrix renormalization-group approaches.

arXiv:1207.0652•Physical Review B•Dec 10, 2012•94 citations

Digital dissipative state preparation for frustration-free gapless quantum systems

Johannes Feldmeier, Yu-Jie Liu, Mikhail D. Lukin +1 more

Preparing algebraically correlated ground states of quantum many-body systems is an important, yet challenging task for quantum simulation. We introduce a protocol that employs local projective measurements and unitary feedback for frustration-free gapless systems. Our approach prepares a priori unknown ground states in time that scales polynomially with system size. We analytically show the performance our protocol for the dynamics of a single-particle; we argue the same mechanism generalizes to many-body systems based on the physics of quasiparticles. Our theory predicts that a transient cooling dynamics directly reveals the system's universal critical properties. In particular, the state preparation time is linear in the inverse of the finite-size gap (up to log correction) when the system's dynamical critical exponent is larger or equal the effective spatial dimension explored by the quasiparticles. We verify these predictions in numerical simulations of ferromagnetic Heisenberg models in one- and two dimensions, a Fredkin spin chain, and a two-dimensional model of resonating valence bond states. Our protocol stabilizes gapless many-body ground states fully digitally without requiring analog rotations, enabling access to high-fidelity states beyond conventional adiabatic approaches in near-term experiments.

quant-pharXiv:2603.10119•Mar 12, 2026•0 citations

Digital Dissipative State Preparation for Frustration-Free Gapless Quantum Systems

Anonymous, Yujie Liu, Mikhail D. Lukin +1 more

Preparing algebraically correlated ground states of quantum many-body systems is an important, yet challenging task for quantum simulation. We introduce a protocol that employs local projective measurements and unitary feedback for frustration-free gapless systems. Our approach prepares a priori unknown ground states in time that scales polynomially with system size. We analytically show the performance of our protocol for the dynamics of a single particle; we argue the same mechanism generalizes to many-body systems based on the physics of quasiparticles. Our theory predicts that the transient cooling dynamics directly reveals the system's universal critical properties. In particular, the state preparation time is linear in the inverse of the finite-size gap (up to log correction) when the system's dynamical critical exponent is larger than or equal to the effective spatial dimension explored by the quasiparticles. We verify these predictions in numerical simulations of ferromagnetic Heisenberg models in one and two dimensions, a Fredkin spin chain, and a two-dimensional model of resonating valence bond states. Our protocol stabilizes gapless many-body ground states fully digitally without requiring analog rotations, enabling access to high-fidelity states beyond conventional adiabatic approaches in near-term experiments.

Physical Review Letters•Sep 21, 2026•0 citations

Adiabatic Quantum Simulation of the Topological Su--Schrieffer--Heeger--Hubbard Model

Ssu-Yi Chen, Bo-Hung Chen, Dah-Wei Chiou +1 more

We develop an adiabatic quantum simulation framework on gate-based quantum computers to probe topological signatures of the one-dimensional fermionic Su--Schrieffer--Heeger--Hubbard (SSHH) model. We present explicit quantum-circuit constructions for initial-state preparation and time evolution, together with a practical measurement protocol and classical post-processing procedure for extracting the many-body Berry phase and the spatial profile of the sublattice polarization. Using classical simulations of the proposed circuits, we demonstrate -- for the first time within a genuine many-body framework -- that the topological characteristics of the SSH model remain robust against weak Hubbard interactions but eventually break down as the chiral-symmetry-breaking component of the interaction exceeds a threshold. The required qubit number, gate complexity, measurement shots, and classical pre- and post-processing costs all scale polynomially with system size. Our results provide a proof-of-concept framework for probing topological properties of interacting many-body systems via adiabatic quantum simulation on future large-scale quantum computers.

quant-pharXiv:2605.11823•May 13, 2026•0 citations

Recipe for local simulation of strongly correlated fermionic matter on quantum computers: The two-dimensional Fermi-Hubbard model

Arash Jafarizadeh, Frank Pollmann, Adam Gammon-Smith

The simulation of quantum many-body systems, relevant for quantum chemistry and condensed matter physics, is one of the most promising applications of near-term quantum computers before fault-tolerance. However, since the vast majority of quantum computing technologies are built around qubits and discrete gate-based operations, the translation of the physical problem into this framework is a crucial step. This translation will often be device specific, and a suboptimal implementation will be punished by the exponential compounding of errors on real devices. The importance of an efficient mapping is already revealed for models of spinful fermions in two or three dimensions, which naturally arise when the relevant physics relates to electrons. Using the most direct and well-known mapping, the Jordan-Wigner transformation, leads to a nonlocal representation of local degrees of freedom, and necessities efficient decompositions of nonlocal unitary gates into a sequence of hardware accessible local gates. In this paper, we provide a step-by-step recipe for simulating the paradigmatic two-dimensional Fermi-Hubbard model on a quantum computer using only local operations. To provide the ingredients for such a recipe, we briefly review the plethora of different approaches that have emerged recently but focus on the Derby-Klassen compact fermion mapping to make our discussion concrete. We provide a detailed recipe for an end-to-end simulation including embedding on a physical device, preparing initial states such as ground states, simulation of unitary time evolution, and measurement of observables and spectral functions. We explicitly compute the resource requirements for simulating a global quantum quench and conclude by discussing the challenges and future directions for simulating strongly correlated fermionic matter on quantum computers.

arXiv:2408.14543•Physical Review Research•Oct 7, 2025•2 citations
Experimental studies of synthetic quantum matter are necessarily restricted to approximate ground states prepared on finite-size quantum simulators.In general, this limits their reliability for strongly correlated systems, for instance, in the vicinity of a quantum phase transition (QPT).Here, we propose a protocol that makes optimal use of a given finite-size simulator by directly preparing, on its bulk region, a mixed state representing the reduced density operator of the translation-invariant infinite-sized system of interest.This protocol is based on coherent evolution with a local deformation of the system Hamiltonian.For systems of free fermions in one and two spatial dimensions, we illustrate and explain the underlying physics, which consists of quasiparticle transport towards the system's boundaries while retaining the bulk "vacuum."For the example of a nonintegrable extended Su-Schrieffer-Heeger model, we demonstrate that our protocol enables a more accurate study of QPTs.In addition, we demonstrate the protocol for an interacting spinful Fermi-Hubbard model with doping for one-dimensional chains and a small two-leg ladder, where the initial state is a random superposition of energetically low-lying states.
In this work we propose to simulate many-body thermodynamics of infinite-size quantum lattice models in one, two, and three dimensions, in terms of few-body models of only O(10) sites, which we coin as quantum entanglement simulators (QES's). The QES is described by a temperature-independent Hamiltonian, with the boundary interactions optimized by the tensor network methods to mimic the entanglement between the bulk and environment in a finite-size canonical ensemble. The reduced density matrix of the physical bulk then gives that of the infinite-size canonical ensemble under interest. We show that the QES can, for instance, accurately simulate varieties of many-body phenomena, including finite-temperature crossover and algebraic excitations of the one-dimensional spin liquid, the phase transitions and low-temperature physics of the two- and three-dimensional antiferromagnets, and the crossovers of the two-dimensional topological system. Our work provides an efficient way to explore the thermodynamics of intractable quantum many-body systems with easily accessible systems.
We propose a formalism to study dynamical properties of a quantum many-body system in the thermodynamic limit by studying a finite system with ``infinite boundary conditions'' where both finite-size effects and boundary effects have been eliminated. For one-dimensional systems, infinite boundary conditions are obtained by attaching two boundary sites to a finite system, where each of these two sites effectively represents a semi-infinite extension of the system. One can then use standard finite-size matrix product state techniques to study a region of the system while avoiding many of the complications normally associated with finite-size calculations such as boundary Friedel oscillations. We illustrate the technique with an example of time evolution of a local perturbation applied to an infinite (translationally invariant) ground state, and use this to calculate the spectral function of the S=1S=1S=1 Heisenberg spin chain. This approach is more efficient and more accurate than conventional simulations based on finite-size matrix product state and density-matrix renormalization-group approaches.
Preparing algebraically correlated ground states of quantum many-body systems is an important, yet challenging task for quantum simulation. We introduce a protocol that employs local projective measurements and unitary feedback for frustration-free gapless systems. Our approach prepares a priori unknown ground states in time that scales polynomially with system size. We analytically show the performance our protocol for the dynamics of a single-particle; we argue the same mechanism generalizes to many-body systems based on the physics of quasiparticles. Our theory predicts that a transient cooling dynamics directly reveals the system's universal critical properties. In particular, the state preparation time is linear in the inverse of the finite-size gap (up to log correction) when the system's dynamical critical exponent is larger or equal the effective spatial dimension explored by the quasiparticles. We verify these predictions in numerical simulations of ferromagnetic Heisenberg models in one- and two dimensions, a Fredkin spin chain, and a two-dimensional model of resonating valence bond states. Our protocol stabilizes gapless many-body ground states fully digitally without requiring analog rotations, enabling access to high-fidelity states beyond conventional adiabatic approaches in near-term experiments.
Preparing algebraically correlated ground states of quantum many-body systems is an important, yet challenging task for quantum simulation. We introduce a protocol that employs local projective measurements and unitary feedback for frustration-free gapless systems. Our approach prepares a priori unknown ground states in time that scales polynomially with system size. We analytically show the performance of our protocol for the dynamics of a single particle; we argue the same mechanism generalizes to many-body systems based on the physics of quasiparticles. Our theory predicts that the transient cooling dynamics directly reveals the system's universal critical properties. In particular, the state preparation time is linear in the inverse of the finite-size gap (up to log correction) when the system's dynamical critical exponent is larger than or equal to the effective spatial dimension explored by the quasiparticles. We verify these predictions in numerical simulations of ferromagnetic Heisenberg models in one and two dimensions, a Fredkin spin chain, and a two-dimensional model of resonating valence bond states. Our protocol stabilizes gapless many-body ground states fully digitally without requiring analog rotations, enabling access to high-fidelity states beyond conventional adiabatic approaches in near-term experiments.
We develop an adiabatic quantum simulation framework on gate-based quantum computers to probe topological signatures of the one-dimensional fermionic Su--Schrieffer--Heeger--Hubbard (SSHH) model. We present explicit quantum-circuit constructions for initial-state preparation and time evolution, together with a practical measurement protocol and classical post-processing procedure for extracting the many-body Berry phase and the spatial profile of the sublattice polarization. Using classical simulations of the proposed circuits, we demonstrate -- for the first time within a genuine many-body framework -- that the topological characteristics of the SSH model remain robust against weak Hubbard interactions but eventually break down as the chiral-symmetry-breaking component of the interaction exceeds a threshold. The required qubit number, gate complexity, measurement shots, and classical pre- and post-processing costs all scale polynomially with system size. Our results provide a proof-of-concept framework for probing topological properties of interacting many-body systems via adiabatic quantum simulation on future large-scale quantum computers.
The simulation of quantum many-body systems, relevant for quantum chemistry and condensed matter physics, is one of the most promising applications of near-term quantum computers before fault-tolerance. However, since the vast majority of quantum computing technologies are built around qubits and discrete gate-based operations, the translation of the physical problem into this framework is a crucial step. This translation will often be device specific, and a suboptimal implementation will be punished by the exponential compounding of errors on real devices. The importance of an efficient mapping is already revealed for models of spinful fermions in two or three dimensions, which naturally arise when the relevant physics relates to electrons. Using the most direct and well-known mapping, the Jordan-Wigner transformation, leads to a nonlocal representation of local degrees of freedom, and necessities efficient decompositions of nonlocal unitary gates into a sequence of hardware accessible local gates. In this paper, we provide a step-by-step recipe for simulating the paradigmatic two-dimensional Fermi-Hubbard model on a quantum computer using only local operations. To provide the ingredients for such a recipe, we briefly review the plethora of different approaches that have emerged recently but focus on the Derby-Klassen compact fermion mapping to make our discussion concrete. We provide a detailed recipe for an end-to-end simulation including embedding on a physical device, preparing initial states such as ground states, simulation of unitary time evolution, and measurement of observables and spectral functions. We explicitly compute the resource requirements for simulating a global quantum quench and conclude by discussing the challenges and future directions for simulating strongly correlated fermionic matter on quantum computers.