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

Strategies for adiabatic state preparation of quantum many-body systems

Dyon van Vreumingen

Published Feb 20, 2025• 0 citations
OpenAlex

Abstract

Quantum computers represent a relatively new and promising development in computing technology. One of the applications of quantum computers is modelling quantum many-body systems, which describe interactions between particles on atomic and subatomic scales. Such systems are highly complex and challenging to model with classical computers due to the vast number of possible states and entanglement of the particles. In this dissertation, we examine the extent to which quantum computers can accelerate the modelling of quantum many-body systems compared to classical computers. Specifically, this dissertation presents research on adiabatic state preparation: a quantum algorithmic technique that uses the adiabatic principle from quantum mechanics to approximate eigenstates. We describe three new techniques that fall within this category and, in certain cases, offer advantages over standard methods. First, we consider cases of ground state preparation for fermionic many-body systems, where standard direct interpolation between the initial and final hamiltonian is hindered by level crossings due to discrete symmetries. As an alternative to direct interpolation, we propose adiabatic paths in a higher-dimensional space, which break the relevant symmetries. Next, we present an adiabatic echo verification protocol which mitigates both coherent and incoherent errors, arising from non-adiabatic transitions and hardware noise, respectively. We show that the estimator bias of the observable is reduced when compared to standard adiabatic preparation, achieving up to a quadratic improvement. Finally, we propose a general, fully gate-based and nonvariational quantum algorithm for counterdiabatic driving. We provide a rigorous quantum gate complexity upper bound in terms of the minimum gap $\Delta$ around this eigenstate. We find that, in the worst case, the algorithm can be run with at most $\tilde O(\Delta^{-(3 + o(1))} \epsilon^{-(1 + o(1))})$ quantum gates such that a target state fidelity of at least $1 - \epsilon^2$ is achieved. In certain cases, the gap dependence can be improved to quadratic.

Related papers

Adiabatic ground-state preparation of fermionic many-body systems from a two-body perspective

Dyon van Vreumingen, Kareljan Schoutens

A well-known method to prepare ground states of fermionic many-body Hamiltonians is adiabatic state preparation, in which an easy-to-prepare state is time-evolved towards an approximate ground state under a specific time-dependent Hamiltonian. However, which path to take in the evolution is often unclear, and a direct linear interpolation, which is the most common method, may not be optimal. In this work, we explore other types of adiabatic paths based on the spectral decomposition of the two-body projection of the residual Hamiltonian (the difference between the final and initial Hamiltonian). The decomposition defines a set of Hamiltonian terms which may be adiabatically interpolated in a piecewise or combined fashion. We demonstrate the usefulness of partially piecewise interpolation through examples involving Fermi-Hubbard models where, due to symmetries, level crossings occur in direct (fully combined) interpolation. We show that this specific deviation from a direct path appropriately breaks the relevant symmetries, thus avoiding level crossings and enabling an adiabatic passage. On the other hand, we show that a fully piecewise scheme, which interpolates every Hamiltonian term separately, exhibits a worst-case complexity of $O({L}^{6}/{\mathrm{\ensuremath{\Delta}}}^{3})$ as compared to $O({L}^{4}/{\mathrm{\ensuremath{\Delta}}}^{3})$ for direct interpolation, in terms of the number of one-body modes $L$ and the minimal gap $\mathrm{\ensuremath{\Delta}}$ along the path. This suboptimality result suggests that only those terms which break necessary symmetries should be taken into account for piecewise interpolation, while the rest is treated with direct interpolation.

arXiv:2305.01284•Physical Review A•Dec 4, 2023•6 citations

Quantum Algorithms with Applications to Simulating Physical Systems

Anirban Ch Narayan Chowdhury

The simulation of quantum physical systems is expected to be an important application for quantum computers. The work presented in this dissertation aims to improve the resource requirements of quantum computers for solving simulation problems, by providing both novel quantum algorithms and improved implementations of existing ones. I present three main results that cover diverse aspects of simulation including equilibrium physics, the preparation of useful quantum states, and simulations based on classical stochastic processes. The results rely on established quantum algorithms and other recent techniques which I review. My first original contribution is a new quantum algorithm to sample from the thermal Gibbs state of quantum Hamiltonians. The complexity of this algorithm has an exponentially improved dependence on precision compared to an earlier quantum algorithm, and also provides polynomial improvements in other parameters. My second contribution is an improved algorithm to implement reflections about the eigenstates of unitary operators and Hamiltonians, an operation that can be used to prepare ground states of many-body Hamiltonians by quantum amplitude amplification. The improved algorithm for implementing reflections significantly reduces the number of ancilla qubits required over earlier implementations. The improvement relies in part on a novel quantum algorithm for efficiently preparing states with Gaussian-like amplitudes, which may have broad applications. I also prove a lower bound for implementing reflections, which shows that our algorithm is almost optimal. My third and final contribution regards quantum algorithms for classical stochastic processes, which are of importance in statistical physics. I present a quantum algorithm that estimates the average running time of a stochastic process, and provides a quadratic speed-up over a comparable classical algorithm.

•Jan 1, 2019•0 citations

Fast digital methods for adiabatic state preparation

Kianna Wan, Isaac H. Kim

We present a quantum algorithm for adiabatic state preparation on a gate-based quantum computer, with complexity polylogarithmic in the inverse error. Our algorithm digitally simulates the adiabatic evolution between two self-adjoint operators $H_0$ and $H_1$, exponentially suppressing the diabatic error by harnessing the theoretical concept of quasi-adiabatic continuation as an algorithmic tool. Given an upper bound $α$ on $\|H_0\|$ and $\|H_1\|$ along with the promise that the $k$th eigenstate $|ψ_k(s)\rangle$ of $H(s) \equiv (1-s)H_0 + sH_1$ is separated from the rest of the spectrum by a gap of at least $γ> 0$ for all $s \in [0,1]$, this algorithm implements an operator $\widetilde{U}$ such that $\||ψ_k(1)\rangle - \widetilde{U}|ψ_k(s)\rangle\| \leq ε$ using $O(α^2/γ^2)\text{polylog}(α/γε)$ queries to block-encodings of $H_0$ and $H_1$. In addition, we develop an algorithm that is applicable only to ground states and requires multiple queries to an oracle that prepares $|ψ_0(0)\rangle$, but has slightly better scaling in all parameters. We also show that the costs of both algorithms can be further reduced under certain reasonable conditions, such as when $\|H_1 - H_0\|$ is small compared to $α$, or when more information about the gap of $H(s)$ is available. For certain problems, the scaling can even be improved to linear in $\|H_1 - H_0\|/γ$ up to polylogarithmic factors.

arXiv:2004.04164•Apr 8, 2020•8 citations

Adiabatic quantum state preparation in integrable models

Maximilian Lutz, Lorenzo Piroli, Georgios Styliaris +1 more

We propose applying the adiabatic algorithm to prepare high-energy eigenstates of integrable models on a quantum computer. We first review the standard adiabatic algorithm to prepare ground states in each magnetization sector of the prototypical XXZ Heisenberg chain. Based on the thermodynamic Bethe ansatz, we show that the algorithm circuit depth is polynomial in the number of qubits N , outperforming previous methods explicitly relying on integrability. Next, we propose a protocol to prepare arbitrary eigenstates of integrable models that satisfy certain conditions. For a given target eigenstate, we construct a suitable parent Hamiltonian written in terms of a complete set of local conserved quantities. We propose using such Hamiltonian as an input for an adiabatic algorithm. After benchmarking this construction in the case of the non-interacting XY spin chain, where we can rigorously prove its efficiency, we apply it to prepare arbitrary eigenstates of the Richardson-Gaudin models. In this case, we provide numerical evidence that the circuit depth of our algorithm is polynomial in N for all eigenstates, despite the models being interacting.

arXiv:2503.21741•Quantum•Mar 18, 2026•0 citations

Simulation of adiabatic quantum computing for molecular ground states

Vladimir Kremenetski, Carlos Mejuto-Zaera, Stephen J. Cotton +1 more

Quantum computation promises to provide substantial speedups in many practical applications with a particularly exciting one being the simulation of quantum many-body systems. Adiabatic state preparation (ASP) is one way that quantum computers could recreate and simulate the ground state of a physical system. In this paper, we explore a novel approach for classically simulating the time dynamics of ASP with high accuracy and with only modest computational resources via an adaptive sampling configuration interaction scheme for truncating the Hilbert space to only the most important determinants. We verify that this truncation introduces negligible error and use this new approach to simulate ASP for sets of small molecular systems and Hubbard models. Furthermore, we examine two approaches to speeding up ASP when performed on quantum hardware: (i) using the complete active space configuration interaction (CASCI) wave function instead of the Hartree-Fock initial state and (ii) a nonlinear interpolation between the initial and target Hamiltonians. We find that starting with a CASCI wave function with a limited active space yields substantial speedups for many of the systems examined, while nonlinear interpolation does not. In additional, we observe interesting trends in the minimum gap location (based on the initial state) as well as how state preparation time can depend on certain molecular properties, such as the number of valence electrons. Importantly, we find that the required state preparation times do not show an immediate exponential wall that would preclude an efficient run of ASP on actual hardware.

arXiv:2103.12059•The Journal of Chemical Physics•Dec 17, 2021•15 citations

Ab initio nuclear structure via quantum adiabatic algorithm

Weijie Du, James P. Vary, Xingbo Zhao +1 more

Background: Solving nuclear many-body problems with an ab initio approach is widely recognized as a computationally challenging problem. Quantum computers offer a promising path to address this challenge. There are urgent needs to develop quantum algorithms for this purpose. Objective: In this work, we explore the application of the quantum algorithm of adiabatic state preparation with quantum phase estimation in ab initio nuclear structure theory. We focus on solving the low-lying spectra (including both the ground and excited states) of simple nuclear systems. Ideas: The efficiency of this algorithm is hindered by the emergence of small energy gaps (level crossings) during the adiabatic evolution. In order to improve the efficiency, we introduce techniques to avoid level crossings: 1) by suitable design of the reference Hamiltonian; 2) by insertions of perturbation terms to modify the adiabatic path. Results: We illustrate this algorithm by solving the deuteron ground state energy and the spectrum of the deuteron bounded in a harmonic oscillator trap implementing the IBM Qiskit quantum simulator. The quantum results agree well the classical results obtained by matrix diagonalization. Outlook: With our improvements to the efficiency, this algorithm provides a promising tool for investigating the low-lying spectra of complex nuclei on future quantum computers.

arXiv:2105.08910•May 19, 2021•2 citations
Quantum computers represent a relatively new and promising development in computing technology. One of the applications of quantum computers is modelling quantum many-body systems, which describe interactions between particles on atomic and subatomic scales. Such systems are highly complex and challenging to model with classical computers due to the vast number of possible states and entanglement of the particles. In this dissertation, we examine the extent to which quantum computers can accelerate the modelling of quantum many-body systems compared to classical computers. Specifically, this dissertation presents research on adiabatic state preparation: a quantum algorithmic technique that uses the adiabatic principle from quantum mechanics to approximate eigenstates. We describe three new techniques that fall within this category and, in certain cases, offer advantages over standard methods. First, we consider cases of ground state preparation for fermionic many-body systems, where standard direct interpolation between the initial and final hamiltonian is hindered by level crossings due to discrete symmetries. As an alternative to direct interpolation, we propose adiabatic paths in a higher-dimensional space, which break the relevant symmetries. Next, we present an adiabatic echo verification protocol which mitigates both coherent and incoherent errors, arising from non-adiabatic transitions and hardware noise, respectively. We show that the estimator bias of the observable is reduced when compared to standard adiabatic preparation, achieving up to a quadratic improvement. Finally, we propose a general, fully gate-based and nonvariational quantum algorithm for counterdiabatic driving. We provide a rigorous quantum gate complexity upper bound in terms of the minimum gap Δ\DeltaΔ around this eigenstate. We find that, in the worst case, the algorithm can be run with at most O~(Δ−(3+o(1))ϵ−(1+o(1)))\tilde O(\Delta^{-(3 + o(1))} \epsilon^{-(1 + o(1))})O~(Δ−(3+o(1))ϵ−(1+o(1))) quantum gates such that a target state fidelity of at least 1−ϵ21 - \epsilon^21−ϵ2 is achieved. In certain cases, the gap dependence can be improved to quadratic.
A well-known method to prepare ground states of fermionic many-body Hamiltonians is adiabatic state preparation, in which an easy-to-prepare state is time-evolved towards an approximate ground state under a specific time-dependent Hamiltonian. However, which path to take in the evolution is often unclear, and a direct linear interpolation, which is the most common method, may not be optimal. In this work, we explore other types of adiabatic paths based on the spectral decomposition of the two-body projection of the residual Hamiltonian (the difference between the final and initial Hamiltonian). The decomposition defines a set of Hamiltonian terms which may be adiabatically interpolated in a piecewise or combined fashion. We demonstrate the usefulness of partially piecewise interpolation through examples involving Fermi-Hubbard models where, due to symmetries, level crossings occur in direct (fully combined) interpolation. We show that this specific deviation from a direct path appropriately breaks the relevant symmetries, thus avoiding level crossings and enabling an adiabatic passage. On the other hand, we show that a fully piecewise scheme, which interpolates every Hamiltonian term separately, exhibits a worst-case complexity of $O({L}^{6}/{\mathrm{\ensuremath{\Delta}}}^{3})$ as compared to $O({L}^{4}/{\mathrm{\ensuremath{\Delta}}}^{3})$ for direct interpolation, in terms of the number of one-body modes LLL and the minimal gap $\mathrm{\ensuremath{\Delta}}$ along the path. This suboptimality result suggests that only those terms which break necessary symmetries should be taken into account for piecewise interpolation, while the rest is treated with direct interpolation.
The simulation of quantum physical systems is expected to be an important application for quantum computers. The work presented in this dissertation aims to improve the resource requirements of quantum computers for solving simulation problems, by providing both novel quantum algorithms and improved implementations of existing ones. I present three main results that cover diverse aspects of simulation including equilibrium physics, the preparation of useful quantum states, and simulations based on classical stochastic processes. The results rely on established quantum algorithms and other recent techniques which I review. My first original contribution is a new quantum algorithm to sample from the thermal Gibbs state of quantum Hamiltonians. The complexity of this algorithm has an exponentially improved dependence on precision compared to an earlier quantum algorithm, and also provides polynomial improvements in other parameters. My second contribution is an improved algorithm to implement reflections about the eigenstates of unitary operators and Hamiltonians, an operation that can be used to prepare ground states of many-body Hamiltonians by quantum amplitude amplification. The improved algorithm for implementing reflections significantly reduces the number of ancilla qubits required over earlier implementations. The improvement relies in part on a novel quantum algorithm for efficiently preparing states with Gaussian-like amplitudes, which may have broad applications. I also prove a lower bound for implementing reflections, which shows that our algorithm is almost optimal. My third and final contribution regards quantum algorithms for classical stochastic processes, which are of importance in statistical physics. I present a quantum algorithm that estimates the average running time of a stochastic process, and provides a quadratic speed-up over a comparable classical algorithm.
We present a quantum algorithm for adiabatic state preparation on a gate-based quantum computer, with complexity polylogarithmic in the inverse error. Our algorithm digitally simulates the adiabatic evolution between two self-adjoint operators H0H_0H0​ and H1H_1H1​, exponentially suppressing the diabatic error by harnessing the theoretical concept of quasi-adiabatic continuation as an algorithmic tool. Given an upper bound ααα on ∥H0∥\|H_0\|∥H0​∥ and ∥H1∥\|H_1\|∥H1​∥ along with the promise that the kkkth eigenstate ∣ψk(s)⟩|ψ_k(s)\rangle∣ψk​(s)⟩ of H(s)≡(1−s)H0+sH1H(s) \equiv (1-s)H_0 + sH_1H(s)≡(1−s)H0​+sH1​ is separated from the rest of the spectrum by a gap of at least γ>0γ> 0γ>0 for all s∈[0,1]s \in [0,1]s∈[0,1], this algorithm implements an operator U~\widetilde{U}U such that ∥∣ψk(1)⟩−U~∣ψk(s)⟩∥≤ε\||ψ_k(1)\rangle - \widetilde{U}|ψ_k(s)\rangle\| \leq ε∥∣ψk​(1)⟩−U∣ψk​(s)⟩∥≤ε using O(α2/γ2)polylog(α/γε)O(α^2/γ^2)\text{polylog}(α/γε)O(α2/γ2)polylog(α/γε) queries to block-encodings of H0H_0H0​ and H1H_1H1​. In addition, we develop an algorithm that is applicable only to ground states and requires multiple queries to an oracle that prepares ∣ψ0(0)⟩|ψ_0(0)\rangle∣ψ0​(0)⟩, but has slightly better scaling in all parameters. We also show that the costs of both algorithms can be further reduced under certain reasonable conditions, such as when ∥H1−H0∥\|H_1 - H_0\|∥H1​−H0​∥ is small compared to ααα, or when more information about the gap of H(s)H(s)H(s) is available. For certain problems, the scaling can even be improved to linear in ∥H1−H0∥/γ\|H_1 - H_0\|/γ∥H1​−H0​∥/γ up to polylogarithmic factors.
We propose applying the adiabatic algorithm to prepare high-energy eigenstates of integrable models on a quantum computer. We first review the standard adiabatic algorithm to prepare ground states in each magnetization sector of the prototypical XXZ Heisenberg chain. Based on the thermodynamic Bethe ansatz, we show that the algorithm circuit depth is polynomial in the number of qubits N , outperforming previous methods explicitly relying on integrability. Next, we propose a protocol to prepare arbitrary eigenstates of integrable models that satisfy certain conditions. For a given target eigenstate, we construct a suitable parent Hamiltonian written in terms of a complete set of local conserved quantities. We propose using such Hamiltonian as an input for an adiabatic algorithm. After benchmarking this construction in the case of the non-interacting XY spin chain, where we can rigorously prove its efficiency, we apply it to prepare arbitrary eigenstates of the Richardson-Gaudin models. In this case, we provide numerical evidence that the circuit depth of our algorithm is polynomial in N for all eigenstates, despite the models being interacting.
Quantum computation promises to provide substantial speedups in many practical applications with a particularly exciting one being the simulation of quantum many-body systems. Adiabatic state preparation (ASP) is one way that quantum computers could recreate and simulate the ground state of a physical system. In this paper, we explore a novel approach for classically simulating the time dynamics of ASP with high accuracy and with only modest computational resources via an adaptive sampling configuration interaction scheme for truncating the Hilbert space to only the most important determinants. We verify that this truncation introduces negligible error and use this new approach to simulate ASP for sets of small molecular systems and Hubbard models. Furthermore, we examine two approaches to speeding up ASP when performed on quantum hardware: (i) using the complete active space configuration interaction (CASCI) wave function instead of the Hartree-Fock initial state and (ii) a nonlinear interpolation between the initial and target Hamiltonians. We find that starting with a CASCI wave function with a limited active space yields substantial speedups for many of the systems examined, while nonlinear interpolation does not. In additional, we observe interesting trends in the minimum gap location (based on the initial state) as well as how state preparation time can depend on certain molecular properties, such as the number of valence electrons. Importantly, we find that the required state preparation times do not show an immediate exponential wall that would preclude an efficient run of ASP on actual hardware.
Background: Solving nuclear many-body problems with an ab initio approach is widely recognized as a computationally challenging problem. Quantum computers offer a promising path to address this challenge. There are urgent needs to develop quantum algorithms for this purpose. Objective: In this work, we explore the application of the quantum algorithm of adiabatic state preparation with quantum phase estimation in ab initio nuclear structure theory. We focus on solving the low-lying spectra (including both the ground and excited states) of simple nuclear systems. Ideas: The efficiency of this algorithm is hindered by the emergence of small energy gaps (level crossings) during the adiabatic evolution. In order to improve the efficiency, we introduce techniques to avoid level crossings: 1) by suitable design of the reference Hamiltonian; 2) by insertions of perturbation terms to modify the adiabatic path. Results: We illustrate this algorithm by solving the deuteron ground state energy and the spectrum of the deuteron bounded in a harmonic oscillator trap implementing the IBM Qiskit quantum simulator. The quantum results agree well the classical results obtained by matrix diagonalization. Outlook: With our improvements to the efficiency, this algorithm provides a promising tool for investigating the low-lying spectra of complex nuclei on future quantum computers.