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:2305.01284 · Physical Review A

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

Dyon van Vreumingen, Kareljan Schoutens

Published Dec 4, 2023• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.108.062603

Related papers

Strategies for adiabatic state preparation of quantum many-body systems

Dyon van Vreumingen

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.

•Feb 20, 2025•0 citations

Adiabatic approximation with better than exponential accuracy for many-body systems and quantum computation

Daniel A. Lidar, A. T. Rezakhani, Alioscia Hamma

We derive a version of the adiabatic theorem that is especially suited for applications in adiabatic quantum computation, where it is reasonable to assume that the adiabatic interpolation between the initial and final Hamiltonians is controllable. Assuming that the Hamiltonian is analytic in a finite strip around the real time axis, that some number of its time-derivatives vanish at the initial and final times, and that the target adiabatic eigenstate is non-degenerate and separated by a gap from the rest of the spectrum, we show that one can obtain an error between the final adiabatic eigenstate and the actual time-evolved state which is exponentially small in the evolution time, where this time itself scales as the square of the norm of the time-derivative of the Hamiltonian, divided by the cube of the minimal gap.

•Aug 20, 2008•4 citations

Adiabatic approximation with exponential accuracy for many-body systems and quantum computation

Daniel A. Lidar, Ali T. Rezakhani, Alioscia Hamma

We derive a version of the adiabatic theorem that is especially suited for applications in adiabatic quantum computation, where it is reasonable to assume that the adiabatic interpolation between the initial and final Hamiltonians is controllable. Assuming that the Hamiltonian is analytic in a finite strip around the real-time axis, that some number of its time derivatives vanish at the initial and final times, and that the target adiabatic eigenstate is nondegenerate and separated by a gap from the rest of the spectrum, we show that one can obtain an error between the final adiabatic eigenstate and the actual time-evolved state which is exponentially small in the evolution time, where this time itself scales as the square of the norm of the time derivative of the Hamiltonian divided by the cube of the minimal gap.

arXiv:0808.2697•Journal of Mathematical Physics•Oct 1, 2009•166 citations

Phase diagram of the Schwinger model by adiabatic preparation of states on a quantum simulator

Oleg Kaikov, Theo Saporiti, Vasily Sazonov +1 more

We argue the feasibility of studying the phase structure of a quantum physical system on quantum devices via adiabatic preparation of states. We introduce a method and successfully test it in application to the Schwinger model in the presence of a topological $\ensuremath{\theta}$ term. We explore the first-order-phase-transition and the no-transition regions of the corresponding phase diagram. The core idea of the method is to separately evolve the ground and the first excited states with a time-dependent Hamiltonian, the time dependence of which interpolates between different values of $\ensuremath{\theta}$. Despite our approach being a direct application of the adiabatic theorem, in some cases we are able to demonstrate its advantages in comparison to a different method from the literature that also employs adiabatic state preparation.

arXiv:2407.09224•Physical Review A•Jun 2, 2025•3 citations

On optimal methods for adiabatic quantum state transformations

Rolando D. Somma

Many problems in science could be solved by preparing the low-energy quantum state (or any eigenstate) of a Hamiltonian. A common example is the Boolean satisfiability problem, where each clause can be mapped to the energy of an interacting many-body system, and the problem reduces to minimizing the energy. In quantum computing, adiabatic quantum state transformations (ASTs) provide a tool for preparing the quantum state. ASTs are conventionally implemented via slow or adiabatic perturbations to the Hamiltonian, relying on the quantum adiabatic theorem. Nevertheless, more efficient implementations of ASTs exist. In this talk I will review recently developed methods for ASTs that are more efficient and require less assumptions on the Hamiltonians than the conventional implementation [1,2]. Such methods involve measurements of the states along the evolution path and have a best-case implementation cost of L/G, where L is the length of the (evolved) state path and G is a lower bound to the spectral gap of the Hamiltonians. I will show that this cost is optimal [3] and comment on results of the gap amplification problem, where the goal is to reduce the cost by increasing G [4].

Bulletin of the American Physical Society•Mar 18, 2013•0 citations

Fast-forward ground-state preparation in finite two-site Bose–Hubbard systems

Iwan Setiawan, Dedy Hamdani, Riska Ekawita +2 more

Abstract We present a method to accelerate the adiabatic quantum dynamics of two-site Bose–Hubbard systems by using the fast-forward method proposed by Masuda and Nakamura. The accelerated scheme is constructed by adding a driving Hamiltonian to the original Hamiltonian and introducing a large time-scaling factor together with an adiabatic parameter, enabling adiabatic quantum dynamics within a shortened timescale. We apply this protocol to a finite-time ground-state preparation in the two-site Bose–Hubbard model. For two bosons, the dynamics reduces to a two-level problem in the symmetric Fock subspace, which yields an analytic current-like auxiliary coupling that suppresses diabatic transitions during an initial ground-state configuration to a desired final ground-state configuration. For three bosons, the Hamiltonian separates into symmetric and antisymmetric parity blocks; the symmetric block governs ground-state preparation from the normalized state 1 2 | 2 , 1 ⟩ + 1 2 | 1 , 2 ⟩ ), while the antisymmetric correction is relevant only for transitionless driving in the full-parity sector. For four bosons, the exchange-symmetric sector is three dimensional. This three-level structure constitutes the principal multilevel extension presented in this work. Numerical solutions of the time-dependent Schrödinger equation show that the fast-forward Hamiltonian maintains high instantaneous ground-state fidelity and reproduces the target population distribution within the prescribed finite protocol time, whereas evolution under the bare Hamiltonian produces appreciable diabatic excitations. The protocol provides an analytically tractable example of fast-forward control in an interacting bosonic dimer.

Physica Scripta•Oct 15, 2026•0 citations
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(L6/\ensuremathΔ3)O({L}^{6}/{\mathrm{\ensuremath{\Delta}}}^{3})O(L6/\ensuremathΔ3) as compared to O(L4/\ensuremathΔ3)O({L}^{4}/{\mathrm{\ensuremath{\Delta}}}^{3})O(L4/\ensuremathΔ3) for direct interpolation, in terms of the number of one-body modes LLL and the minimal gap \ensuremathΔ\mathrm{\ensuremath{\Delta}}\ensuremathΔ 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.
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.
We derive a version of the adiabatic theorem that is especially suited for applications in adiabatic quantum computation, where it is reasonable to assume that the adiabatic interpolation between the initial and final Hamiltonians is controllable. Assuming that the Hamiltonian is analytic in a finite strip around the real time axis, that some number of its time-derivatives vanish at the initial and final times, and that the target adiabatic eigenstate is non-degenerate and separated by a gap from the rest of the spectrum, we show that one can obtain an error between the final adiabatic eigenstate and the actual time-evolved state which is exponentially small in the evolution time, where this time itself scales as the square of the norm of the time-derivative of the Hamiltonian, divided by the cube of the minimal gap.
We derive a version of the adiabatic theorem that is especially suited for applications in adiabatic quantum computation, where it is reasonable to assume that the adiabatic interpolation between the initial and final Hamiltonians is controllable. Assuming that the Hamiltonian is analytic in a finite strip around the real-time axis, that some number of its time derivatives vanish at the initial and final times, and that the target adiabatic eigenstate is nondegenerate and separated by a gap from the rest of the spectrum, we show that one can obtain an error between the final adiabatic eigenstate and the actual time-evolved state which is exponentially small in the evolution time, where this time itself scales as the square of the norm of the time derivative of the Hamiltonian divided by the cube of the minimal gap.
We argue the feasibility of studying the phase structure of a quantum physical system on quantum devices via adiabatic preparation of states. We introduce a method and successfully test it in application to the Schwinger model in the presence of a topological $\ensuremath{\theta}$ term. We explore the first-order-phase-transition and the no-transition regions of the corresponding phase diagram. The core idea of the method is to separately evolve the ground and the first excited states with a time-dependent Hamiltonian, the time dependence of which interpolates between different values of $\ensuremath{\theta}$. Despite our approach being a direct application of the adiabatic theorem, in some cases we are able to demonstrate its advantages in comparison to a different method from the literature that also employs adiabatic state preparation.
Many problems in science could be solved by preparing the low-energy quantum state (or any eigenstate) of a Hamiltonian. A common example is the Boolean satisfiability problem, where each clause can be mapped to the energy of an interacting many-body system, and the problem reduces to minimizing the energy. In quantum computing, adiabatic quantum state transformations (ASTs) provide a tool for preparing the quantum state. ASTs are conventionally implemented via slow or adiabatic perturbations to the Hamiltonian, relying on the quantum adiabatic theorem. Nevertheless, more efficient implementations of ASTs exist. In this talk I will review recently developed methods for ASTs that are more efficient and require less assumptions on the Hamiltonians than the conventional implementation [1,2]. Such methods involve measurements of the states along the evolution path and have a best-case implementation cost of L/G, where L is the length of the (evolved) state path and G is a lower bound to the spectral gap of the Hamiltonians. I will show that this cost is optimal [3] and comment on results of the gap amplification problem, where the goal is to reduce the cost by increasing G [4].
Abstract We present a method to accelerate the adiabatic quantum dynamics of two-site Bose–Hubbard systems by using the fast-forward method proposed by Masuda and Nakamura. The accelerated scheme is constructed by adding a driving Hamiltonian to the original Hamiltonian and introducing a large time-scaling factor together with an adiabatic parameter, enabling adiabatic quantum dynamics within a shortened timescale. We apply this protocol to a finite-time ground-state preparation in the two-site Bose–Hubbard model. For two bosons, the dynamics reduces to a two-level problem in the symmetric Fock subspace, which yields an analytic current-like auxiliary coupling that suppresses diabatic transitions during an initial ground-state configuration to a desired final ground-state configuration. For three bosons, the Hamiltonian separates into symmetric and antisymmetric parity blocks; the symmetric block governs ground-state preparation from the normalized state 1 2 | 2 , 1 ⟩ + 1 2 | 1 , 2 ⟩ ), while the antisymmetric correction is relevant only for transitionless driving in the full-parity sector. For four bosons, the exchange-symmetric sector is three dimensional. This three-level structure constitutes the principal multilevel extension presented in this work. Numerical solutions of the time-dependent Schrödinger equation show that the fast-forward Hamiltonian maintains high instantaneous ground-state fidelity and reproduces the target population distribution within the prescribed finite protocol time, whereas evolution under the bare Hamiltonian produces appreciable diabatic excitations. The protocol provides an analytically tractable example of fast-forward control in an interacting bosonic dimer.