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

New Journal of Physics

Trotterized adiabatic quantum simulation and its application to a simple all-optical system

Yifan Sun, Jun-Yi Zhang, Mark Byrd, Lian-Ao Wu

Published Feb 28, 2020• 12 citations
Publisher

Abstract

Abstract As first proposed for the adiabatic quantum information processing by Wu et al (2002 Phys. Rev. Lett. 89 057904), the Trotterization technique is a very useful tool for universal quantum computing, and in particular, the adiabatic quantum simulation of quantum systems. Given a boson Hamiltonian involving arbitrary bilinear interactions, we propose a static version of this technique to perform an optical simulation that would enable the identification of the ground state of the Hamiltonian. By this method, the dynamical process of the adiabatic evolution is mapped to a static linear optical array which is robust to the errors caused by dynamical fluctuations. We examine the cost of the physical implementation of the Trotterization, i.e. the number of discrete steps required for a given accuracy. Two conclusions are drawn. One is that the number of required steps grows much more slowly than the system size if the number of non-zero matrix elements of Hamiltonian is not too large. The second is that small fluctuations of the parameters of optical elements do not affect the first conclusion. This implies that the method is robust against the certain type of errors as we considered. Last but not least, we present an example of implementation of the simulation on a photonic chip as well as an optimized scheme. By such examples, we show a reduction of the costs compared to its classical counterpart and the potential for further improvement, which promotes a more general application.

DOI
10.1088/1367-2630/ab7a31

Related papers

Alternative adiabatic quantum dynamics with algorithmic applications

Joseph Cunningham, Jérémie Roland

In adiabatic quantum computing the aim is to track an eigenstate as the Hamiltonian changes. In the usual setup this is achieved using the natural time-dependent Hamiltonian evolution of the system and the main technical tool is the adiabatic theorem. We propose several alternative processes that achieve the same goal, but can easily be implemented on a gate-based quantum computer without the overhead of simulating time-dependent Hamiltonian evolution. We give a general framework for deriving `adiabatic' theorems for these processes. As an application, we give various algorithms for solving the Quantum Linear Systems Problem (QLSP) with optimal scaling in the condition number. One of these algorithms was previously developed in [Cunningham, Roland 2024] and another can be seen as a randomised version of the discrete adiabatic algorithm of [Costa et al. 2022]. We also describe versions of Trotterisation in our framework, which allows several results from [An et al. 2025] to be reproduced in a randomised setting. In particular, bounds on the Trotter error in terms of the fidelity are obtained that are asymptotically better than the standard bounds.

quant-pharXiv:2605.30110•May 29, 2026•0 citations

Adiabatic Quantum Simulation Using Trotterization

Yin Sun, Jun-Yi Zhang, Mark Byrd +1 more

As first proposed for the adiabatic quantum information processing by Wu, Byrd and Lidar [ Phys. Rev. Lett. 89, 057904 (2002)], the Trotterization technique is a very useful tool for universal quantum computing, and in particular, the adiabatic quantum simulation of quantum systems. Given a boson Hamiltonian involving arbitrary bilinear interactions, we propose a static version of this technique to perform an optical simulation that would enable the identification of the ground state of the Hamiltonian. By this method, the dynamical process of the adiabatic evolution is mapped to a static linear optical array which avoids the errors caused by dynamical fluctuations. We examine the cost of the physical implementation of the Trotterization, i.e. the number of discrete steps required for a given accuracy. Two conclusions are drawn. One is that number of required steps grows much more slowly than system size if the number of the non-zero matrix elements of Hamiltonian is not too large. The second is that the fluctuation of the parameters of optical elements does not affect the first conclusion. This implies that the method is robust against errors.

arXiv:1805.11568•May 29, 2018•7 citations

Large time-step discretization of adiabatic quantum dynamics

Dong Un An, Pedro C. S. Costa, Dominic William Berry

Adiabatic quantum computing is a general framework for preparing eigenstates of Hamiltonians on quantum devices. However, its digital implementation requires an efficient Hamiltonian simulation subroutine, which may introduce extra computational overhead or complicated quantum control logic. In this work, we show that the time-step sizes in time discretization can be much larger than expected, and the overall complexity is greatly reduced. Remarkably, regardless of the general convergence order of the numerical method, we can choose a uniform time-step size independent of tolerated error and evolution time for sufficiently accurate simulation. Furthermore, with the boundary cancellation condition where the continuous diabatic errors are exponentially suppressed, we provide strong evidence for a superpolynomial convergence of first-order Trotter with uniform time-step size. We apply our analysis to the example of adiabatic unstructured search and show several preferable features of the Trotterized adiabatic approach: It can match the Grover lower bound, it does not require knowledge of the number of marked states, and its performance can be asymptotically comparable with that of the quantum approximate optimization algorithm.

arXiv:2509.00171•Physical Review Research•Oct 2, 2026•0 citations

Digital adiabatic evolution is universally accurate

Yangyu Lu, Yifei Huang, Dong An +3 more

Adiabatic evolution is a central paradigm in quantum physics. Digital simulations of adiabatic processes are generally regarded as resource-intensive, not only because of the long evolution time required, but also because algorithmic errors typically accumulate throughout the evolution, thereby demanding exceptionally deep circuits to preserve accuracy. This work demonstrates that digital adiabatic evolution is intrinsically accurate and robust to simulation errors. We analyze two Hamiltonian simulation methods—Trotterization and generalized quantum signal processing—and prove that the simulation error does not increase with time. We further show that accurate time-dependent adiabatic evolution can be achieved using only time-independent Hamiltonian-simulation algorithms. Numerical simulations of the adiabatic algorithms for molecular systems and linear equations confirm the theory, revealing that digital adiabatic evolution is substantially more efficient than previously assumed. Remarkably, our estimation for the first-order Trotterization error can be 106 times tighter than previous analyses for the transverse field Ising model even with less than 6 qubits. The findings establish fundamental robustness of digital adiabatic evolution and provide a basis for accurate, efficient implementations on fault-tolerant-and potentially near-term–quantum platforms. In this study, the authors show that digital adiabatic evolution is highly robust to simulation errors. Rather than accumulating, these errors self-cancel and even decrease over time, enabling highly efficient algorithms on near-term and future quantum computers.

arXiv:2510.12237•Nature Communications•May 21, 2026•1 citation

Success of digital adiabatic simulation with large Trotter step

Changhao Yi

The simulation of adiabatic evolution has deep connections with adiabatic quantum computation, the quantum approximate optimization algorithm, and adiabatic state preparation. Here we address the error analysis problem in quantum simulation of adiabatic process using Trotter formulas. We show that with additional conditions, the circuit depth can be linear in simulation time $T$. The improvement comes from the observation that the fidelity error here can't be estimated by the norm distance between evolution operators. This phenomenon is termed the robustness of discretization in digital adiabatic simulation. It can be explained in three steps, from analytical and numerical evidence: (1) The fidelity error should be estimated by applying adiabatic theorem on the effective Hamiltonian instead. (2) Because of the specialty of Riemann-Lebesgue lemma, most adiabatic process is naturally robust against discretization. (3) As the Trotter step gets larger, the spectral gap of effective Hamiltonian tends to close, which results in the failure of digital adiabatic simulation.

arXiv:2107.06404•Physical Review A•Nov 8, 2021•15 citations

Robustness of Discretization in Digital Adiabatic Simulation

Changhao Yi

The simulation of adiabatic evolution has deep connections with Adiabatic Quantum Computation, the Quantum Approximate Optimization Algorithm and adiabatic state preparation. Here we address the error analysis problem in quantum simulation of adiabatic process using Trotter formulas. We show that with additional conditions, the circuit depth can be linear in simulation time $T$. The improvement comes from the observation that the fidelity error here can't be estimated by the norm distance between evolution operators. This phenomenon is termed as the robustness of discretization in digital adiabatic simulation. It can be explained in three steps, from analytical and numerical evidence: 1. the fidelity error should be estimated by applying adiabatic theorem on the effective Hamiltonian instead. 2. because of the specialty of Riemann-Lebesgue lemma, most adiabatic process is naturally robust against discretization. 3. as the Trotter step gets larger, the spectral gap of effective Hamiltonian tends to close, which results in the failure of digital adiabatic simulation.

•Jul 13, 2021•1 citation
Abstract As first proposed for the adiabatic quantum information processing by Wu et al (2002 Phys. Rev. Lett. 89 057904), the Trotterization technique is a very useful tool for universal quantum computing, and in particular, the adiabatic quantum simulation of quantum systems. Given a boson Hamiltonian involving arbitrary bilinear interactions, we propose a static version of this technique to perform an optical simulation that would enable the identification of the ground state of the Hamiltonian. By this method, the dynamical process of the adiabatic evolution is mapped to a static linear optical array which is robust to the errors caused by dynamical fluctuations. We examine the cost of the physical implementation of the Trotterization, i.e. the number of discrete steps required for a given accuracy. Two conclusions are drawn. One is that the number of required steps grows much more slowly than the system size if the number of non-zero matrix elements of Hamiltonian is not too large. The second is that small fluctuations of the parameters of optical elements do not affect the first conclusion. This implies that the method is robust against the certain type of errors as we considered. Last but not least, we present an example of implementation of the simulation on a photonic chip as well as an optimized scheme. By such examples, we show a reduction of the costs compared to its classical counterpart and the potential for further improvement, which promotes a more general application.
In adiabatic quantum computing the aim is to track an eigenstate as the Hamiltonian changes. In the usual setup this is achieved using the natural time-dependent Hamiltonian evolution of the system and the main technical tool is the adiabatic theorem. We propose several alternative processes that achieve the same goal, but can easily be implemented on a gate-based quantum computer without the overhead of simulating time-dependent Hamiltonian evolution. We give a general framework for deriving `adiabatic' theorems for these processes. As an application, we give various algorithms for solving the Quantum Linear Systems Problem (QLSP) with optimal scaling in the condition number. One of these algorithms was previously developed in [Cunningham, Roland 2024] and another can be seen as a randomised version of the discrete adiabatic algorithm of [Costa et al. 2022]. We also describe versions of Trotterisation in our framework, which allows several results from [An et al. 2025] to be reproduced in a randomised setting. In particular, bounds on the Trotter error in terms of the fidelity are obtained that are asymptotically better than the standard bounds.
As first proposed for the adiabatic quantum information processing by Wu, Byrd and Lidar [ Phys. Rev. Lett. 89, 057904 (2002)], the Trotterization technique is a very useful tool for universal quantum computing, and in particular, the adiabatic quantum simulation of quantum systems. Given a boson Hamiltonian involving arbitrary bilinear interactions, we propose a static version of this technique to perform an optical simulation that would enable the identification of the ground state of the Hamiltonian. By this method, the dynamical process of the adiabatic evolution is mapped to a static linear optical array which avoids the errors caused by dynamical fluctuations. We examine the cost of the physical implementation of the Trotterization, i.e. the number of discrete steps required for a given accuracy. Two conclusions are drawn. One is that number of required steps grows much more slowly than system size if the number of the non-zero matrix elements of Hamiltonian is not too large. The second is that the fluctuation of the parameters of optical elements does not affect the first conclusion. This implies that the method is robust against errors.
Adiabatic quantum computing is a general framework for preparing eigenstates of Hamiltonians on quantum devices. However, its digital implementation requires an efficient Hamiltonian simulation subroutine, which may introduce extra computational overhead or complicated quantum control logic. In this work, we show that the time-step sizes in time discretization can be much larger than expected, and the overall complexity is greatly reduced. Remarkably, regardless of the general convergence order of the numerical method, we can choose a uniform time-step size independent of tolerated error and evolution time for sufficiently accurate simulation. Furthermore, with the boundary cancellation condition where the continuous diabatic errors are exponentially suppressed, we provide strong evidence for a superpolynomial convergence of first-order Trotter with uniform time-step size. We apply our analysis to the example of adiabatic unstructured search and show several preferable features of the Trotterized adiabatic approach: It can match the Grover lower bound, it does not require knowledge of the number of marked states, and its performance can be asymptotically comparable with that of the quantum approximate optimization algorithm.
Adiabatic evolution is a central paradigm in quantum physics. Digital simulations of adiabatic processes are generally regarded as resource-intensive, not only because of the long evolution time required, but also because algorithmic errors typically accumulate throughout the evolution, thereby demanding exceptionally deep circuits to preserve accuracy. This work demonstrates that digital adiabatic evolution is intrinsically accurate and robust to simulation errors. We analyze two Hamiltonian simulation methods—Trotterization and generalized quantum signal processing—and prove that the simulation error does not increase with time. We further show that accurate time-dependent adiabatic evolution can be achieved using only time-independent Hamiltonian-simulation algorithms. Numerical simulations of the adiabatic algorithms for molecular systems and linear equations confirm the theory, revealing that digital adiabatic evolution is substantially more efficient than previously assumed. Remarkably, our estimation for the first-order Trotterization error can be 106 times tighter than previous analyses for the transverse field Ising model even with less than 6 qubits. The findings establish fundamental robustness of digital adiabatic evolution and provide a basis for accurate, efficient implementations on fault-tolerant-and potentially near-term–quantum platforms. In this study, the authors show that digital adiabatic evolution is highly robust to simulation errors. Rather than accumulating, these errors self-cancel and even decrease over time, enabling highly efficient algorithms on near-term and future quantum computers.
The simulation of adiabatic evolution has deep connections with adiabatic quantum computation, the quantum approximate optimization algorithm, and adiabatic state preparation. Here we address the error analysis problem in quantum simulation of adiabatic process using Trotter formulas. We show that with additional conditions, the circuit depth can be linear in simulation time TTT. The improvement comes from the observation that the fidelity error here can't be estimated by the norm distance between evolution operators. This phenomenon is termed the robustness of discretization in digital adiabatic simulation. It can be explained in three steps, from analytical and numerical evidence: (1) The fidelity error should be estimated by applying adiabatic theorem on the effective Hamiltonian instead. (2) Because of the specialty of Riemann-Lebesgue lemma, most adiabatic process is naturally robust against discretization. (3) As the Trotter step gets larger, the spectral gap of effective Hamiltonian tends to close, which results in the failure of digital adiabatic simulation.
The simulation of adiabatic evolution has deep connections with Adiabatic Quantum Computation, the Quantum Approximate Optimization Algorithm and adiabatic state preparation. Here we address the error analysis problem in quantum simulation of adiabatic process using Trotter formulas. We show that with additional conditions, the circuit depth can be linear in simulation time TTT. The improvement comes from the observation that the fidelity error here can't be estimated by the norm distance between evolution operators. This phenomenon is termed as the robustness of discretization in digital adiabatic simulation. It can be explained in three steps, from analytical and numerical evidence: 1. the fidelity error should be estimated by applying adiabatic theorem on the effective Hamiltonian instead. 2. because of the specialty of Riemann-Lebesgue lemma, most adiabatic process is naturally robust against discretization. 3. as the Trotter step gets larger, the spectral gap of effective Hamiltonian tends to close, which results in the failure of digital adiabatic simulation.