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:2311.05544 · PRX Quantum

Towards Adiabatic Quantum Computing Using Compressed Quantum Circuits

Conor Mc Keever, Michael Lubasch

Published Jun 14, 2024• 73 citations
arXivHTMLPDF

Abstract

We describe tensor network algorithms to optimize quantum circuits for adiabatic quantum computing. To suppress diabatic transitions, we include counterdiabatic driving in the optimization and utilize variational matrix product operators to represent adiabatic gauge potentials. Traditionally, Trotter product formulas are used to turn adiabatic time evolution into quantum circuits and the addition of counterdiabatic driving increases the circuit depth per time step. Instead, we classically optimize a parameterized quantum circuit of fixed depth to simultaneously capture adiabatic evolution together with counterdiabatic driving over many time steps. The methods are applied to the ground-state preparation of quantum Ising chains with transverse and longitudinal fields. We show that the classically optimized circuits can significantly outperform Trotter product formulas. Additionally, we discuss how the approach can be used for combinatorial optimization. Published by the American Physical Society 2024

DOI
10.1103/prxquantum.5.020362

Related papers

Optimizing counterdiabaticity by variational quantum circuits

Dan Sun, Pranav Chandarana, Zi‐Hua Xin +1 more

Using counterdiabatic (CD) driving-aiming at suppression of diabatic transition-in digitized adiabatic evolution has garnered immense interest in quantum protocols and algorithms. However, improving the approximate CD terms with a nested commutator ansatz is a challenging task. In this work, we propose a technique of finding optimal coefficients of the CD terms using a variational quantum circuit. By classical optimization routines, the parameters of this circuit are optimized to provide the coefficients corresponding to the CD terms. Then their improved performance is exemplified in Greenberger-Horne-Zeilinger state preparation on the nearest-neighbour Ising model. Finally, we also show the advantage over the usual quantum approximation optimization algorithm, in terms of fidelity with bounded time. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.

arXiv:2208.02087•Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Nov 6, 2022•16 citations

Constant Depth Digital-Analog Counterdiabatic Quantum Computing

Balaganchi A. Bhargava, Shubham Kumar, Anne-Maria Visuri +3 more

We introduce a digital-analog quantum computing framework that enables counterdiabatic protocols to be implemented at constant circuit depth, allowing fast and resource-efficient quantum state preparation on current quantum hardware. Counterdiabatic protocols suppress diabatic excitations in finite-time adiabatic evolution, but their practical application is limited by the non-local structure of the required Hamiltonians and the resource overhead of fully digital implementations. Counterdiabatic terms can be expressed as truncated expansions of nested commutators of the adiabatic Hamiltonian and its parametric derivative. Here, we show how this algebraic structure can be efficiently realized in a digital-analog setting using commutator product formulas. Using native multi-qubit analog interactions augmented by local single-qubit rotations, this approach enables higher-order counterdiabatic protocols whose implementation requires a constant number of analog blocks for any fixed truncation order, independent of system size. We demonstrate the method for two-dimensional spin models and analyze the associated approximation errors. These results show that digital-analog quantum computing enables a qualitatively new resource scaling for counterdiabatic protocols and related quantum control primitives, with direct implications for quantum simulation, optimization, and algorithmic state preparation on current quantum devices.

quant-pharXiv:2601.01154•Jan 6, 2026•0 citations

Scalable simulation of nonequilibrium quantum dynamics via classically optimized unitary circuits

Luke Causer, F. Jung, Asimpunya Mitra +2 more

The advent of near-term digital quantum computers could offer us an exciting opportunity to investigate quantum many-body phenomena beyond that of classical computing. To make the best use of the hardware available, it is paramount that we have methods that accurately simulate Hamiltonian dynamics for limited circuit depths. In this paper, we propose a method to classically optimize unitary brickwall circuits to approximate quantum time evolution operators. Our method is scalable in system size through the use of tensor networks. We demonstrate that, for various three-body Hamiltonians, our approach produces quantum circuits that can outperform trotterization in both their accuracy and the quantum circuit depth needed to implement the dynamics, with the exact details being dependent on the Hamiltonian. We also explain how to choose an optimal time step that minimizes the combined errors of the quantum device and the brickwall circuit approximation. Published by the American Physical Society 2024

arXiv:2312.14245•Physical Review Research•Jul 15, 2024•9 citations

Algebraic compression of quantum circuits for Hamiltonian evolution

Efekan Kökcü, Daan Camps, Lindsay Bassman Oftelie +4 more

Unitary evolution under a time-dependent Hamiltonian is a key component of simulation on quantum hardware. Synthesizing the corresponding quantum circuit is typically done by breaking the evolution into small time steps, also known as Trotterization, which leads to circuits the depth of which scales with the number of steps. When the circuit elements are limited to a subset of $SU(4)$---or equivalently, when the Hamiltonian may be mapped onto free fermionic models---several identities exist that combine and simplify the circuit. Based on this, we present an algorithm that compresses the Trotter steps into a single block of quantum gates using algebraic relations between adjacent circuit elements. This results in a fixed depth time evolution for certain classes of Hamiltonians. We explicitly show how this algorithm works for several spin models, and demonstrate its use for adiabatic state preparation of the transverse field Ising model.

arXiv:2108.03282•Physical Review A•Mar 10, 2022•46 citations

Variationally Compressing Quantum Circuits to Approximate Nonadiabatic Molecular Quantum Dynamics

Joshua M. Courtney, P. C. Stancil

Quantum simulation has begun to penetrate the field of quantum chemistry in hopes of efficiently calculating ground state energies and approximating real-time evolution. With modern research highlighting nonadiabatic dynamics, tunably approximating deep circuits representing potential landscapes becomes crucial for simulating real quantum systems. Variationally approximating unitaries allows for shallower circuits and accuracy tunable to hardware fidelity, so long as the observable quantities are preserved. We show the variational compression of Trotter terms preserve reaction rate coefficients via classical emulation of a hybrid quantum-classical optimization method, as well as fast-forwarded adiabatic dynamics on quantum hardware. Compressed circuits can be incorporated with product-formula-based time evolution to approximate dynamics of a particle in two coupled harmonic potentials, allowing tunability when removing high-cost qubit interactions. Approximate rate coefficients are recovered after substituting terms in a nonadiabatic dynamic process, giving proof-of-principle for observable preservation under variational optimization. Attention is paid to minimizing qubit and gate-count resources.

quant-pharXiv:2605.06122•May 8, 2026•1 citation

Counterdiabatic quantum optimization for efficient state preparation in the Schwinger model

Ethan Laval, Bipasha Chakraborty, Stefano Cipolla

The Quantum Approximate Optimization Algorithm (QAOA), whose design is underpinned by the adiabatic theorem, is one of the leading variational quantum algorithms for preparing the ground states of gauge theories. A recently proposed variant, DC-QAOA, incorporates counterdiabatic driving to accelerate the adiabatic process, reducing both circuit depth and runtime. In this work, we present a systematic analysis, from both theoretical and computational perspectives, of DC-QAOA and related counterdiabatic variants for preparing the ground state of the Schwinger model, the paradigmatic (1+1)-dimensional lattice gauge theory. Benchmarking these methods against standard QAOA, we show that counterdiabatic driving improves ground-state preparation while lowering circuit depth requirements. Our results establish counterdiabatic protocols as a practical route towards efficient quantum simulation of gauge theories.

hep-latCross-listedarXiv:2609.31400•Sep 28, 2026•0 citations
We describe tensor network algorithms to optimize quantum circuits for adiabatic quantum computing. To suppress diabatic transitions, we include counterdiabatic driving in the optimization and utilize variational matrix product operators to represent adiabatic gauge potentials. Traditionally, Trotter product formulas are used to turn adiabatic time evolution into quantum circuits and the addition of counterdiabatic driving increases the circuit depth per time step. Instead, we classically optimize a parameterized quantum circuit of fixed depth to simultaneously capture adiabatic evolution together with counterdiabatic driving over many time steps. The methods are applied to the ground-state preparation of quantum Ising chains with transverse and longitudinal fields. We show that the classically optimized circuits can significantly outperform Trotter product formulas. Additionally, we discuss how the approach can be used for combinatorial optimization. Published by the American Physical Society 2024
Using counterdiabatic (CD) driving-aiming at suppression of diabatic transition-in digitized adiabatic evolution has garnered immense interest in quantum protocols and algorithms. However, improving the approximate CD terms with a nested commutator ansatz is a challenging task. In this work, we propose a technique of finding optimal coefficients of the CD terms using a variational quantum circuit. By classical optimization routines, the parameters of this circuit are optimized to provide the coefficients corresponding to the CD terms. Then their improved performance is exemplified in Greenberger-Horne-Zeilinger state preparation on the nearest-neighbour Ising model. Finally, we also show the advantage over the usual quantum approximation optimization algorithm, in terms of fidelity with bounded time. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.
We introduce a digital-analog quantum computing framework that enables counterdiabatic protocols to be implemented at constant circuit depth, allowing fast and resource-efficient quantum state preparation on current quantum hardware. Counterdiabatic protocols suppress diabatic excitations in finite-time adiabatic evolution, but their practical application is limited by the non-local structure of the required Hamiltonians and the resource overhead of fully digital implementations. Counterdiabatic terms can be expressed as truncated expansions of nested commutators of the adiabatic Hamiltonian and its parametric derivative. Here, we show how this algebraic structure can be efficiently realized in a digital-analog setting using commutator product formulas. Using native multi-qubit analog interactions augmented by local single-qubit rotations, this approach enables higher-order counterdiabatic protocols whose implementation requires a constant number of analog blocks for any fixed truncation order, independent of system size. We demonstrate the method for two-dimensional spin models and analyze the associated approximation errors. These results show that digital-analog quantum computing enables a qualitatively new resource scaling for counterdiabatic protocols and related quantum control primitives, with direct implications for quantum simulation, optimization, and algorithmic state preparation on current quantum devices.
The advent of near-term digital quantum computers could offer us an exciting opportunity to investigate quantum many-body phenomena beyond that of classical computing. To make the best use of the hardware available, it is paramount that we have methods that accurately simulate Hamiltonian dynamics for limited circuit depths. In this paper, we propose a method to classically optimize unitary brickwall circuits to approximate quantum time evolution operators. Our method is scalable in system size through the use of tensor networks. We demonstrate that, for various three-body Hamiltonians, our approach produces quantum circuits that can outperform trotterization in both their accuracy and the quantum circuit depth needed to implement the dynamics, with the exact details being dependent on the Hamiltonian. We also explain how to choose an optimal time step that minimizes the combined errors of the quantum device and the brickwall circuit approximation. Published by the American Physical Society 2024
Unitary evolution under a time-dependent Hamiltonian is a key component of simulation on quantum hardware. Synthesizing the corresponding quantum circuit is typically done by breaking the evolution into small time steps, also known as Trotterization, which leads to circuits the depth of which scales with the number of steps. When the circuit elements are limited to a subset of SU(4)SU(4)SU(4)---or equivalently, when the Hamiltonian may be mapped onto free fermionic models---several identities exist that combine and simplify the circuit. Based on this, we present an algorithm that compresses the Trotter steps into a single block of quantum gates using algebraic relations between adjacent circuit elements. This results in a fixed depth time evolution for certain classes of Hamiltonians. We explicitly show how this algorithm works for several spin models, and demonstrate its use for adiabatic state preparation of the transverse field Ising model.
Quantum simulation has begun to penetrate the field of quantum chemistry in hopes of efficiently calculating ground state energies and approximating real-time evolution. With modern research highlighting nonadiabatic dynamics, tunably approximating deep circuits representing potential landscapes becomes crucial for simulating real quantum systems. Variationally approximating unitaries allows for shallower circuits and accuracy tunable to hardware fidelity, so long as the observable quantities are preserved. We show the variational compression of Trotter terms preserve reaction rate coefficients via classical emulation of a hybrid quantum-classical optimization method, as well as fast-forwarded adiabatic dynamics on quantum hardware. Compressed circuits can be incorporated with product-formula-based time evolution to approximate dynamics of a particle in two coupled harmonic potentials, allowing tunability when removing high-cost qubit interactions. Approximate rate coefficients are recovered after substituting terms in a nonadiabatic dynamic process, giving proof-of-principle for observable preservation under variational optimization. Attention is paid to minimizing qubit and gate-count resources.
The Quantum Approximate Optimization Algorithm (QAOA), whose design is underpinned by the adiabatic theorem, is one of the leading variational quantum algorithms for preparing the ground states of gauge theories. A recently proposed variant, DC-QAOA, incorporates counterdiabatic driving to accelerate the adiabatic process, reducing both circuit depth and runtime. In this work, we present a systematic analysis, from both theoretical and computational perspectives, of DC-QAOA and related counterdiabatic variants for preparing the ground state of the Schwinger model, the paradigmatic (1+1)-dimensional lattice gauge theory. Benchmarking these methods against standard QAOA, we show that counterdiabatic driving improves ground-state preparation while lowering circuit depth requirements. Our results establish counterdiabatic protocols as a practical route towards efficient quantum simulation of gauge theories.