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

Physica Scripta

Spectral gap estimation via adiabatic preparation

Davide Cugini, Francesco Ghisoni, Angela Rosy Morgillo, Francesco Scala

Published Jun 2, 2026• 0 citations
Publisher

Abstract

Abstract Estimating energy gaps, i.e. the energy difference between two different states, in quantum systems is crucial for understanding their properties. Conventionally, spectral gap estimation relies on independently computing the ground-state and first-excited-state energies and then taking their difference. This work introduces an alternative procedure for estimating spectral gaps on digital quantum devices using the adiabatic preparation technique to create a specific superposition state. The expectation values of observables measured on such a state exhibit time-dependent fluctuations which, through a fitting process, can be used to estimate the energy gap. We successfully test our method on the 1D and 2D Ising models, and H 2 and He 2 molecules, implementing relatively shallow circuits both on noiseless and noisy simulators. The robustness of the approach is corroborated by additional experiments on the real IonQ Aria device for the 1D Ising model up to 20 qubits, demonstrating the applicability of the proposed method for currently available digital quantum devices and paving the way for more complex energy gap calculation requiring deeper circuits in the fault-tolerant era to come.

DOI
10.1088/1402-4896/ae7674

Related papers

Spectral Gap Estimation via Adiabatic Preparation

Davide Cugini, Francesco Ghisoni, Angela Rosy Morgillo +1 more

Estimating energy gaps, i.e. the energy difference between two different states, in quantum systems is crucial for understanding their properties. Conventionally, spectral gap estimation relies on independently computing the ground-state and first-excited-state energies and then taking their difference. This work introduces an alternative procedure for estimating spectral gaps on digital quantum devices using the Adiabatic Preparation technique to create a specific superposition state. The expectation values of observables measured on such a state exhibit time-dependent fluctuations which, through a fitting process, can be used to estimate the energy gap. We successfully test our method on the 1D and 2D Ising models, and H2 and He2 molecules, implementing relatively shallow circuits both on noiseless and noisy simulators. The robustness of the approach is corroborated by additional experiments on the real IonQ Aria device for the 1D Ising model up to 20 qubits, demonstrating the applicability of the proposed method for currently available digital quantum devices and paving the way for more complex energy gap calculation requiring deeper circuits in the fault-tolerant era to come.

quant-pharXiv:2512.19288•Dec 23, 2025•0 citations

Spectral Gap Superposition States

Davide Cugini, Francesco Ghisoni, Angela Rosy Morgillo +1 more

This work introduces a novel NISQ-friendly procedure for estimating spectral gaps in quantum systems. By leveraging Adiabatic Thermalization, we are able to create the Spectral Gap Superposition state, a newly defined quantum state exhibiting observable fluctuations in time that allow for the accurate estimation of any energy gap. Our method is tested by estimating the energy gap between the ground and the first excited state for the 1D and 2D Ising model, the Hydrogen molecule H2 and Helium molecule He2. Despite limiting our circuit design to have at most 40 Trotter steps, our numerical experiments of both noiseless and noisy devices for the presented systems give relative errors in the order of $10^{-2}$ and $10^{-1}$. Further experiments on the IonQ Aria device lead to spectral gap estimations with a relative error of $10^{-2}$ for a 4-site Ising chain, demonstrating the validity of the procedure for NISQ devices and charting a path towards a new way of calculating energy gaps.

arXiv:2402.17668•Feb 27, 2024•0 citations

Importance of the Spectral gap in Estimating Ground-State Energies

Abhinav Deshpande, Alexey Vyacheslavovich Gorshkov, Bill Fefferman

The circuit complexity in preparing the ground state of a Hamiltonian is studied as a function of the spectral gap---the energy difference between the ground and the first excited state---and an optimistic outlook for quantum variational methods is presented.

arXiv:2007.11582•PRX Quantum•Dec 9, 2022•16 citations

MQTE: A Measurement-Based Quantum Algorithm for Robust Energy Spectrum Estimation in the NISQ Era

Qing-Xing Xie, Yong-Kang Duan, Fa-Hui Liu +1 more

Extracting energy spectra from quantum Hamiltonians is a fundamental task for quantum simulation, yet remains challenging on noisy intermediate-scale quantum (NISQ) devices. We propose Measured Quantum Time Evolution (MQTE), an ancilla-free algorithm that estimates energy gaps by applying real-time evolution to a reference state and measuring time-resolved probabilities via repeated projective measurements. Spectral analysis of these signals reveals oscillation frequencies corresponding to eigenvalue differences. Crucially, MQTE exhibits inherent robustness to quantum hardware noise and sampling errors: these disturbances manifest as a white-noise background, which does not distort the underlying spectral structure but rather obscures the frequency information. By increasing the number of measurement samples, the intensity of the background white noise can be suppressed, thereby recovering the original spectral content. We validate the algorithm's performance via numerical simulations on one- and two-dimensional Heisenberg models, demonstrating accurate extraction of energy gaps and resilience against both sampling and circuit-level noise. Experimental implementation on the superconducting quantum processor Tianyan-176-II further confirms the practical feasibility and noise tolerance of MQTE under real hardware conditions. This work provides a robust and scalable framework for quantum spectral estimation in the NISQ era.

quant-pharXiv:2603.17959•Mar 19, 2026•0 citations

Simulating adiabatic evolution of gapped spin systems

Tobias J. Osborne

We show that adiabatic evolution of a low-dimensional lattice of quantum spins with a spectral gap can be simulated efficiently. In particular, we show that as long as the spectral gap $\ensuremath{\Delta}E$ between the ground state and the first excited state is any constant independent of $n$, the total number of spins, then the ground-state expectation values of local operators, such as correlation functions, can be computed using polynomial space and time resources. Our results also imply that the local ground-state properties of any two spin models in the same quantum phase can be efficiently obtained from each other. A consequence of these results is that adiabatic quantum algorithms can be simulated efficiently if the spectral gap does not scale with $n$. The simulation method we describe takes place in the Heisenberg picture and does not make use of the finitely correlated state--matrix product state formalism.

arXiv:quant-ph/0601019•Physical Review A•Mar 14, 2007•91 citations

Direct estimation of the energy gap between the ground state and excited state with quantum annealing

Yuichiro Matsuzaki, Hideaki Hakoshima, Kenji Sugisaki +2 more

Quantum chemistry is one of the important applications of quantum information technology.Especially, an estimation of the energy gap between a ground state and excited state of a target Hamiltonian corresponding to a molecule is essential.In the previous approach, an energy of the ground state and that of the excited state are estimated separately, and the energy gap can be calculated from the subtraction between them.Here, we propose a direct estimation of the energy gap between the ground state and excited state of the target Hamiltonian with quantum annealing.The key idea is to combine a Ramsey type measurement with the quantum annealing.This provides an oscillating signal with a frequency of the energy gap, and a Fourier transform of the signal let us know the energy gap.Based on typical parameters of superconducting qubits, we numerically investigate the performance of our scheme when we estimate an energy gap between the ground state and first excited state of the Hamiltonian.We show robustness against non-adiabatic transitions between the ground state and first-excited state.Our results pave a new way to estimate the energy gap of the Hamiltonian for quantum chemistry.

International Conference on Solid State Devices and Materials (SSDM)•Sep 29, 2020•2 citations
Abstract Estimating energy gaps, i.e. the energy difference between two different states, in quantum systems is crucial for understanding their properties. Conventionally, spectral gap estimation relies on independently computing the ground-state and first-excited-state energies and then taking their difference. This work introduces an alternative procedure for estimating spectral gaps on digital quantum devices using the adiabatic preparation technique to create a specific superposition state. The expectation values of observables measured on such a state exhibit time-dependent fluctuations which, through a fitting process, can be used to estimate the energy gap. We successfully test our method on the 1D and 2D Ising models, and H 2 and He 2 molecules, implementing relatively shallow circuits both on noiseless and noisy simulators. The robustness of the approach is corroborated by additional experiments on the real IonQ Aria device for the 1D Ising model up to 20 qubits, demonstrating the applicability of the proposed method for currently available digital quantum devices and paving the way for more complex energy gap calculation requiring deeper circuits in the fault-tolerant era to come.
Estimating energy gaps, i.e. the energy difference between two different states, in quantum systems is crucial for understanding their properties. Conventionally, spectral gap estimation relies on independently computing the ground-state and first-excited-state energies and then taking their difference. This work introduces an alternative procedure for estimating spectral gaps on digital quantum devices using the Adiabatic Preparation technique to create a specific superposition state. The expectation values of observables measured on such a state exhibit time-dependent fluctuations which, through a fitting process, can be used to estimate the energy gap. We successfully test our method on the 1D and 2D Ising models, and H2 and He2 molecules, implementing relatively shallow circuits both on noiseless and noisy simulators. The robustness of the approach is corroborated by additional experiments on the real IonQ Aria device for the 1D Ising model up to 20 qubits, demonstrating the applicability of the proposed method for currently available digital quantum devices and paving the way for more complex energy gap calculation requiring deeper circuits in the fault-tolerant era to come.
This work introduces a novel NISQ-friendly procedure for estimating spectral gaps in quantum systems. By leveraging Adiabatic Thermalization, we are able to create the Spectral Gap Superposition state, a newly defined quantum state exhibiting observable fluctuations in time that allow for the accurate estimation of any energy gap. Our method is tested by estimating the energy gap between the ground and the first excited state for the 1D and 2D Ising model, the Hydrogen molecule H2 and Helium molecule He2. Despite limiting our circuit design to have at most 40 Trotter steps, our numerical experiments of both noiseless and noisy devices for the presented systems give relative errors in the order of 10−210^{-2}10−2 and 10−110^{-1}10−1. Further experiments on the IonQ Aria device lead to spectral gap estimations with a relative error of 10−210^{-2}10−2 for a 4-site Ising chain, demonstrating the validity of the procedure for NISQ devices and charting a path towards a new way of calculating energy gaps.
Extracting energy spectra from quantum Hamiltonians is a fundamental task for quantum simulation, yet remains challenging on noisy intermediate-scale quantum (NISQ) devices. We propose Measured Quantum Time Evolution (MQTE), an ancilla-free algorithm that estimates energy gaps by applying real-time evolution to a reference state and measuring time-resolved probabilities via repeated projective measurements. Spectral analysis of these signals reveals oscillation frequencies corresponding to eigenvalue differences. Crucially, MQTE exhibits inherent robustness to quantum hardware noise and sampling errors: these disturbances manifest as a white-noise background, which does not distort the underlying spectral structure but rather obscures the frequency information. By increasing the number of measurement samples, the intensity of the background white noise can be suppressed, thereby recovering the original spectral content. We validate the algorithm's performance via numerical simulations on one- and two-dimensional Heisenberg models, demonstrating accurate extraction of energy gaps and resilience against both sampling and circuit-level noise. Experimental implementation on the superconducting quantum processor Tianyan-176-II further confirms the practical feasibility and noise tolerance of MQTE under real hardware conditions. This work provides a robust and scalable framework for quantum spectral estimation in the NISQ era.
We show that adiabatic evolution of a low-dimensional lattice of quantum spins with a spectral gap can be simulated efficiently. In particular, we show that as long as the spectral gap $\ensuremath{\Delta}E$ between the ground state and the first excited state is any constant independent of nnn, the total number of spins, then the ground-state expectation values of local operators, such as correlation functions, can be computed using polynomial space and time resources. Our results also imply that the local ground-state properties of any two spin models in the same quantum phase can be efficiently obtained from each other. A consequence of these results is that adiabatic quantum algorithms can be simulated efficiently if the spectral gap does not scale with nnn. The simulation method we describe takes place in the Heisenberg picture and does not make use of the finitely correlated state--matrix product state formalism.
Quantum chemistry is one of the important applications of quantum information technology.Especially, an estimation of the energy gap between a ground state and excited state of a target Hamiltonian corresponding to a molecule is essential.In the previous approach, an energy of the ground state and that of the excited state are estimated separately, and the energy gap can be calculated from the subtraction between them.Here, we propose a direct estimation of the energy gap between the ground state and excited state of the target Hamiltonian with quantum annealing.The key idea is to combine a Ramsey type measurement with the quantum annealing.This provides an oscillating signal with a frequency of the energy gap, and a Fourier transform of the signal let us know the energy gap.Based on typical parameters of superconducting qubits, we numerically investigate the performance of our scheme when we estimate an energy gap between the ground state and first excited state of the Hamiltonian.We show robustness against non-adiabatic transitions between the ground state and first-excited state.Our results pave a new way to estimate the energy gap of the Hamiltonian for quantum chemistry.