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:2302.10486

Quantifying the Energy Relaxation Rate of Quantum States Using D-Wave Device and the Discovery of Long-Lived Multiqubit States

Takashi Imoto, Yuki Susa, Ryoji Miyazaki, Yuichiro Matsuzaki

Published Feb 21, 2023• 0 citations
arXivHTMLPDF

Abstract

Quantum annealing has been demonstrated with superconducting qubits. Such a quantum annealer has been used to solve combinatorial optimization problems. Moreover, it serves as a quantum simulator for investigating the properties of quantum many-body systems. However, the coherence properties of multi-qubit states provided by D-Wave Quantum Inc. have not been explored sufficiently. Here, using the D-Wave device, we measure the energy relaxation rate of superconducting qubits and find long-lived multi-qubit states. Specifically, we investigate the energy relaxation rate of the first excited states of a fully connected Ising model with a transverse field. We find that the decay rate of the excited states of such a system with four qubits is orders of magnitude smaller than that of the excited state of a single qubit, which demonstrates the existence of long-lived multi-qubit states. We elucidate the mechanism using an independent decoherence model that qualitatively describes the phenomenon. In addition, by using such a mechanism, we theoretically predict a long-lived entangled state whose energy relaxation rate is smaller than that of the separable states.

DOI
10.48550/arxiv.2302.10486

Related papers

Measurement of the incoherent decay rate of quantum states in quantum annealing with a D-Wave machine

Takashi Imoto, Yuki Susa, Tadashi Kadowaki +2 more

Abstract Quantum annealing has been demonstrated with superconducting qubits. Such a quantum annealer has been used to solve combinational optimization problems. Moreover, it serves as a quantum simulator for investigating the properties of the quantum many-body systems. However, the coherence properties of actual devices provided by D-Wave Quantum Inc. have not been explored sufficiently. Here, we measure the energy relaxation of the excited state in quantum annealing with the D-Wave device. Specifically, we investigate the incoherent decay rate of the first excited states of a fully connected Ising model with a transverse field. We find that the decay rate of the excited states of the model is orders of magnitude smaller than that of the excited state of a single qubit, and we qualitatively explain this phenomenon by using theoretical methods. Since our numerical simulations show that the first excited state during QA for the model is entangled, our experimental results indicate that the long-lived entangled state can be generated during QA with the D-Wave machine.

•Jan 3, 2024•0 citations

Experimental Measurement and Theoretical Analysis of Energy Relaxation Rates of an Interacting Two-Qubit System on a D-Wave Quantum Annealer

Yusei Amano, Sorato Suzuki, Hiroki Kuji +3 more

In D-Wave quantum annealers, various properties of the ground state have been clarified, whereas the correspondence between theory and experiment for energy relaxation rates in multiqubit excited states remains insufficiently understood. Here, we measured the energy relaxation rates of the first excited states in single-qubit systems and interacting two-qubit systems using a D-Wave quantum annealer. We analyzed the measured relaxation rates using a Gorini-Kossakowski-Sudarshan-Lindblad master equation with independent local $σ^{\,\,z}$-type noise channels. The calculated relaxation rates reproduced the overall trends observed experimentally, supporting the model at a qualitative level. We then used the relaxation rates measured for the uncoupled single-qubit systems to calibrate the local relaxation parameters and predict the relaxation rates of the interacting two-qubit systems. The predicted rates remained within a factor of approximately four of the measured rates. These results show that the relaxation measurements on individual qubits can provide a practical estimate of relaxation in small interacting quantum systems and may help clarify relaxation mechanisms in programmable quantum annealers.

quant-pharXiv:2609.21598•Sep 21, 2026•0 citations

Demonstration of the excited-state search on the D-wave quantum annealer

Takashi Imoto, Yuki Susa, Ryoji Miyazaki +2 more

Quantum annealing is a way to prepare an eigenstate of the problem Hamiltonian. Starting from an eigenstate of a trivial Hamiltonian, we slowly change the Hamiltonian to the problem Hamiltonian, and the system remains in the eigenstate of the Hamiltonian as long as the so-called adiabatic condition is satisfied. By using devices provided by D-Wave Systems Inc., there were experimental demonstrations to prepare a ground state of the problem Hamiltonian. However, up to date, there are no demonstrations to prepare the excited state of the problem Hamiltonian with quantum annealing. Here, we demonstrate the excited-state search by using the D-wave processor. The key idea is to use the reverse quantum annealing with a hot start where the initial state is the excited state of the trivial Hamiltonian. During the reverse quantum annealing, we control not only the transverse field but also the longitudinal field and slowly change the Hamiltonian to the problem Hamiltonian so that we can obtain the desired excited state. As an example of the exited state search, we adopt a two-qubit Ising model as the problem Hamiltonian and succeed to prepare the excited state. Also, we solve the shortest vector problem where the solution is embedded into the first excited state of the Ising Hamiltonian. Our results pave the way for new applications of quantum annealers to use the excited states.

arXiv:2305.15974•May 25, 2023•1 citation

Finite-size scaling in quantum annealing with decoherence

Phillip Weinberg

Quantum annealing represents an essential milestone towards the goal of adiabatic quantum computing. In quantum annealing, the computation involves finding the ground state of a classical Ising-like Hamiltonian realized as interactions between qubits. Quantum fluctuations are introduced to allow the wavefunction of the qubits to explore the energy landscape, the hope being that the wavefunction finds a minimum energy configuration and possibly giving the result of the computation. While quantum annealing likely may not be as powerful as adiabatic quantum computing, it is possible that it may be better at optimization compared to analogous classical algorithms. In physical realizations of quantum annealing, there are still questions as to the role of quantum fluctuations in the operation of a device given the short coherence times of the individual qubits. These questions have consistently posed a serious theoretical challenge making it difficult to verify experimental results. Here we simplify the problem by considering a system of qubits with ferromagnetic interactions, modeling the decoherence effects as classical noise in the transverse-field of each qubit. We compare the calculations to data collected from a system of manufactured qubits produced by D-wave Systems by performing a finite-size scaling analysis that captures the competition between quantum fluctuations of the transverse-field and bit-flip errors from the noise. We argue that on time-scales larger than the single-qubit decoherence time, the device produces the expected quantum fluctuations for the many-body system. Using this finite-size scaling, one can diagnose sources of noise in the system. Hopefully, in the near future, these devices will not only be realizing coherent quantum annealing but will likely be useful as another example of synthetic quantum matter.

•Jan 1, 2020•0 citations

How can the D-Wave machine exhibit long-time quantum behaviour

D. Drakova, G. Doyen

Extensive experiments have demonstrated quantum behaviour in the long-time operation of the D-Wave quantum computer. The decoherence time of a single flux qubit is reported to be on the order of nanoseconds [1], which is much shorter than the time required to carry out a computation on the timescale of seconds [2, 3]. Previous judgements of whether the D-Wave device should be thought of as a quantum computer have been based on correlations of the input-output behaviour of the D-Wave machine with a quantum model, called simulated quantum annealing, or classical models, called simulated annealing and classical spin dynamics [4]. Explanations for a factor of 10 8 discrepancy between the single flux qubit decoherence time and the long-time coherent quantum behaviour of many integrated flux qubits of the D-Wave device have not been offered so far. In our contribution we investigate a model of four qubits with one qubit coupled to a phonon and (optionally) to environmental particles of high density of states, called gravonons. The calculations indicate that when no gravonons are present, the current in the qubit is flipped at some time and adiabatic evolution is discontinued. The time dependent wave functional becomes a non-correctable superposition of many excited states. The results demonstrate the possibility of effectively suppressing the current flip and allowing for continued adiabatic evolution when the entanglement to gravonons is included. This adiabatic evolution is, however, a coherent evolution in high dimensional spacetime and cannot be understood as a solution of Schrödinger's time dependent equation in 4 dimensional spacetime. Compared to Schrödinger's time development in 4D, the evolution is considerably slowed down, though still adiabatic. The properties of our model reflect correctly the experimentally found behaviour of the D-Wave machine and explain the factor of 10 8 discrepancy between decoherence time and quantum computation time. The observation and our explanation are in anology to the 108 discrepancy factor found, when comparing experimental results on adsorbate quantum diffusion rate with predictions of Schrödinger's time dependent equation, which can also be resolved in a model with the coupling to gravonons included.

Journal of Physics Conference Series•Jul 3, 2015•1 citation

Energy relaxation via quantum thermalization: A superconducting qubit coupled to an interacting many-body two-level system

Xue-Yi Guo

Two-level systems (TLS) are widely recognized as a dominant source of energy relaxation in superconducting qubits, limiting coherence times and device performance. While TLS-induced dissipation is often modeled as independent channels, interacting TLS can form finite many-body environments whose dynamical role in qubit relaxation remains insufficiently understood. Building on the information-erasure-based framework for irreversible thermalization developed in our previous work, we present a microscopic model and numerical simulations of a superconducting qubit coupled to a finite interacting many-body TLS environment as a concrete physical realization of this mechanism. We show that effective irreversible energy relaxation can emerge from intrinsic many-body dynamics without invoking external baths or phenomenological dissipation. The introduction of information erasure drives a transition from coherent oscillatory energy exchange to nonoscillatory exponential relaxation of the qubit. The relaxation times exhibit the scaling $T_1, T_2 \propto J_{q,τ}^{-2}$ with respect to the qubit-TLS coupling strength, consistent with Fermi's golden rule and Lindblad-type descriptions. Importantly, both exponential decay and its scaling behavior arise directly from microscopic many-body dynamics. These results provide quantitative insight into TLS-induced decoherence mechanisms and establish a microscopic link between information erasure, many-body thermalization, and irreversible relaxation in superconducting quantum systems.

quant-pharXiv:2603.13322•APS Open Science•Mar 5, 2026•0 citations
Quantum annealing has been demonstrated with superconducting qubits. Such a quantum annealer has been used to solve combinatorial optimization problems. Moreover, it serves as a quantum simulator for investigating the properties of quantum many-body systems. However, the coherence properties of multi-qubit states provided by D-Wave Quantum Inc. have not been explored sufficiently. Here, using the D-Wave device, we measure the energy relaxation rate of superconducting qubits and find long-lived multi-qubit states. Specifically, we investigate the energy relaxation rate of the first excited states of a fully connected Ising model with a transverse field. We find that the decay rate of the excited states of such a system with four qubits is orders of magnitude smaller than that of the excited state of a single qubit, which demonstrates the existence of long-lived multi-qubit states. We elucidate the mechanism using an independent decoherence model that qualitatively describes the phenomenon. In addition, by using such a mechanism, we theoretically predict a long-lived entangled state whose energy relaxation rate is smaller than that of the separable states.
Abstract Quantum annealing has been demonstrated with superconducting qubits. Such a quantum annealer has been used to solve combinational optimization problems. Moreover, it serves as a quantum simulator for investigating the properties of the quantum many-body systems. However, the coherence properties of actual devices provided by D-Wave Quantum Inc. have not been explored sufficiently. Here, we measure the energy relaxation of the excited state in quantum annealing with the D-Wave device. Specifically, we investigate the incoherent decay rate of the first excited states of a fully connected Ising model with a transverse field. We find that the decay rate of the excited states of the model is orders of magnitude smaller than that of the excited state of a single qubit, and we qualitatively explain this phenomenon by using theoretical methods. Since our numerical simulations show that the first excited state during QA for the model is entangled, our experimental results indicate that the long-lived entangled state can be generated during QA with the D-Wave machine.
In D-Wave quantum annealers, various properties of the ground state have been clarified, whereas the correspondence between theory and experiment for energy relaxation rates in multiqubit excited states remains insufficiently understood. Here, we measured the energy relaxation rates of the first excited states in single-qubit systems and interacting two-qubit systems using a D-Wave quantum annealer. We analyzed the measured relaxation rates using a Gorini-Kossakowski-Sudarshan-Lindblad master equation with independent local σ  zσ^{\,\,z}σz-type noise channels. The calculated relaxation rates reproduced the overall trends observed experimentally, supporting the model at a qualitative level. We then used the relaxation rates measured for the uncoupled single-qubit systems to calibrate the local relaxation parameters and predict the relaxation rates of the interacting two-qubit systems. The predicted rates remained within a factor of approximately four of the measured rates. These results show that the relaxation measurements on individual qubits can provide a practical estimate of relaxation in small interacting quantum systems and may help clarify relaxation mechanisms in programmable quantum annealers.
Quantum annealing is a way to prepare an eigenstate of the problem Hamiltonian. Starting from an eigenstate of a trivial Hamiltonian, we slowly change the Hamiltonian to the problem Hamiltonian, and the system remains in the eigenstate of the Hamiltonian as long as the so-called adiabatic condition is satisfied. By using devices provided by D-Wave Systems Inc., there were experimental demonstrations to prepare a ground state of the problem Hamiltonian. However, up to date, there are no demonstrations to prepare the excited state of the problem Hamiltonian with quantum annealing. Here, we demonstrate the excited-state search by using the D-wave processor. The key idea is to use the reverse quantum annealing with a hot start where the initial state is the excited state of the trivial Hamiltonian. During the reverse quantum annealing, we control not only the transverse field but also the longitudinal field and slowly change the Hamiltonian to the problem Hamiltonian so that we can obtain the desired excited state. As an example of the exited state search, we adopt a two-qubit Ising model as the problem Hamiltonian and succeed to prepare the excited state. Also, we solve the shortest vector problem where the solution is embedded into the first excited state of the Ising Hamiltonian. Our results pave the way for new applications of quantum annealers to use the excited states.
Quantum annealing represents an essential milestone towards the goal of adiabatic quantum computing. In quantum annealing, the computation involves finding the ground state of a classical Ising-like Hamiltonian realized as interactions between qubits. Quantum fluctuations are introduced to allow the wavefunction of the qubits to explore the energy landscape, the hope being that the wavefunction finds a minimum energy configuration and possibly giving the result of the computation. While quantum annealing likely may not be as powerful as adiabatic quantum computing, it is possible that it may be better at optimization compared to analogous classical algorithms. In physical realizations of quantum annealing, there are still questions as to the role of quantum fluctuations in the operation of a device given the short coherence times of the individual qubits. These questions have consistently posed a serious theoretical challenge making it difficult to verify experimental results. Here we simplify the problem by considering a system of qubits with ferromagnetic interactions, modeling the decoherence effects as classical noise in the transverse-field of each qubit. We compare the calculations to data collected from a system of manufactured qubits produced by D-wave Systems by performing a finite-size scaling analysis that captures the competition between quantum fluctuations of the transverse-field and bit-flip errors from the noise. We argue that on time-scales larger than the single-qubit decoherence time, the device produces the expected quantum fluctuations for the many-body system. Using this finite-size scaling, one can diagnose sources of noise in the system. Hopefully, in the near future, these devices will not only be realizing coherent quantum annealing but will likely be useful as another example of synthetic quantum matter.
Extensive experiments have demonstrated quantum behaviour in the long-time operation of the D-Wave quantum computer. The decoherence time of a single flux qubit is reported to be on the order of nanoseconds [1], which is much shorter than the time required to carry out a computation on the timescale of seconds [2, 3]. Previous judgements of whether the D-Wave device should be thought of as a quantum computer have been based on correlations of the input-output behaviour of the D-Wave machine with a quantum model, called simulated quantum annealing, or classical models, called simulated annealing and classical spin dynamics [4]. Explanations for a factor of 10 8 discrepancy between the single flux qubit decoherence time and the long-time coherent quantum behaviour of many integrated flux qubits of the D-Wave device have not been offered so far. In our contribution we investigate a model of four qubits with one qubit coupled to a phonon and (optionally) to environmental particles of high density of states, called gravonons. The calculations indicate that when no gravonons are present, the current in the qubit is flipped at some time and adiabatic evolution is discontinued. The time dependent wave functional becomes a non-correctable superposition of many excited states. The results demonstrate the possibility of effectively suppressing the current flip and allowing for continued adiabatic evolution when the entanglement to gravonons is included. This adiabatic evolution is, however, a coherent evolution in high dimensional spacetime and cannot be understood as a solution of Schrödinger's time dependent equation in 4 dimensional spacetime. Compared to Schrödinger's time development in 4D, the evolution is considerably slowed down, though still adiabatic. The properties of our model reflect correctly the experimentally found behaviour of the D-Wave machine and explain the factor of 10 8 discrepancy between decoherence time and quantum computation time. The observation and our explanation are in anology to the 108 discrepancy factor found, when comparing experimental results on adsorbate quantum diffusion rate with predictions of Schrödinger's time dependent equation, which can also be resolved in a model with the coupling to gravonons included.
Two-level systems (TLS) are widely recognized as a dominant source of energy relaxation in superconducting qubits, limiting coherence times and device performance. While TLS-induced dissipation is often modeled as independent channels, interacting TLS can form finite many-body environments whose dynamical role in qubit relaxation remains insufficiently understood. Building on the information-erasure-based framework for irreversible thermalization developed in our previous work, we present a microscopic model and numerical simulations of a superconducting qubit coupled to a finite interacting many-body TLS environment as a concrete physical realization of this mechanism. We show that effective irreversible energy relaxation can emerge from intrinsic many-body dynamics without invoking external baths or phenomenological dissipation. The introduction of information erasure drives a transition from coherent oscillatory energy exchange to nonoscillatory exponential relaxation of the qubit. The relaxation times exhibit the scaling T1,T2∝Jq,τ−2T_1, T_2 \propto J_{q,τ}^{-2}T1​,T2​∝Jq,τ−2​ with respect to the qubit-TLS coupling strength, consistent with Fermi's golden rule and Lindblad-type descriptions. Importantly, both exponential decay and its scaling behavior arise directly from microscopic many-body dynamics. These results provide quantitative insight into TLS-induced decoherence mechanisms and establish a microscopic link between information erasure, many-body thermalization, and irreversible relaxation in superconducting quantum systems.