Three phases of quantum annealing: Fast, slow, and very slow

Soriani, Artur; Nazé, Pierre; Bonança, Marcus V. S.; Gardas, Bartłomiej; Deffner, Sebastian

doi:10.1103/physreva.105.042423

Cited by 7 publications

(16 citation statements)

References 72 publications

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“…This will complement what was presented in Ref. [25], where most of the discussion focused on only linear driving. In order to avoid redundancy, some technical details are omitted here, but they can be found in Ref.…”

Section: Its Hamiltonian Issupporting

confidence: 78%

“…Starting the evolution of the system in its ground state, we can work only with positive momentum values. In this case, the dynamics of the TI chain can be simplified as the dynamics of N/2 two-level systems [25,28] (known as Landau-Zener (LZ) systems [43][44][45][46]), one for each positive value of k. Thus the time-dependent state of the system can be written as…”

Section: Its Hamiltonian Ismentioning

confidence: 99%

“…In order to avoid redundancy, some technical details are omitted here, but they can be found in Ref. [25].…”

Section: Its Hamiltonian Ismentioning

confidence: 99%

“…In particular, in Ref. [25], we characterized the finite-time dynamics of the driven transverse field Ising chain, a model of undeniable importance to quantum annealing. We were able to identify three parameter regions of a dynamic phase diagram with intrinsically different behaviors.…”

Section: Introductionmentioning

confidence: 99%

“…For simplicity, we focused exclusively on linear driving protocols in Ref. [25], as many other authors have done [26][27][28][29][30][31] (exceptions can be found in Refs. [32][33][34] for analytical studies and Refs.…”

Section: Introductionmentioning

confidence: 99%

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Assessing the performance of quantum annealing with nonlinear driving

et al. 2022

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Current-generation quantum annealers have already proven to be successful problem solvers. Yet quantum annealing is still very much in its infancy, with suboptimal applicability. For instance, to date it is still an open question which annealing protocol causes the fewest diabatic excitations for a given eigenspectrum, and even whether there is a universally optimal strategy. Therefore, in this paper, we report analytical and numerical studies of the diabatic excitations arising from nonlinear protocols applied to the transverse field Ising chain, the exactly solvable model that serves as a quantum annealing playground. Our analysis focuses on several driving schemes that inhibit or facilitate the dynamic phases discussed in a previous work. Rather remarkably, we find that the paradigmatic Kibble-Zurek behavior can be suppressed with "pauses" in the evolution, both for crossing and for stopping at the quantum critical point of the system.

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Section: Its Hamiltonian Issupporting

confidence: 78%

Section: Its Hamiltonian Ismentioning

confidence: 99%

“…In order to avoid redundancy, some technical details are omitted here, but they can be found in Ref. [25].…”

Section: Its Hamiltonian Ismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Assessing the performance of quantum annealing with nonlinear driving

et al. 2022

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Efficiency optimization in quantum computing: balancing thermodynamics and computational performance

Śmierzchalski,

Mzaouali,

Deffner

et al. 2024

Sci Rep

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We investigate the computational efficiency and thermodynamic cost of the D-Wave quantum annealer under reverse-annealing with and without pausing. Our demonstration on the D-Wave 2000Q annealer shows that the combination of reverse-annealing and pausing leads to improved computational efficiency while minimizing the thermodynamic cost compared to reverse-annealing alone. Moreover, we find that the magnetic field has a positive impact on the performance of the quantum annealer during reverse-annealing but becomes detrimental when pausing is involved. Our results, which are reproducible, provide strategies for optimizing the performance and energy consumption of quantum annealing systems employing reverse-annealing protocols.

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Failure of the geometric approach prediction of excess work scaling for open and isolated quantum systems

2022

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The task of finding optimal protocols that minimize the energetic cost of thermodynamic processes of long yet finite duration $\tau$ is a pressing one. We approach this problem here in a rigorous and systematic fashion by means of the adiabatic perturbation theory of closed Hamiltonian quantum systems. Our main finding is a $1/\tau^2$ scaling of the excess work for large $\tau$ in gapped systems. This result is at odds with the asymptotic $1/\tau$ prediction of the geometric approach to optimization, which is predicated on the slow evolution of open systems close to canonical equilibrium. In contrast, our approach does not lead to an obvious geometric interpretation. Furthermore, as the thermodynamic work does not depend on how an isolated quantum system is split into a system of interest and its environment, our results imply the failure of the geometric approach prediction even for open systems. Additionally, we provide alternative optimization procedures, both for slowly-varying processes described by adiabatic perturbation theory and for weakly-varying processes described by linear response theory. Our findings are benchmarked and confirmed through the application to the driven transverse-field Ising chain.

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Three phases of quantum annealing: Fast, slow, and very slow

Cited by 7 publications

References 72 publications

Assessing the performance of quantum annealing with nonlinear driving

Assessing the performance of quantum annealing with nonlinear driving

Efficiency optimization in quantum computing: balancing thermodynamics and computational performance

Failure of the geometric approach prediction of excess work scaling for open and isolated quantum systems

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