Quantum annealing and the Schrödinger-Langevin-Kostin equation

Falco, Diego de; Tamascelli, Dario

doi:10.1103/physreva.79.012315

Cited by 11 publications

(10 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The study of its solutions without stochastic term has been carried out in many specific cases, either analytically [18,31,32,41,42,43,44,45,46] or numerically [24,33,41,47,48,49,50,51]. Along these analysis, it has been advocated that the stationary eigenstates of H 0 are also stationary states of the equation [18,43].…”

Section: Introductionmentioning

confidence: 99%

The Schrödinger–Langevin equation with and without thermal fluctuations

2016

View full text Add to dashboard Cite

The Schrödinger-Langevin equation (SLE) is considered as an effective open quantum system formalism suitable for phenomenological applications involving a quantum subsystem interacting with a thermal bath. We focus on two open issues relative to its solutions: the stationarity of the excited states of the non-interacting subsystem when one considers the dissipation only and the thermal relaxation toward asymptotic distributions with the additional stochastic term. We first show that a proper application of the Madelung/polar transformation of the wave function leads to a non zero damping of the excited states of the quantum subsystem. We then study analytically and numerically the SLE ability to bring a quantum subsystem to the thermal equilibrium of statistical mechanics. To do so, concepts about statistical mixed states and quantum noises are discussed and a detailed analysis is carried with two kinds of noise and potential. We show that within our assumptions the use of the SLE as an effective open quantum system formalism is possible and discuss some of its limitations.

show abstract

Section: Introductionmentioning

confidence: 99%

The Schrödinger–Langevin equation with and without thermal fluctuations

2016

View full text Add to dashboard Cite

show abstract

“…Our results provide an alternative route to characterize qubit systems and confirm the relevance of nonlocal measurements, which have already been suggested as a convenient toolbox for quantum circuits based on trapped ions [40,41] and supeconducting qubits [42,43]. Feynman probes could also be employed to estimate the current in out of equilibrium quantum wires [53,54] or the amount of disorder in linear lattices [55,56].…”

Section: Discussionmentioning

confidence: 86%

Characterization of qubit chains by Feynman probes

et al. 2016

Self Cite

View full text Add to dashboard Cite

We address the characterization of qubit chains and assess the performances of local measurements compared to those provided by Feynman probes, i.e. nonlocal measurements realized by coupling a single qubit register to the chain. We show that local measurements are suitable to estimate small values of the coupling and that a Bayesian strategy may be successfully exploited to achieve optimal precision. For larger values of the coupling Bayesian local strategies do not lead to a consistent estimate. In this regime, Feynman probes may be exploited to build a consistent Bayesian estimator that saturates the Cramér-Rao bound, thus providing an effective characterization of the chain. Finally, we show that ultimate bounds to precision, i.e. saturation of the quantum Cramér-Rao bound, may be achieved by a two-step scheme employing Feynman probes followed by local measurements.

show abstract

“…In DQAEM, the updating equations for θ are determined by the derivative of the function U Γ (θ, θ ′ ) in (11) with respect to θ, and then P(σ (i) = 1 k |y (i) ; θ (t) ) in (13), (14) and (15) are replaced by P QA (σ (i) = 1 k |y (i) ; θ (t) ) = σ (i) = 1 k |P Γ (σ (i) |y (i) ; θ (t) )|σ (i) = 1 k . That is, the updating equations for DQAEM are given by…”

Section: A Mathematical Setupmentioning

confidence: 99%

Relaxation of the EM algorithm via quantum annealing for Gaussian mixture models

Miyahara

Tsumura

Sughiyama

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

We propose a modified expectation-maximization algorithm by introducing the concept of quantum annealing, which we call the deterministic quantum annealing expectation-maximization (DQAEM) algorithm. The expectation-maximization (EM) algorithm is an established algorithm to compute maximum likelihood estimates and applied to many practical applications. However, it is known that EM heavily depends on initial values and its estimates are sometimes trapped by local optima. To solve such a problem, quantum annealing (QA) was proposed as a novel optimization approach motivated by quantum mechanics. By employing QA, we then formulate DQAEM and present a theorem that supports its stability. Finally, we demonstrate numerical simulations to confirm its efficiency.

show abstract

Quantum annealing and the Schrödinger-Langevin-Kostin equation

Cited by 11 publications

References 27 publications

The Schrödinger–Langevin equation with and without thermal fluctuations

The Schrödinger–Langevin equation with and without thermal fluctuations

Characterization of qubit chains by Feynman probes

Relaxation of the EM algorithm via quantum annealing for Gaussian mixture models

Contact Info

Product

Resources

About