Entanglement in a Quantum Annealing Processor

Lanting, T.; Przybysz, Anthony; Smirnov, Anatoly Yu.; Spedalieri, Federico M.; Amin, M. H. S.; Berkley, A. J.; Harris, Richard E.; Altomare, Fabio; Boixo, Sergio; Bunyk, P.; Dickson, Neil G.; Enderud, C.; Hilton, Jeremy; Hoskinson, Emile; Johnson, Mark W.; Ladizinsky, E.; Ladizinsky, N.; Neufeld, R. B.; Oh, T.; Perminov, I.; Rich, Chris; Thom, M. C.; Tolkacheva, E.; Uchaikin, S.; Wilson, A. B.; Rose, Geordie

doi:10.1103/physrevx.4.021041

Cited by 268 publications

(326 citation statements)

References 41 publications

(111 reference statements)

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“…Up to now many experiments have confirmed the existence of quantum phenomena in such processors [15,[35][36][37][38], which includes entanglement [39]. A quantum annealing processor implements the time-dependent Hamiltonian…”

Section: Qbm With a Quantum Annealing Processormentioning

confidence: 98%

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Quantum Boltzmann Machine

et al. 2018

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Inspired by the success of Boltzmann machines based on classical Boltzmann distribution, we propose a new machine-learning approach based on quantum Boltzmann distribution of a quantum Hamiltonian. Because of the noncommutative nature of quantum mechanics, the training process of the quantum Boltzmann machine (QBM) can become nontrivial. We circumvent the problem by introducing bounds on the quantum probabilities. This allows us to train the QBM efficiently by sampling. We show examples of QBM training with and without the bound, using exact diagonalization, and compare the results with classical Boltzmann training. We also discuss the possibility of using quantum annealing processors for QBM training and application.

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Section: Qbm With a Quantum Annealing Processormentioning

confidence: 98%

“…If the input x appears with a very small probability (P x ≪ 1), it would require a large amount of samples from P x;y and P x to reliably calculate P yjx using Eq. (39).…”

Section: A Generative Learningmentioning

confidence: 99%

Quantum Boltzmann Machine

et al. 2018

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“…Similarly as above in subsection 2.3, the total dephasing rate is denoted by Γ 2 = Γ 1 /2+Γ φ .. The master equation (38) allows us to calculate the two-time correlator by using the quantum regression theorem [54]. The result can be written [60] …”

Section: Probe Spectrummentioning

confidence: 99%

Quantum systems under frequency modulation

et al. 2017

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Abstract. We review the physical phenomena that arise when quantum mechanical energy levels are modulated in time. The dynamics resulting from changes in the transition frequency is a problem studied since the early days of quantum mechanics. It has been of constant interest both experimentally and theoretically since, with the simple two-state model providing an inexhaustible source of novel concepts. When the transition frequency of a quantum system is modulated, several phenomena can be observed, such as Landau-Zener-Stückelberg-Majorana interference, motional averaging and narrowing, and the formation of dressed states with the presence of sidebands in the spectrum. Adiabatic changes result in the accumulation of geometric phases, which can be used to create topological states. In recent years, an exquisite experimental control in the time domain was gained through the parameters entering the Hamiltonian, and high-fidelity readout schemes allowed the state of the system to be monitored non-destructively. These developments were made in the field of quantum devices, especially in superconducting qubits, as a well as in atomic physics, in particular in ultracold gases. As a result of these advances, it became possible to demonstrate many of the fundamental effects that arise in a quantum system when its transition frequencies are modulated. The purpose of this review is to present some of these developments, from two-state atoms and harmonic oscillators to multilevel and many-particle systems.

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“…However, the speed-up of quantum annealing has been only shown for certain classes of problems [19,20] and for devices running at finite temperature AQO has been put into question entirely [30,34]. In all of this, the precise role of quantum effects during the sweep is an open question, although the presence of entanglement during quantum annealing at finite temperature has recently been demonstrated in superconducting qubits [31].…”

Section: Introductionmentioning

confidence: 99%

Probing entanglement in adiabatic quantum optimization with trapped ions

et al. 2015

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Adiabatic quantum optimization has been proposed as a route to solve NP-complete problems, with a possible quantum speedup compared to classical algorithms. However, the precise role of quantum effects, such as entanglement, in these optimization protocols is still unclear. We propose a setup of cold trapped ions that allows one to quantitatively characterize, in a controlled experiment, the interplay of entanglement, decoherence, and non-adiabaticity in adiabatic quantum optimization. We show that, in this way, a broad class of NP-complete problems becomes accessible for quantum simulations, including the knapsack problem, number partitioning, and instances of the max-cut problem. Moreover, a general theoretical study reveals correlations of the success probability with entanglement at the end of the protocol. From exact numerical simulations for small systems and linear ramps, however, we find no substantial correlations with the entanglement during the optimization. For the final state, we derive analytically a universal upper bound for the success probability as a function of entanglement, which can be measured in experiment. The proposed trapped-ion setups and the presented study of entanglement address pertinent questions of adiabatic quantum optimization, which may be of general interest across experimental platforms.

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Entanglement in a Quantum Annealing Processor

Cited by 268 publications

References 41 publications

Quantum Boltzmann Machine

Quantum Boltzmann Machine

Quantum systems under frequency modulation

Probing entanglement in adiabatic quantum optimization with trapped ions

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