Quantum versus classical annealing of Ising spin glasses

Heim, Bettina; Rønnow, Troels F.; Isakov, Sergei V.; Troyer, Matthias

doi:10.1126/science.aaa4170

Cited by 215 publications

(234 citation statements)

References 29 publications

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“…Heim et al [7] among others have shown that qmc methods outperform classical sa in several cases. In other situations Battaglia et al [8] showed that sa can perform better than qmc.…”

Section: Introduction a Backgroundmentioning

confidence: 99%

Quantum Monte Carlo simulations of tunneling in quantum adiabatic optimization

Brady

Dam

2016

Phys. Rev. A

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We explore to what extent path-integral quantum Monte Carlo methods can efficiently simulate the tunneling behavior of quantum adiabatic optimization algorithms. Specifically we look at symmetric cost functions defined over n bits with a single potential barrier that a successful optimization algorithm will have to tunnel through. The height and width of this barrier depend on n, and by tuning these dependencies, we can make the optimization algorithm succeed or fail in polynomial time. In this article we compare the strength of quantum adiabatic tunneling with that of pathintegral quantum Monte Carlo methods. We find numerical evidence that quantum Monte Carlo algorithms will succeed in the same regimes where quantum adiabatic optimization succeeds.

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“…Heim et al [7] among others have shown that qmc methods outperform classical sa in several cases. In other situations Battaglia et al [8] showed that sa can perform better than qmc.…”

Section: Introduction a Backgroundmentioning

confidence: 99%

Quantum Monte Carlo simulations of tunneling in quantum adiabatic optimization

Brady

Dam

2016

Phys. Rev. A

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“…It is often stated that quantum annealing (QA) [5][6][7][8][9] uses tunneling instead of thermal excitations to escape from local minima, which can be advantageous in systems with tall but thin barriers that are easier to tunnel through than to thermally climb over [4,9,10]. It is with this potential tunneling-induced advantage over classical annealing that QA and the quantum adiabatic algorithm [11] were proposed.…”

Section: Introductionmentioning

confidence: 99%

Tunneling and Speedup in Quantum Optimization for Permutation-Symmetric Problems

2016

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Tunneling is often claimed to be the key mechanism underlying possible speedups in quantum optimization via quantum annealing (QA), especially for problems featuring a cost function with tall and thin barriers. We present and analyze several counterexamples from the class of perturbed Hamming weight optimization problems with qubit permutation symmetry. We first show that, for these problems, the adiabatic dynamics that make tunneling possible should be understood not in terms of the cost function but rather the semiclassical potential arising from the spin-coherent path-integral formalism. We then provide an example where the shape of the barrier in the final cost function is short and wide, which might suggest no quantum advantage for QA, yet where tunneling renders QA superior to simulated annealing in the adiabatic regime. However, the adiabatic dynamics turn out not be optimal. Instead, an evolution involving a sequence of diabatic transitions through many avoided-level crossings, involving no tunneling, is optimal and outperforms adiabatic QA. We show that this phenomenon of speedup by diabatic transitions is not unique to this example, and we provide an example where it provides an exponential speedup over adiabatic QA. In yet another twist, we show that a classical algorithm, spin-vector dynamics, is at least as efficient as diabatic QA. Finally, in a different example with a convex cost function, the diabatic transitions result in a speedup relative to both adiabatic QA with tunneling and classical spin-vector dynamics.

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“…The tunneling from the metastable well has to be at energy and spin values, E and k, at which a state exists in the ground state well, i.e., E ≥ min fE R ðkÞg, which is not always satisfied in the system with large entropy of states; i.e., F L < F R does not necessarily imply E L < E R . Equation (17) has a solution in a range of energies E such that T min ≤ TðEÞ < ∞ (see inset in Fig. 3, left).…”

Section: Quantum Tunnelingmentioning

confidence: 99%

“…For β < T min , there are no solutions to Eq. (17), and therefore, the optimal energy is at the edge of the interval E ¼ Uðq max Þ − Uðq min Þ corresponding to the height of the barrier. In other words, in this regime, the over-the-barrier escape process dominates, with β ∼ T min being the point of a quantum-to-classical phase transition.…”

Section: Quantum Tunnelingmentioning

confidence: 99%

“…Initial numerical analysis of the two-dimensional (2D) spin-glass problem [15] suggested a superior scaling of the outcome of finitetemperature quantum annealing compared to simulated annealing [11]. However, this observation turned out to be an artifact of the numerical discretization scheme and therefore cannot be reproduced using analog hardware [17].…”

Section: Introductionmentioning

confidence: 99%

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Open-System Quantum Annealing in Mean-Field Models with Exponential Degeneracy

Kechedzhi

Smelyanskiy

2016

Phys. Rev. X

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Real-life quantum computers are inevitably affected by intrinsic noise resulting in dissipative nonunitary dynamics realized by these devices. We consider an open-system quantum annealing algorithm optimized for such a realistic analog quantum device which takes advantage of noise-induced thermalization and relies on incoherent quantum tunneling at finite temperature. We theoretically analyze the performance of this algorithm considering a p-spin model that allows for a mean-field quasiclassical solution and, at the same time, demonstrates the first-order phase transition and exponential degeneracy of states, typical characteristics of spin glasses. We demonstrate that finite-temperature effects introduced by the noise are particularly important for the dynamics in the presence of the exponential degeneracy of metastable states. We determine the optimal regime of the open-system quantum annealing algorithm for this model and find that it can outperform simulated annealing in a range of parameters. Large-scale multiqubit quantum tunneling is instrumental for the quantum speedup in this model, which is possible because of the unusual nonmonotonous temperature dependence of the quantum-tunneling action in this model, where the most efficient transition rate corresponds to zero temperature. This model calculation is the first analytically tractable example where open-system quantum annealing algorithm outperforms simulated annealing, which can, in principle, be realized using an analog quantum computer.

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Quantum versus classical annealing of Ising spin glasses

Cited by 215 publications

References 29 publications

Quantum Monte Carlo simulations of tunneling in quantum adiabatic optimization

Quantum Monte Carlo simulations of tunneling in quantum adiabatic optimization

Tunneling and Speedup in Quantum Optimization for Permutation-Symmetric Problems

Open-System Quantum Annealing in Mean-Field Models with Exponential Degeneracy

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