Quantum annealing (QA) has been proposed as a quantum enhanced optimization heuristic exploiting tunneling. Here, we demonstrate how finite range tunneling can provide considerable computational advantage. For a crafted problem designed to have tall and narrow energy barriers separating local minima, the D-Wave 2X quantum annealer achieves significant runtime advantages relative to Simulated Annealing (SA). For instances with 945 variables, this results in a time-to-99%success-probability that is ∼ 10 8 times faster than SA running on a single processor core. We also compared physical QA with Quantum Monte Carlo (QMC), an algorithm that emulates quantum tunneling on classical processors. We observe a substantial constant overhead against physical QA: D-Wave 2X again runs up to ∼ 10 8 times faster than an optimized implementation of QMC on a single core. We note that there exist heuristic classical algorithms that can solve most instances of Chimera structured problems in a timescale comparable to the D-Wave 2X. However, we believe that such solvers will become ineffective for the next generation of annealers currently being designed. To investigate whether finite range tunneling will also confer an advantage for problems of practical interest, we conduct numerical studies on binary optimization problems that cannot yet be represented on quantum hardware. For random instances of the number partitioning problem, we find numerically that QMC, as well as other algorithms designed to simulate QA, scale better than SA. We discuss the implications of these findings for the design of next generation quantum annealers.

Quantum tunnelling is a phenomenon in which a quantum state traverses energy barriers higher than the energy of the state itself. Quantum tunnelling has been hypothesized as an advantageous physical resource for optimization in quantum annealing. However, computational multiqubit tunnelling has not yet been observed, and a theory of co-tunnelling under high- and low-frequency noises is lacking. Here we show that 8-qubit tunnelling plays a computational role in a currently available programmable quantum annealer. We devise a probe for tunnelling, a computational primitive where classical paths are trapped in a false minimum. In support of the design of quantum annealers we develop a nonperturbative theory of open quantum dynamics under realistic noise characteristics. This theory accurately predicts the rate of many-body dissipative quantum tunnelling subject to the polaron effect. Furthermore, we experimentally demonstrate that quantum tunnelling outperforms thermal hopping along classical paths for problems with up to 200 qubits containing the computational primitive.

Read, Hartmut Neven and colleagues at Google's Quantum AI Laboratory set out investment opportunities on the road to the ultimate quantum machines.F rom aspects of quantum entanglement to chemical reactions with large molecules, many features of the world cannot be described efficiently with conventional computers based on binary logic. The solution, as physicist Richard Feynman realized three decades ago 1 , is to use quantum processors that adopt a blend of classical states simultaneously, as matter does. Many technical hurdles must be overcome for such quantum machines to be practical, however. These include noise control and improving the fidelity of operations acting on the quantum states that encode the information.The quantum-computing community is channelling most of its efforts towards building the ultimate machine: a digital quantum computer that tolerates noise and errors, and that in principle can be applied to any problem. In theory, such a machinewhich will need large processors comprising many quantum bits, or qubits -should be able to calculate faster than a conventional computer. Such capability is at least a decade away 2 . Correcting for errors requires redundancy, and the number of qubits needed quickly mounts. For example, factorizing a 2,000-bit number in one day, a task believed to be intractable using classical computers 3 , would take 100 million qubits, even if individual quantum operations failed just once in every 10,000 operations. We have yet to assemble digital quantum processors with tens of qubits.This conservative view of quantum computing gives the impression that investors will benefit only in the long term. We contend that short-term returns are possible with the small devices that will emerge within the next five years, even though these will lack full error correction.A lack of theoretical guarantees need not preclude success. Heuristic 'hybrid' methods that blend quantum and classical approaches could be the foundation for powerful future applications. The recent success of neural networks in machine learning is a good example. In the 1990s, when the computing power required to train deep neural networks was unavailable, it was fashionable in the field to focus on 'convex' methods (based on functions with a clear minimum solution) that had a strong theoretical basis. Today, these methods are no match for deep learning. The underlying algorithms of neural networks COMMENT © 2 0 1 7 M a c m i l l a n P u b l i s h e r s L i m i t e d , p a r t o f S p r i n g e r N a t u r e . A l l r i g h t s r e s e r v e d .

Quantum tunneling is a phenomenon in which a quantum state traverses energy barriers above the energy of the state itself [1,2]. Tunneling has been hypothesized as an advantageous physical resource for optimization [3][4][5][6][7]. Here we present the first experimental evidence of a computational role of multiqubit quantum tunneling in the evolution of a programmable quantum annealer. We develop a theoretical model based on a NIBA Quantum Master Equation to describe the multiqubit dissipative tunneling effects under the complex noise characteristics of such quantum devices. We start by considering a computational primitive, an optimization problem consisting of just one global and one false minimum. The quantum evolutions enable tunneling to the global minimum while the corresponding classical paths are trapped in a false minimum. In our study the non-convex potentials are realized by frustrated networks of qubit clusters with strong intra-cluster coupling. We show that the collective effect of the quantum environment is suppressed in the "critical" phase during the evolution where quantum tunneling "decides" the right path to solution. In a later stage dissipation facilitates the multiqubit tunneling leading to the solution state. The predictions of the model accurately describe the experimental data from the D-Wave Two quantum annealer at NASA Ames. In our computational primitive the temperature dependence of the probability of success in the quantum model is opposite to that of the classical paths with thermal hopping. Specifically, we provide an analysis of an optimization problem with sixteen qubits, demonstrating eight qubit tunneling that increases success probabilities. Furthermore, we report results for larger problems with up to 200 qubits that contain the primitive as subproblems.

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