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Register a new userScalable effective temperature reduction for quantum annealers via nested quantum annealing correction
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Nested quantum annealing correction (NQAC) is an error correcting scheme for quantum annealing that allows for the encoding of a logical qubit into an arbitrarily large number of physical qubits. The encoding replaces each logical qubit by a complete graph of degree $C$. The nesting level $C$ represents the distance of the error-correcting code and controls the amount of protection against thermal and control errors. Theoretical mean-field analyses and empirical data obtained with a D-Wave Two quantum annealer (supporting up to $512$ qubits) showed that NQAC has the potential to achieve a scalable effective temperature reduction, $T_{rm eff} sim C^{-eta}$, with $eta leq 2$. We confirm that this scaling is preserved when NQAC is tested on a D-Wave 2000Q device (supporting up to $2048$ qubits). In addition, we show that NQAC can be also used in sampling problems to lower the effective temperature of a quantum annealer. Such effective temperature reduction is relevant for machine-learning applications. Since we demonstrate that NQAC achieves error correction via an effective reduction of the temperature of the quantum annealing device, our results address the problem of the temperature scaling law for quantum annealers, which requires the temperature of quantum annealers to be reduced as problems of larger sizes are attempted to be solved.
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We present a general error-correcting scheme for quantum annealing that allows for the encoding of a logical qubit into an arbitrarily large number of physical qubits. Given any Ising model optimization problem, the encoding replaces each logical qubit by a complete graph of degree $C$, representing the distance of the error-correcting code. A subsequent minor-embedding step then implements the encoding on the underlying hardware graph of the quantum annealer. We demonstrate experimentally that the performance of a D-Wave Two quantum annealing device improves as $C$ grows. We show that the performance improvement can be interpreted as arising from an effective increase in the energy scale of the problem Hamiltonian, or equivalently, an effective reduction in the temperature at which the device operates. The number $C$ thus allows us to control the amount of protection against thermal and control errors, and in particular, to trade qubits for a lower effective temperature that scales as $C^{-eta}$, with $eta leq 2$. This effective temperature reduction is an important step towards scalable quantum annealing.
The performance of open-system quantum annealing is adversely affected by thermal excitations out of the ground state. While the presence of energy gaps between the ground and excited states suppresses such excitations, error correction techniques are required to ensure full scalability of quantum annealing. Quantum annealing correction (QAC) is a method that aims to improve the performance of quantum annealers when control over only the problem (final) Hamiltonian is possible, along with decoding. Building on our earlier work [S. Matsuura et al., Phys. Rev. Lett. 116, 220501 (2016)], we study QAC using analytical tools of statistical physics by considering the effects of temperature and a transverse field on the penalty qubits in the ferromagnetic $p$-body infinite-range transverse-field Ising model. We analyze the effect of QAC on second ($p=2$) and first ($pgeq 3$) order phase transitions, and construct the phase diagram as a function of temperature and penalty strength. Our analysis reveals that for sufficiently low temperatures and in the absence of a transverse field on the penalty qubit, QAC breaks up a single, large free energy barrier into multiple smaller ones. We find theoretical evidence for an optimal penalty strength in the case of a transverse field on the penalty qubit, a feature observed in QAC experiments. Our results provide further compelling evidence that QAC provides an advantage over unencoded quantum annealing.
Quantum annealing provides a promising route for the development of quantum optimization devices, but the usefulness of such devices will be limited in part by the range of implementable problems as dictated by hardware constraints. To overcome constraints imposed by restricted connectivity between qubits, a larger set of interactions can be approximated using minor embedding techniques whereby several physical qubits are used to represent a single logical qubit. However, minor embedding introduces new types of errors due to its approximate nature. We introduce and study quantum annealing correction schemes designed to improve the performance of quantum annealers in conjunction with minor embedding, thus leading to a hybrid scheme defined over an encoded graph. We argue that this scheme can be efficiently decoded using an energy minimization technique provided the density of errors does not exceed the per-site percolation threshold of the encoded graph. We test the hybrid scheme using a D-Wave Two processor on problems for which the encoded graph is a 2-level grid and the Ising model is known to be NP-hard. The problems we consider are frustrated Ising model problem instances with planted (a priori known) solutions. Applied in conjunction with optimized energy penalties and decoding techniques, we find that this approach enables the quantum annealer to solve minor embedded instances with significantly higher success probability than it would without error correction. Our work demonstrates that quantum annealing correction can and should be used to improve the robustness of quantum annealing not only for natively embeddable problems, but also when minor embedding is used to extend the connectivity of physical devices.
New annealing schedules for quantum annealing are proposed based on the adiabatic theorem. These schedules exhibit faster decrease of the excitation probability than a linear schedule. To derive this conclusion, the asymptotic form of the excitation probability for quantum annealing is explicitly obtained in the limit of long annealing time. Its first-order term, which is inversely proportional to the square of the annealing time, is shown to be determined only by the information at the initial and final times. Our annealing schedules make it possible to drop this term, thus leading to a higher order (smaller) excitation probability. We verify these results by solving numerically the time-dependent Schrodinger equation for small size systems
By exploiting the exotic quantum states of a probe, it is possible to realize efficient sensors that are attractive for practical metrology applications and fundamental studies. Similar to other quantum technologies, quantum sensing is suffering from noises and thus the experimental developments are hindered. Although theoretical schemes based on quantum error correction (QEC) have been proposed to combat noises, their demonstrations are prevented by the stringent experimental requirements, such as perfect quantum operations and the orthogonal condition between the sensing interaction Hamiltonian and the noise Lindbladians. Here, we report an experimental demonstration of a quantum enhancement in sensing with a bosonic probe with different encodings, by exploring the large Hilbert space of the bosonic mode and developing both the approximate QEC and the quantum jump tracking approaches. In a practical radiometry scenario, we attain a 5.3 dB enhancement of sensitivity, which reaches $9.1times10^{-4},mathrm{Hz}^{-1/2}$ when measuring the excitation population of a receiver mode. Our results demonstrate the potential of quantum sensing with near-term quantum technologies, not only shedding new light on the quantum advantage of sensing by revealing its difference from other quantum applications, but also stimulating further efforts on bosonic quantum technologies.
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