Various sources of noise limit the performance of quantum computers by altering qubit states in an uncontrolled manner throughout computations and reducing their coherence time. In quantum annealers, this noise introduces additional fluctuations to the parameters defining the original problem Hamiltonian, such that they find the ground states of problems perturbed from those originally programmed. Here, we describe a method to benchmark the amount of noise affecting the programmed Hamiltonian of a quantum annealer. We show that a sequence of degenerate runs with the coefficients of the programmed Hamiltonian set to zero leads to an estimate of the noise spectral density affecting Hamiltonian parameters “in situ” during the quantum annealing protocol. The method is demonstrated in D-Wave's lower noise 2000 qubit device (DW_2000Q_6) and in its recently released 5000 qubit device (Advantage_system1.1). Our benchmarking of DW_2000Q_6 shows Hamiltonian noise dominated by the 1/f0.7frequency dependence characteristic of flux noise intrinsic to the materials forming flux qubits. In contrast, Advantage_system1.1 is found to be affected by additional noise sources for low annealing times, with underlying intrinsic flux noise amplitudes 2-3 times higher than in DW_2000Q_6 for all annealing times.
Various sources of noise limit the performance of quantum computers by altering qubit states in an uncontrolled manner throughout computations and reducing their coherence time. In quantum annealers, this noise introduces additional fluctuations to the parameters defining the original problem Hamiltonian, such that they find the ground states of problems perturbed from those originally programmed. Here, we describe a method to benchmark the amount of noise affecting the programmed Hamiltonian of a quantum annealer. We show that a sequence of degenerate runs with the coefficients of the programmed Hamiltonian set to zero leads to an estimate of the noise spectral density affecting Hamiltonian parameters “in situ” during the quantum annealing protocol. The method is demonstrated in D-Wave's lower noise 2000 qubit device (DW_2000Q_6) and in its recently released 5000 qubit device (Advantage_system1.1). Our benchmarking of DW_2000Q_6 shows Hamiltonian noise dominated by the 1/f0.7frequency dependence characteristic of flux noise intrinsic to the materials forming flux qubits. In contrast, Advantage_system1.1 is found to be affected by additional noise sources for low annealing times, with underlying intrinsic flux noise amplitudes 2-3 times higher than in DW_2000Q_6 for all annealing times.
Various sources of noise limit the performance of quantum computers based on superconducting flux qubits by altering their states in an uncontrolled manner throughout computations and reducing their coherence time. In quantum annealers, this introduces fluctuations to the linear constants of the original problem Hamiltonian, such that they find the ground states of problems perturbed from those programmed. Here we describe how to turn this drawback into a method to probe the frequency dependence of the noise in situ of the D-Wave 2000Q quantum annealer. The method relates the autocorrelation of the readout-state of a qubit repeatedly collapsed from uniform superposition to that of the noise impingent on the qubit. We show that this leads to an estimate for the noise spectral density affecting D-Wave qubits under normal operating conditions. The method is general and can be used to characterize noise in all architectures for quantum annealing.
Despite being considered as the next frontier in computation, Quantum Computing is still in an early stage of development. Indeed, current commercial quantum computers suffer from some critical restraints, such as noisy processes and a limited amount of qubits, among others, that affect the performance of quantum algorithms. Despite these limitations, researchers have devoted much effort to propose different frameworks for efficiently using these Noisy Intermediate-Scale Quantum (NISQ) devices. One of these procedures is D'WAVE Systems' quantum-annealer, which can be used to solve optimization problems by translating them into an energy minimization problem. In this context, this work is focused on providing useful insights and information into the behaviour of the quantum-annealer when addressing real-world combinatorial optimization problems. Our main motivation with this study is to open some quantum computing frontiers to non-expert stakeholders. To this end, we perform an extensive experimentation, in the form of a parameter sensitive analysis. This experimentation has been conducted using the Traveling Salesman Problem as benchmarking problem, and adopting two QUBOs: state-of-the-art and a heuristically generated. Our analysis has been performed on a single 7-noded instance, and it is based on more than 200 different parameter configurations, comprising more than 3700 unitary runs and 7 million of quantum reads. Thanks to this study, findings related to the energy distribution and most appropriate parameter settings have been obtained. Finally, an additional study has been performed, aiming to determine the efficiency of the heuristically built QUBO in further TSP instances.
Recent tests performed on the D-Wave Two quantum annealer have revealed no clear evidence of speedup over conventional silicon-based technologies. Here we present results from classical parallel-tempering Monte Carlo simulations combined with isoenergetic cluster moves of the archetypal benchmark problem---an Ising spin glass---on the native chip topology. Using realistic uncorrelated noise models for the D-Wave Two quantum annealer, we study the best-case resilience, i.e., the probability that the ground-state configuration is not affected by random fields and random-bond fluctuations found on the chip. We thus compute classical upper-bound success probabilities for different types of disorder used in the benchmarks and predict that an increase in the number of qubits will require either error correction schemes or a drastic reduction of the intrinsic noise found in these devices. We restrict this study to the exact ground state, however, the approach can be trivially extended to the inclusion of excited states if the success metric is relaxed. We outline strategies to develop robust, as well as hard benchmarks for quantum annealing devices, as well as any other (black box) computing paradigm affected by noise.
Quantum devices are affected by intrinsic and environmental noises. An in-depth characterization of noise effects is essential for exploiting noisy quantum computing. To this end, we studied the energy dissipative behavior of a quantum annealer via experiments and numerical simulations. Our investigation adopts a recently proposed technique that interpolates between pure quantum dynamics and pure thermodynamics. Experiments were conducted on a quantum annealer with an anneal pause function, which inserts a thermal relaxation period into the annealing schedule by pausing the transverse field, which is a source of quantum fluctuation. After investigating the special Hamiltonian that characterizes the quantum thermodynamics of the system, we then observed enhancement of thermodynamic signature depending on the anneal pause parameter. The time development of the state vector, observed in the open quantum simulation, provides rich information for investigating phenomena beyond energy-gap analysis. We identified a special eigenstate bridges ground states far-separated in Hilbert space and the transfer probabilities from one ground state to another. This finding can improve the sampling uniformity by reducing the sampling bias in finding the classical ground states in the quantum annealer. Our study does not only characterize the open quantum phenomenon of the specific Hamiltonian but also demonstrates the usefulness of the method in investigating noisy quantum devices.
Quantum annealing represents an essential milestone towards the goal of adiabatic quantum computing. In quantum annealing, the computation involves finding the ground state of a classical Ising-like Hamiltonian realized as interactions between qubits. Quantum fluctuations are introduced to allow the wavefunction of the qubits to explore the energy landscape, the hope being that the wavefunction finds a minimum energy configuration and possibly giving the result of the computation. While quantum annealing likely may not be as powerful as adiabatic quantum computing, it is possible that it may be better at optimization compared to analogous classical algorithms. In physical realizations of quantum annealing, there are still questions as to the role of quantum fluctuations in the operation of a device given the short coherence times of the individual qubits. These questions have consistently posed a serious theoretical challenge making it difficult to verify experimental results. Here we simplify the problem by considering a system of qubits with ferromagnetic interactions, modeling the decoherence effects as classical noise in the transverse-field of each qubit. We compare the calculations to data collected from a system of manufactured qubits produced by D-wave Systems by performing a finite-size scaling analysis that captures the competition between quantum fluctuations of the transverse-field and bit-flip errors from the noise. We argue that on time-scales larger than the single-qubit decoherence time, the device produces the expected quantum fluctuations for the many-body system. Using this finite-size scaling, one can diagnose sources of noise in the system. Hopefully, in the near future, these devices will not only be realizing coherent quantum annealing but will likely be useful as another example of synthetic quantum matter.
In solving optimization problems, objective functions generally need to be minimized or maximized. However, objective functions cannot always be formulated explicitly in a mathematical form for complicated problem settings. Although several regression techniques infer the approximate forms of objective functions, they are at times expensive to evaluate. Optimal points of "black-box" objective functions are computed in such scenarios, while effectively using a small number of clues. Recently, an efficient method by use of inference by sparse prior for a black-box objective function with binary variables has been proposed. In this method, a surrogate model was proposed in the form of a quadratic unconstrained binary optimization (QUBO) problem, and was iteratively solved to obtain the optimal solution of the black-box objective function. In the present study, we employ the D-Wave 2000Q quantum annealer, which can solve QUBO by driving the binary variables by quantum fluctuations. The D-Wave 2000Q quantum annealer does not necessarily output the ground state at the end of the protocol due to freezing effect during the process. We investigate effects from the output of the D-Wave quantum annealer in performing black-box optimization. We demonstrate a benchmark test by employing the sparse Sherrington-Kirkpatrick (SK) model as the black-box objective function, by introducing a parameter controlling the sparseness of the interaction coefficients. Comparing the results of the D-Wave quantum annealer to those of the simulated annealing (SA) and semidefinite programming (SDP), our results by the D-Wave quantum annealer and SA exhibit superiority in black-box optimization with SDP. On the other hand, we did not find any advantage of the D-Wave quantum annealer over the simulated annealing. As far as in our case, any effects by quantum fluctuation are not found.