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.
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.
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.
Abstract Quantum annealing is a type of analog computation that aims to use quantum mechanical fluctuations in search of optimal solutions of QUBO (quadratic unconstrained binary optimization) or, equivalently, Ising problems. Since NP-hard problems can in general be mapped to Ising and QUBO formulations, the quantum annealing paradigm has the potential to help solve various NP-hard problems. Current quantum annealers, such as those manufactured by D-Wave Systems, Inc. have various practical limitations including the size (number of qubits) of the problem that can be solved, the qubit connectivity, and error due to the environment or system calibration, which can reduce the quality of the solutions. Typically, for an arbitrary problem instance, the corresponding QUBO (or Ising) structure will not natively embed onto the available qubit architecture on the quantum chip. Thus, in these cases, a minor embedding of the problem structure onto the device is necessary. However, minor embeddings on these devices do not always make use of the full sparse chip hardware graph, and a large portion of the available qubits stay unused during quantum annealing. In this work, we embed a disjoint random QUBO on the unused parts of the chip alongside the QUBO to be solved, which acts as an indicator of the solution quality of the device over time. Using experiments on three different D-Wave quantum annealers, we demonstrate that (i) long term trends in solution quality exist on the D-Wave device, and (ii) the unused qubits can be used to measure the current level of noise of the quantum system.
Quantum devices offer a highly useful function - that is generating random numbers in a non-deterministic way since the measurement of a quantum state is not deterministic. This means that quantum devices can be constructed that generate qubits in a uniform superposition and then measure the state of those qubits. If the preparation of the qubits in a uniform superposition is unbiased, then quantum computers can be used to create high entropy, secure random numbers. Typically, preparing and measuring such quantum systems requires more time compared to classical pseudo random number generators (PRNGs) which are inherently deterministic algorithms. Therefore, the typical use of quantum random number generators (QRNGs) is to provide high entropy secure seeds for PRNGs. Quantum annealing (QA) is a type of analog quantum computation that is a relaxed form of adiabatic quantum computation and uses quantum fluctuations in order to search for ground state solutions of a programmable Ising model. Here we present extensive experimental random number results from a D-Wave 2000Q quantum annealer, totaling over 20 billion bits of QA measurements, which is significantly larger than previous D-Wave QA random number generator studies. Current quantum annealers are susceptible to noise from environmental sources and calibration errors, and are not in general unbiased samplers. Therefore, it is of interest to quantify whether noisy quantum annealers can effectively function as an unbiased QRNG. The amount of data that was collected from the quantum annealer allows a comprehensive analysis of the random bits to be performed using the NIST SP 800-22 Rev 1a testsuite, as well as min-entropy estimates from NIST SP 800-90B. The randomness tests show that the generated random bits from the D-Wave 2000Q are biased, and not unpredictable random bit sequences. With no server-side sampling post-processing, the 1 microsecond annealing time measurements had a min-entropy of 0.824.
To gain better insight into the complexity theory of quantum annealing, we propose and solve a class of spin systems which contain bottlenecks of the kind expected to dominate the runtime of quantum annealing as it tries to solve difficult optimization problems. We uncover a noise amplification effect at these bottlenecks, whereby tunneling rates caused by flux-qubit noise scale in proportion to the number of qubits N in the limit that $\mathcal{N}\ensuremath{\rightarrow}\ensuremath{\infty}$. By solving the incoherent annealing dynamics exactly, we find a wide range of regimes where the probability that a quantum annealer remains in the ground state upon exiting the bottleneck is close to one-half. We corroborate our analysis with detailed simulations of the performance of the D-Wave 2X quantum annealer on our class of computational problems.
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.
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.