Two-level-system (TLS) defects in amorphous dielectrics are a major source of noise and decoherence in solid-state qubits. Gate-dependent non-Markovian errors caused by TLS-qubit couplingare detrimental to fault-tolerant quantum computation and have not been rigorously treated in the existing literature. In this work, we derive the non-Markovian dynamics between TLS and qubits during a SWAP-like two-qubit gate and the associated average gate fidelity for frequency-tunable Transmon qubits. This gate dependent error model facilitates using qubits as sensors to simultaneously learn practical imperfections in both the qubit’s environment and control waveforms. We combine the-state-of-art machine learning algorithm with Moiré-enhanced swap spectroscopy to achieve robust learning using noisy experimental data. Deep neural networks are used to represent the functional map from experimental data to TLS parameters and are trained through an evolutionary algorithm. Our method achieves the highest learning efficiency and robustness against experimental imperfections to-date, representing an important step towards in-situ quantum control optimization over environmental and control defects.
A critical question for the field of quantum computing in the near future is whether quantum devices without error correction can perform a well-defined computational task beyond thecapabilities of state-of-the-art classical computers, achieving so-called quantum supremacy. We study the task of sampling from the output distributions of (pseudo-)random quantum circuits, a natural task for benchmarking quantum computers. Crucially, sampling this distribution classically requires a direct numerical simulation of the circuit, with computational cost exponential in the number of qubits. This requirement is typical of chaotic systems. We extend previous results in computational complexity to argue more formally that this sampling task must take exponential time in a classical computer. We study the convergence to the chaotic regime using extensive supercomputer simulations, modeling circuits with up to 42 qubits – the largest quantum circuits simulated to date for a computational task that approaches quantum supremacy. We argue that while chaotic states are extremely sensitive to errors, quantum supremacy can be achieved in the near-term with approximately fifty superconducting qubits. We introduce cross entropy as a useful benchmark of quantum circuits which approximates the circuit fidelity. We show that the cross entropy can be efficiently measured when circuit simulations are available. Beyond the classically tractable regime, the cross entropy can be extrapolated and compared with theoretical estimates of circuit fidelity to define a practical quantum supremacy test.
Quantum annealing (QA) has been proposed as a quantum enhanced optimization heuristic exploiting tunneling. Here, we demonstrate how finite range tunneling can provide considerablecomputational 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 ∼108 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 runs up to ∼108 times faster than an optimized implementation of QMC on a single core. 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 and better than the best known classical algorithms for this problem. We discuss the implications of these findings for the design of next generation quantum annealers.
Quantum tunneling, a phenomenon in which a quantum state traverses energy barriers above the energy of the state itself, has been hypothesized as an advantageous physical resource foroptimization. Here we show that multiqubit tunneling plays a computational role in a currently available, albeit noisy, programmable quantum annealer. We develop a non-perturbative theory of open quantum dynamics under realistic noise characteristics predicting the rate of many-body dissipative quantum tunneling. We devise a computational primitive with 16 qubits where quantum evolutions enable tunneling to the global minimum while the corresponding classical paths are trapped in a false minimum. Furthermore, we experimentally demonstrate that quantum tunneling can outperform thermal hopping along classical paths for problems with up to 200 qubits containing the computational primitive. Our results indicate that many-body quantum phenomena could be used for finding better solutions to hard optimization problems.
Quantum tunneling is a phenomenon in which a quantum state traverses energy barriers above the energy of the state itself. Tunneling has been hypothesized as an advantageous physicalresource for optimization. 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, the simplest non-convex optimization problem consisting of just one global and one local 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.
The development of small-scale digital and analog quantum devices raises the question of how to fairly assess and compare the computational power of classical and quantum devices, andof how to detect quantum speedup. Here we show how to define and measure quantum speedup in various scenarios, and how to avoid pitfalls that might mask or fake quantum speedup. We illustrate our discussion with data from a randomized benchmark test on a D-Wave Two device with up to 503 qubits. Comparing the performance of the device on random spin glass instances with limited precision to simulated classical and quantum annealers, we find no evidence of quantum speedup when the entire data set is considered, and obtain inconclusive results when comparing subsets of instances on an instance-by-instance basis. Our results for one particular benchmark do not rule out the possibility of speedup for other classes of problems and illustrate that quantum speedup is elusive and can depend on the question posed.
At a time when quantum effects start to pose limits to further miniaturisation of devices and the exponential performance increase due to Moore’s law, quantum technology is maturingto the point where quantum devices, such as quantum communication systems, quantum random number generators and quantum simulators, may be built with powers exceeding the performance of classical computers. A quantum annealer, in particular, finds solutions to hard optimisation problems by evolving a known initial configuration towards the ground state of a Hamiltonian that encodes an optimisation problem. Here, we present results from experiments on a 108 qubit D-Wave One device based on superconducting flux qubits. The correlations between the device and a simulated quantum annealer demonstrate that the device performs quantum annealing: unlike classical thermal annealing it exhibits a bimodal separation of hard and easy problems, with small-gap avoided level crossings characterizing the hard problems. To assess the computational power of the quantum annealer we compare it to optimised classical algorithms. We discuss how quantum speedup could be detected on devices scaled to a larger number of qubits where the limits of classical algorithms are reached.
Quantum annealing is a general strategy for solving difficult optimization
problems with the aid of quantum adiabatic evolution. Both analytical and
numerical evidence suggests thatunder idealized, closed system conditions,
quantum annealing can outperform classical thermalization-based algorithms such
as simulated annealing. Do engineered quantum annealing devices effectively
perform classical thermalization when coupled to a decohering thermal
environment? To address this we establish, using superconducting flux qubits
with programmable spin-spin couplings, an experimental signature which is
consistent with quantum annealing, and at the same time inconsistent with
classical thermalization, in spite of a decoherence timescale which is orders
of magnitude shorter than the adiabatic evolution time. This suggests that
programmable quantum devices, scalable with current superconducting technology,
implement quantum annealing with a surprising robustness against noise and
imperfections.