Scientific Publications

Kevin Chern, Kelly Boothby, Jack Raymond, Pau Farré, Andrew D. King

Front. Comput. Sci., 15 September 2023
Sec. Theoretical Computer Science
Volume 5 - 2023 | https://doi.org/10.3389/fcomp.2023.1238988

Quantum annealing has emerged as a powerful platform for simulating and optimizing classical and quantum Ising models. Quantum annealers, like other quantum and/or analog computing devices, are susceptible to non-idealities including crosstalk, device variation, and environmental noise. Compensating for these effects through calibration refinement or “shimming” can significantly improve performance but often relies on ad-hoc methods that exploit symmetries in both the problem being solved and the quantum annealer itself. In this tutorial, we attempt to demystify these methods. We introduce methods for finding exploitable symmetries in Ising models and discuss how to use these symmetries to suppress unwanted bias. We work through several examples of increasing complexity and provide complete Python code. We include automated methods for two important tasks: finding copies of small subgraphs in the qubit connectivity graph and automatically finding symmetries of an Ising model via generalized graph automorphism. We conclude the tutorial by surveying additional methods, providing practical implementation tips, and discussing limitations and remedies of the calibration procedure. Code is available at: https://github.com/dwavesystems/shimming-tutorial.

Catherine C. McGeoch, Pau Farre.

We introduce quantum utility, a new approach to evaluating quantum performance that aims to capture the user experience by including overhead costs associated with the quantum computation. A demonstration of quantum utility by a quantum processing unit (QPU) shows that the QPU can outperform classical solvers at some tasks of interest to practitioners, when considering computational overheads. We consider overhead costs that arise in standalone use of the QPU (as opposed to a hybrid computation context). We define three early milestones on the path to broad-scale quantum utility that focus on restricted subsets of overheads: Milestone 0 considers pure anneal time (no overheads) and has been demonstrated in previous work; Milestone 1 includes overhead times to access the QPU (that is, programming and readout); and Milestone 2 incorporates an indirect cost associated with minor embedding.

We evaluate the performance of a D-Wave Advantage QPU with respect to Milestones 1 and 2, using a testbed of 13 input classes and seven classical solvers implemented on CPUs and GPUs. For Milestone 1, the QPU outperformed all classical solvers in 99% of our tests. For Milestone 2, the QPU outperformed all classical solvers in 19% of our tests, and the scenarios in which the QPU found success correspond to cases where classical solvers most frequently failed.
Analysis of test results on specific inputs reveals fundamentally distinct underlying mechanisms that explain the observed differences in quantum and classical performance profiles. We present evidence-based arguments that these distinctions bode well for future annealing quantum processors to support demonstrations of quantum utility on ever-expanding classes of inputs and for more challenging milestones.

King, A.D., Raymond, J., Lanting, T. et al. Quantum critical dynamics in a 5,000-qubit programmable spin glass. Nature 617, 61–66 (2023). https://doi.org/10.1038/s41586-023-05867-2

Experiments on disordered alloys suggest that spin glasses can be brought into low-energy states faster by annealing quantum fluctuations than by conventional thermal annealing. Owing to the importance of spin glasses as a paradigmatic computational testbed, reproducing this phenomenon in a programmable system has remained a central challenge in quantum optimization4–13. Here we achieve this goal by realizing quantum-critical spin-glass dynamics on thousands of qubits with a superconducting quantum annealer. We first demonstrate quantitative agreement between quantum annealing and timeevolution of the Schrödinger equation in small spin glasses. We then measure dynamics in three-dimensional spin glasses on thousands of qubits, for which classical simulation of many-body quantum dynamics is intractable. We extract critical exponents that clearly distinguish quantum annealing from the slower stochastic dynamics of analogous Monte Carlo algorithms, providing both theoretical and experimental support for large-scale quantum simulation and a scaling advantage in energy optimization.

Alexander M. Whiticar, et al.

We report on measurements of flux and charge noise in an rf-SQUID (superconducting quantum interference device) flux qubit using macroscopic resonant tunneling (MRT). We measure rates of incoherent tunneling from the lowest energy state in the initial well to the ground and first excited states in the target well. The result of the measurement consists of two peaks. The first peak corresponds to tunneling to the ground state of the target well, and is dominated by flux noise. The second peak is due to tunneling to the excited state and is wider due to an intrawell relaxation process dominated by charge noise. We develop a theoretical model that allows us to extract information about flux and charge noise within one experimental setup. The model agrees very well with experimental data over a wide dynamic range and provides parameters that characterize charge and flux noise.

Anatoly Y. Smirnov, et al.

Macroscopic resonant tunneling (MRT) in flux qubits is an important experimental tool for extracting information about noise produced by a qubit's surroundings. Here we present a detailed derivation of the MRT signal in the RF-SQUID flux qubit allowing for effects of flux and charge fluctuations on the interwell and intrawell transitions in the system. Taking into consideration transitions between the ground state in the initial well and excited states in the target well enable us to characterize both flux and charge noise source affecting the operation of the flux qubit. The MRT peak is formed by the dominant noise source affecting specific transition, with flux noise determining the lineshape of the ground to ground tunneling, whereas charge noise reveals itself as additional broadening of the ground to excited peak.

King, A.D., Suzuki, S., Raymond, J. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nat. Phys. (2022)

Quantum simulation has emerged as a valuable arena for demonstrating and understanding the capabilities of near-term quantum computers. Quantum annealing has been successfully used in simulating a range of open quantum systems, both at equilibrium and out of equilibrium. However, in all previous experiments, annealing has been too slow to coherently simulate a closed quantum system, due to the onset of thermal effects from the environment. Here we demonstrate coherent evolution through a quantum phase transition in the paradigmatic setting of a one-dimensional transverse-field Ising chain, using up to 2,000 superconducting flux qubits in a programmable quantum annealer. In large systems, we observe the quantum Kibble–Zurek mechanism with theoretically predicted kink statistics, as well as characteristic positive kink–kink correlations, independent of temperature. In small chains, excitation statistics validate the picture of a Landau–Zener transition at a minimum gap. In both cases, the results are in quantitative agreement with analytical solutions to the closed-system quantum model. For slower anneals, we observe anti-Kibble–Zurek scaling in a crossover to the open quantum regime. The coherent dynamics of large-scale quantum annealers demonstrated here can be exploited to perform approximate quantum optimization, machine learning and simulation tasks.

T. Morstyn, "Annealing-based Quantum Computing for Combinatorial Optimal Power Flow," in IEEE Transactions on Smart Grid, 2022,

This paper proposes the use of annealing-based quantum computing for solving combinatorial optimal power flow problems. Quantum annealers provide a physical computing platform which utilises quantum phase transitions to solve specific classes of combinatorial problems. These devices have seen rapid increases in scale and performance, and are now approaching the point where they could be valuable for industrial applications. This paper shows how an optimal power flow problem incorporating linear multiphase network modelling, discrete sources of energy flexibility, renewable generation placement/sizing and network upgrade decisions can be formulated as a quadratic unconstrained binary optimisation problem, which can be solved by quantum annealing. Case studies with these components integrated with the IEEE European Low Voltage Test Feeder are implemented using D-Wave Systems’ 5,760 qubit Advantage quantum processing unit and hybrid quantum-classical solver.

Jack Raymond, et al.

Quantum processing units (QPUs) executing annealing algorithms have shown promise in optimization and simulation applications. Hybrid algorithms are a natural bridge to additional applications of larger scale. We present a straightforward and effective method for solving larger-than-QPU lattice-structured Ising optimization problems. Performance is compared against simulated annealing with promising results, and improvement is shown as a function of the generation of D-Wave QPU used.

Matthew R.C. Fitzpatrick, et al.

We present an essentially exact numerical method for modeling flux qubit chains subject to charge and flux noise. We define an essentially exact method as one that introduces errors that are completely controlled such that they can be made arbitrarily small by tuning the simulation parameters. The method adopts the quasi-adiabatic path integral formalism to express the system's reduced density matrix as a time-discretized path integral, comprising a series of influence functionals that encode the non-Markovian dynamics of the system. We present a detailed derivation of the path integral expression for the system's reduced density matrix and describe in detail the tensor network algorithm used to evaluate the path integral expression. We have implemented our method in an open-sourced Python library called "spinbosonchain". When appropriate, we draw connections between concepts covered in this manuscript and the library's code.

Kelly Boothby, et al.

Early generations of superconducting quantum annealing processors have provided a valuable platform for studying the performance of a scalable quantum computing technology. These studies have directly informed our approach to the design of the next-generation processor. Our design priorities for this generation include an increase in per-qubit connectivity, a problem Hamiltonian energy scale similar to previous generations, reduced Hamiltonian specification errors, and an increase in the processor scale that also leaves programming and readout times fixed or reduced. Here we discuss the specific innovations that resulted in a processor architecture that satisfies these design priorities.

Andrew D. King, et al.

Artificial spin ices are frustrated spin systems that can be engineered, in which fine-tuning of geometry and topology has allowed the design and characterization of exotic emergent phenomena at the constituent level. Here, we report a realization of spin ice in a lattice of superconducting qubits. Unlike conventional artificial spin ice, our system is disordered by both quantum and thermal fluctuations. The ground state is classically described by the ice rule, and we achieved control over a fragile degeneracy point, leading to a Coulomb phase. The ability to pin individual spins allows us to demonstrate Gauss’s law for emergent effective monopoles in two dimensions. The demonstrated qubit control lays the groundwork for potential future study of topologically protected artificial quantum spin liquids.

Eleni Marina Lykiardopoulou, et al.

Nonstoquastic Hamiltonians are hard to simulate due to the sign problem in quantum Monte Carlo simulation. It is, however, unclear whether nonstoquasticity can lead to an advantage in quantum annealing. Here we show that YY interactions between the qubits make the adiabatic path during quantum annealing, and therefore the performance, dependent on spin-reversal transformations. With the right choice of spin-reversal transformation, a nonstoquastic Hamiltonian with YY interaction can outperform stoquastic Hamiltonians with similar parameters. We introduce an optimization protocol to determine the optimal transformation and discuss the effect of suboptimality.

Andrew D. King, et al.

The promise of quantum computing lies in harnessing programmable quantum devices for practical applications such as efficient simulation of quantum materials and condensed matter systems. One important task is the simulation of geometrically frustrated magnets in which topological phenomena can emerge from competition between quantum and thermal fluctuations. Here we report on experimental observations of equilibration in such simulations, measured on up to 1440 qubits with microsecond resolution. By initializing the system in a state with topological obstruction, we observe quantum annealing (QA) equilibration timescales in excess of one microsecond. Measurements indicate a dynamical advantage in the quantum simulation compared with spatially local update dynamics of path-integral Monte Carlo (PIMC). The advantage increases with both system size and inverse temperature, exceeding a million-fold speedup over an efficient CPU implementation. PIMC is a leading classical method for such simulations, and a scaling advantage of this type was recently shown to be impossible in certain restricted settings. This is therefore an important piece of experimental evidence that PIMC does not simulate QA dynamics even for sign-problem-free Hamiltonians, and that near-term quantum devices can be used to accelerate computational tasks of practical relevance.

Andrew D. King, et al.

Geometrically frustrated spin-chain compounds such as Ca3Co2O6 exhibit extremely slow relaxation under a changing magnetic field. Consequently, both low-temperature laboratory experiments and Monte Carlo simulations have shown peculiar out-of-equilibrium magnetization curves, which arise from trapping in metastable configurations. In this work we simulate this phenomenon in a superconducting quantum annealing processor, allowing us to probe the impact of quantum fluctuations on both equilibrium and dynamics of the system. Increasing the quantum fluctuations with a transverse field reduces the impact of metastable traps in out-of-equilibrium samples, and aids the development of three-sublattice ferrimagnetic (up-up-down) long-range order. At equilibrium we identify a finite-temperature shoulder in the 1/3-to-saturated phase transition, promoted by quantum fluctuations but with entropic origin. This work demonstrates the viability of dynamical as well as equilibrium studies of frustrated magnetism using large-scale programmable quantum systems, and is therefore an important step toward programmable simulation of dynamics in materials using quantum hardware.

Paul Kairys, et al.

A core concept in condensed matter physics is geometric frustration that leads to emergent spin phases in magnetic materials. These distinct phases, which depart from the conventional ferromagnet or the antiferromagnet, require unique computational techniques to decipher. In this study, we use the canonical Ising Shastry-Sutherland lattice to demonstrate new techniques for solving frustrated Hamiltonians using a quantum annealer of programmable superconducting qubits. This Hamiltonian can be tuned to produce a variety of intriguing ground states ranging from short- and long-range orders and fractional order parameters. We show that a large-scale finite-field quantum annealing experiment is possible on 468 logical spins of this model embedded into the quantum hardware. We determine microscopic spin configurations using an iterative quantum annealing protocol and develop mean-field boundary conditions to attenuate finite-size effects and defects. We not only recover all phases of the Shastry-Sutherland Ising model—including the well-known fractional magnetization plateau in a longitudinal field—but also predict the spin behavior at the critical points with significant ground-state degeneracy and in the presence of defects. The results lead us to establish the connection to the diffuse neutron scattering experiments by calculation of the static structure factors.