Scientific Publications

Ramin Ayanzadeh, John Dorband, Milton Halem & Tim Finin

We present multi-qubit correction (MQC) as a novel postprocessing method for quantum annealers that views the evolution in an open-system as a Gibbs sampler and reduces a set of excited states to a new synthetic state with lower energy value. After sampling from the ground state of a given (Ising) Hamiltonian, MQC compares pairs of excited states to recognize virtual tunnels—i.e., a group of qubits that changing their states simultaneously can result in a new state with lower energy value—and successively converges to the ground state. Experimental results using D-Wave 2000Q quantum annealers demonstrate that MQC finds samples with notably lower energy values and improves the reproducibility of results when compared to recent hardware/software advances in the realm of quantum annealing, such as spin-reversal transforms, classical postprocessing techniques, and increased inter-sample delay between successive measurements.

Sci Rep 11, 16119 (2021). https://doi.org/10.1038/s41598-021-95482-w

Matthew R.C. Fitzpatrick, Jack Raymond, Malcolm P. Kennett

We present an essentially exact numerical method for modelling 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.

(4 Oct 2021) arXiv:2110.01647

Kelly Boothby 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.

See arXiv: http://arxiv.org/abs/2108.02322

Andrew D. King, Cristiano Nisoli, Edward D. Dahl, Gabriel Poulin-Lamarre, Alejandro Lopez-Benzanilla 

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.

(30 July 2021) DOI: 10.1126/science.abe2824

Eleni Marina Lykiardopoulou, Alex Zucca, Sam A. Scivier, and Mohammad H. Amin

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.

(July 29, 2021) https://journals.aps.org/pra/abstract/10.1103/PhysRevA.104.012619

Alexander Teplukhin, et al.

The possibility of using quantum computers for electronic structure calculations has opened up a promising avenue for computational chemistry. Towards this direction, numerous algorithmic advances have been made in the last five years. The potential of quantum annealers, which are the prototypes of adiabatic quantum computers, is yet to be fully explored. In this work, we demonstrate the use of a D-Wave quantum annealer for the calculation of excited electronic states of molecular systems. These simulations play an important role in a number of areas, such as photovoltaics, semiconductor technology and nanoscience. The excited states are treated using two methods, time-dependent Hartree-Fock (TDHF) and time-dependent density-functional theory (TDDFT), both within a commonly used Tamm-Dancoff approximation (TDA). The resulting TDA eigenvalue equations are solved on a D-Wave quantum annealer using the Quantum Annealer Eigensolver (QAE), developed previously. The method is shown to reproduce a typical basis set convergence on the example H2 molecule and is also applied to several other molecular species. 

(2021 July 1) https://arxiv.org/abs/2107.00162

Addressing the world’s climate emergency is an uphill battle, requiring a multifaceted approach including optimal deployment of green-energy alternatives. Such undertakings often involve computationally-expensive optimisation of black-box models in a continuous parameter space. We observe good performance on the DW-2000Q QPU - even using default settings - and higher sensitivity of performance to number of samples and annealing time for the Advantage QPU. These results are promising and potentially justify further investment in hardware, software, and optimisation research, in particular, in the area of solvers for dense QUBOs.

(2021 May 24) https://arxiv.org/pdf/2105.11322.pdf

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.

(18 Feb 2021) Nature Communications (DOI 10.1038/s41467-021-20901-5)

Andrew D. King, Cristian D. Batista, Jack Raymond, Trevor Lanting, Isil Ozfidan, Gabriel Poulin-Lamarre, Hao Zhang, Mohammad H. Amin

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.

(7 Jan 2021) https://arxiv.org/abs/2101.02769

Paul Kairys, Andrew D. King, Isil Ozfidan, Kelly Boothby, Jack Raymond, Arnab Banerjee, and Travis S. Humble

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.

(23 Nov 2020) PRX Quantum https://doi.org/10.1103/PRXQuantum.1.020320

Jack Raymond; Ndiamé Ndiaye; Gautam Rayaprolu; Andrew D. King

Optimization or sampling of arbitrary pairwise Ising models, in a quantum annealing protocol of constrained interaction topology, can be enabled by a minor-embedding procedure. The logical problem of interest is transformed to a physical (device programmable) problem, where one binary variable is represented by a logical qubit consisting of multiple physical qubits. In this paper we discuss tuning of this transformation for the cases of clique, biclique, and cubic lattice problems on the D-Wave 2000Q quantum computer. We demonstrate parameter tuning protocols in spin glasses and channel communication problems, focusing on anneal duration, chain strength, and mapping from the result on physical qubits back to the logical space. Inhomogeneities in effective coupling strength arising from minor-embedding are shown to be mitigated by an efficient reweighting of programmed couplings, accounting for logical qubit topology.

(16 Oct 2020) IEEE Xplore https://ieeexplore.ieee.org/abstract/document/9259935

Nicholas Chancellor, Philip J. D. Crowley, Tanja Đurić, Walter Vinci, Mohammad H. Amin, Andrew G. Green, Paul A. Warburton, Gabriel Aeppli

In this manuscript we explore an experimentally observed statistical phenomenon by which domain walls on an Ising chain programmed onto a flux qubit quantum annealer tend toward a non-uniform distribution. We find that this distribution can be theoretically well described by a combination of control errors and thermal effects. Interestingly, the effect that produces this distribution is purely entropic, as it appears in cases where the average energy of all domain-wall locations is equal by definition. As well as being a counterintuitive statistical effect, we also show that our method can be applied to measure the strength of the noise on the device. The noise measured in this way is smaller than what is seen by other methods suggesting that the freeze time of a chain of coupled qubits on the device may be different than for isolated qubits with all couplings turned off, despite the fact that a qubit adjacent to a domain wall should effectively experience no coupling due to cancellation of the couplings one either side.

(13 Jun 2020) https://arxiv.org/abs/2006.07685