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arXiv:0903.3906

Implementation of a Quantum Annealing Algorithm Using a Superconducting Circuit

R. Harris, A. J. Berkley, Johansson, J., Mark W. Johnson, Trevor M. Lanting, P. Bunyk, E. Tolkacheva, E. Ladizinsky, Bruce Bumble, A. Fung, Anupama B. Kaul, Alan W. Kleinsasser, Siyuan Han

Published Mar 23, 2009• 9 citations
arXivHTMLPDF

Abstract

A circuit consisting of a network of coupled compound Josephson junction rf-SQUID flux qubits has been used to implement an adiabatic quantum optimization algorithm. It is shown that detailed knowledge of the magnitude of the persistent current as a function of annealing parameters is key to implementation of the algorithm on this particular type of hardware. Experimental results contrasting two annealing protocols, one with and one without active compensation for the growth of the qubit persistent current during annealing, are presented in order to illustrate this point.

DOI
10.48550/arxiv.0903.3906

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A circuit consisting of a network of coupled compound Josephson junction rf-SQUID flux qubits has been used to implement an adiabatic quantum optimization algorithm. It is shown that detailed knowledge of the magnitude of the persistent current as a function of annealing parameters is key to implementation of the algorithm on this particular type of hardware. Experimental results contrasting two annealing protocols, one with and one without active compensation for the growth of the qubit persistent current during annealing, are presented in order to illustrate this point.
This chapter focuses on the application of Nb Josephson junctions (JJs) in quantum annealing (QA). It begins with a brief introduction to diffident strategies for implementing quantum computation (QC) with an emphasis on quantum annealing. The chapter presents the basic physics of the simplest superconducting flux qubit: radio frequency superconducting quantum interference devices (RF-SQUID). It gives a brief description on the design and realization of couplers, and control and measurement circuitry using Nb Josephson junctions. The chapter describes a scalable architecture upon which quantum annealing processors consisting up to 1024 superconducting flux qubits made of more than 104 Nb Josephson junctions. It discusses evidence on whether D-Wave 2X, which is the latest quantum annealing processor available, works as expected. The chapter also focuses on the physics and application of RF-SQUID flux qubits because the fundamental building blocks of the most advanced quantum annealers demonstrated so far are variations of superconducting flux qubits with one Josephson junction, a.k.a. the RF-SQUID.
Abstract : Quantum annealing is a general strategy for solving difficult optimization problems with the aid of quantum adiabatic evolution [1, 2]. Both analytical and numerical evidence suggests that under idealized, closed system conditions, quantum annealing can outperform classical thermalization-based algorithms such as simulated annealing [3, 4]. 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.
The superconducting quantum annealing circuit is constructed with four Nb layers and Josephson junctions with a critical current density of 1 μA/μm2. Three key points exist to perform the quantum annealing in experiments. First, the shape of the energy potential of the qubit should be accurately designed. Second, the current pulses for modulation of the shape of the energy potential must propagate to the qubit accurately. Third is the suppression of noise in the environment where the qubit is placed. Furthermore, calibration of the measurement data is necessary with consideration of the experimental environment. In this paper, I will present a mechanism for realizing quantum annealing from two perspectives: a theoretical model and an experiment. Experimental findings on quantum annealing will contribute to study of the surrounding circuit of a gate-type quantum computer.
Although quantum annealing has received considerable interest as a potential computing paradigm, it has not met the key criterion of improved scaling over classical methods. Qubit coherence is currently a major limitation. Starting from a detailed theoretical understanding of the system, the authors demonstrate tunably coupled flux qubits with a circuit geometry similar to those used in existing annealers, but with coherence times that are roughly two orders of magnitude longer. Their design concepts are not limited to superconducting qubits, and could be generalized to other types being considered for quantum annealing.
A practical strategy for synchronizing the properties of compound Josephson junction (CJJ) radio frequency monitored superconducting quantum interference device (rf-SQUID) qubits on a multi-qubit chip has been demonstrated. The impact of small (∼1%) fabrication variations in qubit inductance and critical current can be minimized by the application of a custom-tuned flux offset to the CJJ structure of each qubit. This strategy allows for a simultaneous synchronization of the qubit persistent current and tunnel splitting over a range of external bias parameters that is relevant for the implementation of an adiabatic quantum processor.
The applicability of quantum annealing to various problems can be improved by expressing the Hamiltonian using a circuit satisfiability problem. We investigate the detailed characteristics of the NOR/NAND functions of a superconducting quantum circuit, which are the basic building blocks to implementing various types of problem Hamiltonians. The circuit is composed of superconducting flux qubits with all-to-all connectivity, where direct magnetic couplers are utilized instead of the variable couplers in the conventional superconducting quantum circuit. This configuration provides efficient scalability because the problem Hamiltonian is implemented using fewer qubits. We present an experiment with a complete logic operation of NOR/NAND, in which the circuit produces results with a high probability of success for arbitrary combinations of inputs. The features of the quantum circuit agree qualitatively with the theory, especially the mechanism for an operation under external flux modulation. Moreover, by calibrating the bias conditions to compensate for the offset flux from the surrounding circuit, the quantum circuit quantitatively agrees with the theory. To achieve true quantum annealing, we discuss the effects of the reduction in electric noise in quantum annealing.