# Andrew BerkleyD-Wave Systems Inc.

Andrew Berkley

## About

88

Publications

18,798

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5,742

Citations

Citations since 2017

Introduction

Additional affiliations

January 2004 - present

January 2000 - December 2004

## Publications

Publications (88)

Experiments on disordered alloys1–3 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 processing units (QPUs) executing annealing algorithms have shown promise in optimization and simulation applications. Hybrid algorithms are a natural bridge to larger applications. We present a simple greedy method for solving larger-than-QPU lattice-structured Ising optimization problems. The method, implemented in the open-source D-Wave...

Quantum simulation has emerged as a valuable arena for demonstrating and understanding the capabilities of near-term quantum computers1–3. Quantum annealing4,5 has been successfully used in simulating a range of open quantum systems, both at equilibrium6–8 and out of equilibrium9–11. However, in all previous experiments, annealing has been too slow...

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. Due to the importance of spin glasses as a paradigmatic computational testbed, reproducing this phenomenon in a programmable system has remained a central challenge in quan...

Quantum simulation has emerged as a valuable arena for demonstrating and understanding the capabilities of near-term quantum computers. Quantum annealing has been used successfully 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 simulate...

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...

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 conn...

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 fl...

Hamiltonian-based quantum computation is a class of quantum algorithms in which the problem is encoded in a Hamiltonian and the evolution is performed by a continuous transformation of the Hamiltonian. Universal adiabatic quantum computing, quantum simulation, and quantum annealing are examples of such algorithms. Up to now, all implementations of...

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 fl...

Quantum annealing (QA) is a heuristic algorithm for finding low-energy configurations of a system, with applications in optimization, machine learning, and quantum simulation. Up to now, all implementations of QA have been limited to qubits coupled via a single degree of freedom. This gives rise to a stoquastic Hamiltonian that has no sign problem...

The celebrated work of Berezinskii, Kosterlitz and Thouless in the 1970s revealed exotic phases of matter governed by topological properties of low-dimensional materials such as thin films of superfluids and superconductors. Key to this phenomenon is the appearance and interaction of vortices and antivortices in an angular degree of freedom---typif...

Understanding magnetic phases in quantum mechanical systems is one of the essential goals in condensed matter physics, and the advent of prototype quantum simulation hardware has provided new tools for experimentally probing such systems. We report on the experimental realization of a quantum simulation of interacting Ising spins on three-dimension...

The coherent Ising machine is an optical processor that uses coherent laser pulses, but does not employ coherent quantum dynamics in a computational role. Core to its operation is the iterated simulation of all-to-all spin coupling via mean-field calculation in a classical FPGA coprocessor. Although it has been described as "operating at the quantu...

SQUIDs may detect local magnetic fields. SQUIDS of varying sizes, and hence sensitivities may detect different magnitudes of magnetic fields. SQUIDs may be oriented to detect magnetic fields in a variety of orientations, for example along an orthogonal reference frame of a chip or wafer. The SQUIDS may be formed or carried on the same chip or wafer...

Superconducting microresonators have been successfully utilized as detection
elements for a wide variety of applications. With multiplexing factors
exceeding 1,000 detectors per transmission line, they are the most scalable
low-temperature detector technology demonstrated to date. For high-throughput
applications, fewer detectors can be coupled to...

Quantum annealing may include applying and gradually removing disorder terms to qubits of a quantum processor, for example superconducting flux qubits of a superconducting quantum processor. A problem Hamiltonian may be established by applying control signals to the qubits, an evolution Hamiltonian established by applying disorder terms, and anneal...

Systems and methods for reading out the states of superconducting flux qubits may couple magnetic flux representative of a qubit state to a DC-SQUID in a variable transformer circuit. The DC-SQUID is electrically coupled in parallel with a primary inductor such that a time-varying (e.g., AC) drive current is divided between the DC-SQUID and the pri...

SQUIDs may detect local magnetic fields. SQUIDS of varying sizes, and hence sensitivities may detect different magnitudes of magnetic fields. SQUIDs may be oriented to detect magnetic fields in a variety of orientations, for example along an orthogonal reference frame of a chip or wafer. The SQUIDS may be formed or carried on the same chip or wafer...

A superconducting flux digital-to-analog converter includes a superconducting inductor ladder circuit. The ladder circuit includes a plurality of closed superconducting current paths that each includes at least two superconducting inductors coupled in series to form a respective superconducting loop, successively adjacent or neighboring superconduc...

Entanglement lies at the core of quantum algorithms designed to solve
problems that are intractable by classical approaches. One such algorithm,
quantum annealing (QA), provides a promising path to a practical quantum
processor. We have built a series of scalable QA processors consisting of
networks of manufactured interacting spins (qubits). Here,...

Analog processors for solving various computational problems are provided. Such analog processors comprise a plurality of quantum devices, arranged in a lattice, together with a plurality of coupling devices. The analog processors further comprise bias control systems each configured to apply a local effective bias on a corresponding quantum device...

Hysteretic dc SQUIDs provide an easy method to read the state of hundreds
of qubits1. However, this approach becomes impractical for circuits with an even
larger number of qubits due to heating when dc SQUIDs switch, the relatively slow
retrapping dynamics of high quality devices, and suboptimal scaling of the number
of control lines with increasin...

We have developed a quantum annealing processor, based on an array of tunably
coupled rf-SQUID flux qubits, fabricated in a superconducting integrated
circuit process [1]. Implementing this type of processor at a scale of 512
qubits and 1472 programmable inter-qubit couplers and operating at ~ 20 mK has
required attention to a number of considerati...

The intrinsic flux noise observed in superconducting quantum interference devices (SQUIDs) is thought to be due to the fluctuation of electron-spin impurities, but the frequency and temperature dependence observed in experiments do not agree with the usual 1/f models. We present theoretical calculations and experimental measurements of flux noise i...

Systems, methods and apparatus for a scalable quantum processor architecture. A quantum processor is locally programmable by providing a memory register with a signal embodying device control parameter(s), converting the signal to an analog signal; and administering the analog signal to one or more programmable devices.

Various adaptations to adiabatic quantum computation and quantum annealing are described. These adaptations generally involve tailoring an initial Hamiltonian so that a local minimum is avoided when a quantum processor is evolved from the initial Hamiltonian to a problem Hamiltonian. The initial Hamiltonian may represent a mixed Hamiltonian that in...

Efforts to develop useful quantum computers have been blocked primarily by environmental noise. Quantum annealing is a scheme of quantum computation that is predicted to be more robust against noise, because despite the thermal environment mixing the system's state in the energy basis, the system partially retains coherence in the computational bas...

An I/O system and device for use with superconducting device provides multi-stage filtering using superconducting electrical pathways, while providing good thermal conductivity to maintain low temperature of the various components and allowing the easy mounting and dismounting of a device sample from a refrigerated environment. Filtering may includ...

We present the results of our investigation of the energy levels of
systems of flux qubits using tunneling spectroscopy. Tunneling
spectroscopy is a technique by which we use macroscopic resonant
tunneling processes of a neighboring qubit to probe the energy spectrum
of a system of flux qubits. We used this technique to measure the energy
gap of a...

We describe a quantum tunneling spectroscopy technique that requires only low
bandwidth control. The method involves coupling a probe qubit to the system
under study to create a localized probe state. The energy of the probe state is
then scanned with respect to the unperturbed energy levels of the probed
system. Incoherent tunneling transitions th...

A localized area is at least partially contained within a perimeter of a shield ring formed by a closed superconducting current path of a material that is superconductive below a critical temperature. The shield ring is at least partially within a perimeter of a compensation coil that is coupled to a current source. One or more measurement devices...

Many interesting but practically intractable problems can be reduced to that of finding the ground state of a system of interacting spins; however, finding such a ground state remains computationally difficult. It is believed that the ground state of some naturally occurring spin systems can be effectively attained through a process called quantum...

We have developed a method for extracting the high-frequency noise spectral
density of an rf-SQUID flux qubit from macroscopic resonant tunneling (MRT)
rate measurements. The extracted noise spectral density is consistent with that
of an ohmic environment up to frequencies ~ 4 GHz. We have also derived an
expression for the MRT lineshape expected f...

Magnetic shields and magnetic shielding systems are described. The excessive spatial demands of known mu-metal/cryoperm and superconducting shielding systems are reduced by a new multi-piece shield construction approach. A complete magnetic shielding system for use with superconducting-based computing systems, such as superconducting quantum comput...

We have designed, fabricated and tested an XY-addressable readout system that is specifically tailored for the reading of superconducting flux qubits in an integrated circuit that could enable adiabatic quantum optimization. In such a system, the flux qubits only need to be read at the end of an adiabatic evolution when quantum mechanical tunneling...

A superconducting chip containing a regular array of flux qubits, tunable
interqubit inductive couplers, an XY-addressable readout system, on-chip
programmable magnetic memory, and a sparse network of analog control lines has
been studied. The architecture of the chip and the infrastructure used to
control it were designed to facilitate the impleme...

We report measurements of macroscopic resonant tunneling between the two lowest energy states of a pair of magnetically coupled rf-SQUID flux qubits. This technique provides a direct means of observing two-qubit dynamics and a probe of the environment coupled to the pair of qubits. Measurements of the tunneling rate as a function of qubit flux bias...

We have designed, fabricated and operated a scalable system for applying
independently programmable time-independent, and limited time-dependent flux
biases to control superconducting devices in an integrated circuit. Here we
report on the operation of a system designed to supply 64 flux biases to
devices in a circuit designed to be a unit cell for...

A practical strategy for synchronizing the properties of compound Josephson
junction rf-SQUID qubits on a multiqubit chip has been demonstrated. The
impacts of small ($\sim1%$) 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 st...

A novel rf-SQUID flux qubit that is robust against fabrication variations in
Josephson junction critical currents and device inductance has been
implemented. Measurements of the persistent current and of the tunneling energy
between the two lowest lying states, both in the coherent and incoherent
regime, are presented. These experimental results ar...

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 o...

An improved tunable coupling element for building networks of coupled
rf-SQUID flux qubits has been experimentally demonstrated. This new form of
coupler, based upon the compound Josephson junction rf-SQUID, provides a sign
and magnitude tunable mutual inductance between qubits with minimal nonlinear
crosstalk from the coupler tuning parameter into...

A general method for directly measuring the low-frequency flux noise (below 10 Hz) in compound Josephson junction superconducting flux qubits has been used to study a series of 85 devices of varying design. The variation in flux noise across sets of qubits with identical designs was observed to be small. However, the levels of flux noise systematic...

Macroscopic resonant tunneling between the two lowest lying states of a bistable rf SQUID is used to characterize noise in a flux qubit. Measurements of the incoherent decay rate as a function of flux bias revealed a Gaussian-shaped profile that is not peaked at the resonance point but is shifted to a bias at which the initial well is higher than t...

We report an experimental measurement of Landau-Zener transitions on an
individual flux qubit within a multi-qubit superconducting chip designed for
adiabatic quantum computation. The method used isolates a single qubit, tunes
its tunneling amplitude Delta into the limit where Delta is much less than both
the temperature T and the decoherence-induc...

Macroscopic resonant tunneling between the two lowest lying states of a bistable RF-SQUID is used to characterize flux noise in a potential qubit. Detailed measurements of incoherent decay rates as a function of flux bias revealed that the Gaussian shaped tunneling rate is not peaked at the resonance point, but is shifted to a flux bias at which th...

We experimentally confirm the functionality of a coupling element for
flux-based superconducting qubits, with a coupling strength $J$ whose sign and
magnitude can be tuned {\it in situ}. To measure the effective $J$, the
groundstate of a coupled two-qubit system has been mapped as a function of the
local magnetic fields applied to each qubit. The s...

We report upon experimental results from a system consisting of four flux qubits linked via in-situ sign and magnitude tunable coupling elements. The device was operated as an adiabatic quantum computer to solve NP-complete problems whose solutions are encoded in the groundstate configuration of the qubits. Each qubit was coupled to its own dedicat...

We report on measurements of a superconducting sign-tunable magnetic
coupling element. This device could be used as part of a programmable
adiabatic quantum computer utilizing flux qubits. The sign-tunability is
achieved by mediating the coupling between two flux qubits through a
third rf SQUID device [1]. We are able to tune the resulting coupling...

It is sketched how a monostable rf- or dc-SQUID can mediate an inductive coupling between two adjacent flux qubits. The non-trivial dependence of the SQUID's susceptibility on external flux makes it possible to continuously tune the induced coupling from antiferromagnetic (AF) to ferromagnetic (FM). In particular, for suitable parameters, the induc...

We calculate the effective capacitance of a Cooper-pair box and demonstrate that the Cooper-pair box can be used as a variable capacitor. The gate voltage modulates the charge transfer through the small junction in the Cooper-pair box, leading to a gate-dependent capacitance. We describe ongoing experiments to use an Al/AlO<sub>x</sub>/Al Cooper-pa...

The search for a quantum computer has been stimulated by the development of algorithms that would solve intractable problems (exponential time) if the massive parallel processing of the anticipated quantum computer were available. Foremost among these problems is the determination of the prime factors of a large integer. We discuss our studies of s...

We analyze the effect of dissipation and low-frequency current noise on quantum coherence in a current-biased Josephson junction that has low damping. Developing a stochastic Bloch equation for the reduced density matrix of the system, we determine the resonance response of the system to a weak external microwave current drive. We characterize the...

We study the quantum mechanical behavior of a macroscopic, three-body, superconducting circuit. Microwave spectroscopy on our system, a resonator coupling two large Josephson junctions, produced complex energy spectra well explained by quantum theory over a large frequency range. By tuning each junction separately into resonance with the resonator,...

We report on measurements of two coupled rf SQUID phase qubits. With both qubits initially in their ground states, the first is excited with a pi pulse. Being initially detuned they are brought into resonance with a coupling pulse that allows the qubits to be put into a maximally entangled state. By varying the length of the interaction time we are...

When a Josephson junction in the zero-voltage state is current-biased below its critical current, the rate that it escapes to the finite-voltage state depends on the quantum state of the junction. By employing a slow current sweep, it is possible to observe experimentally the emptying of the thermally populated first excited level as a well-defined...

We calculate the input impedance of a Cooper pair box with different junction parameters and demonstrate how the junction parameters can affect the input impedence. In particular we show how the input capacitance can be modulated by the gate voltage, suggesting that the Cooper pair box can be used as a tunable circuit element. We describe ongoing e...

Can spectroscopic data provide evidence for quantum mechanics? I will
discuss how spectroscopy of coupled nonlinear Josephson junction (phase)
qubits provides persuasive evidence for a quantum mechanical, rather
than a classical, picture of their behavior: Their measured behavior,
both qualitative and quantitative, differs substantially from that o...

Weak magnetic field detection using a non-hysteretic DC SQUID with Flux-Locked-Loop electronics is typically limited to 1MHz bandwidth or less. However, there is demand for larger bandwidth magnetic field detection for use in the semiconductor industry. We have studied the possibility of using a 4.2K hysteretic trilayer Nb DC SQUID, fabricated by H...

The energy relaxation time T1 of a qubit, which determines the rate at which an excited state of the system decays to the ground state, is an important measure of its potential use for quantum computation. For a current-biased Josephson junction in the zero-voltage state, T1 can be measured by increasing the bias current slowly enough so that the j...

The zero-voltage state of a Josephson junction biased with constant current consists of a set of metastable quantum energy levels. We probe the spacings of these levels by using microwave spectroscopy to enhance the escape rate to the voltage state. The widths of the resonances give a measurement of the coherence time of the two states involved in...

We present spectroscopic evidence for the creation of entangled macroscopic quantum states in two current-biased Josephson-junction qubits coupled by a capacitor. The individual junction bias currents are used to control the interaction between the qubits by tuning the energy level spacings of the junctions in and out of resonance with each other....

The energy states of a well-isolated hysteretic Josephson junction in the "phase" regime can be used as a qubit. The state of the junction can be determined by measuring when the junction switches from the zero-voltage (qubit) state to the running voltage state, since different levels have different switching rates. The experimental challenge is to...

We examine resonant activation from the zero-voltage state of a current-biased Josephson junction in the limit of low damping. In this limit, the quantum dynamics of a Josephson junction can be described by a master equation. Our finite temperature analysis includes transitions between any two levels in the potential well and accounts for escape ne...

We describe how single Josephson junctions can be connected together capacitively to form a two-qubit system. We discuss the general behavior of this system show the energy level dependence on various junction parameters and choice of coupling strengths. We also discuss measurement techniques for reading out both qubits which are relevant to our on...

We analyze the effect of current noise on resonant activation from the zero-voltage state of a current-biased Josephson junction in the limit of low damping. In this limit, the dynamics of the system can be described by the evolution of a density matrix which simplifies to a Bloch-like equation under the two-level approximation. In the presence of...

The zero-voltage state of a current-biased Josephson junction in the phase regime consists of a set of metastable quantum energy levels. We use microwave spectroscopy to obtain a measure of the coherence time of the system. Isolation of the junction from its dissipative leads is provided by an LC isolation circuit. While increasing the dissipation...

A key step towards building any quantum computer is demonstrating the quantum entanglement of the states of two or more qubits. We describe how current-biased Josephson junction qubits can be coupled together capacitively to form multi-qubit systems. A novel feature in these coupled qubit systems is the entanglement of states which lead to quantum...

Capacitively-coupled Josephson junctions may allow fundamentally important observations of macroscopically entangled quantum states and the construction of quantum gates. We show how the quantum states and energy levels of this simple system may be effectively tuned and controlled by numerically computing the metastable states in the full, nonlinea...

We demonstrate high-fidelity nontrivial quantum gates by modeling the dynamics of two-dimensional coupled Josephson junction wavefunctions with respect to the full, nonlinear Hamiltonian. Our quantum gate implementation overcomes a number of challenges revealed by a theoretical study of the quantum spectroscopy, and our methods are a powerful tool...