Published Papers
D-Wave Science and Technology Publications
We have studied numerically the evolution of an adiabatic quantum computer in the presence of a Markovian Ohmic environment by considering Ising spin-glass systems with up to 20 qubits independently coupled to this environment via two conjugate degrees of freedom. The required computation time is demonstrated to be of the same order as that for an isolated system and is not limited by the single-qubit decoherence time T_2*, even when the minimum gap is much smaller than the temperature and decoherence-induced level broadening. For small minimum gap, the system can be described by an effective two-state model coupled only longitudinally to environment.The Role of Single Qubit Decoherence Time in Adiabatic Quantum Computation
Phys. Rev. A 80, 022303 (2009)
arXiv: 0803.1196
A compound Josephson Junction Coupler for flux qubits with minimal crosstalk
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 the qubits. Quantitative agreement is shown between an effective one-dimensional model of the coupler's potential and measurements of the coupler persistent current and susceptibility.
Phys. Rev. B 80, 052506 (2009)
arXiv: 0904.3784
Landau-Zener transitions in a superconducting flux qubit
We report an experimental measurement of Landau-Zener transitions on an individual flux qubit within a multiqubit superconducting chip. The method used isolates a single qubit, tunes its tunneling amplitude 
into the limit where is much less than both the temperature T and the decoherence-induced energy level broadening, and forces it to undergo a Landau-Zener transition. We find that the behavior of the qubit agrees to a high degree of accuracy with theoretical predictions for Landau-Zener transition probabilities for a double-well quantum system coupled to a non-Markovian 1/f noise.
Phys. Rev. B 80, 012507 (2009)
arXiv: 0807.0797
Landau-Zener transitions in the presence of spin environment
We study the effect of an environment consisting of noninteracting two level systems on Landau-Zener transitions with an interest on the performance of an adiabatic quantum computer. We show that if the environment is initially at zero temperature, it does not affect the transition probability. An excited environment, however, will always increase the probability of making a transition out of the ground state. For the case of equal intermediate gaps, we find an analytical upper bound for the transition probability in the limit of large number of environmental spins. We show that such an environment will only suppress the probability of success for adiabatic quantum computation by at most a factor close to 1/2.
Int. J. Quant. Inf. 7, 725 (2009)
Consistency of the Adiabatic Theorem
The adiabatic theorem provides the basis for the adiabatic model of quantum computation. Recently the conditions required for the adiabatic theorem to hold have become a subject of some controversy. Here we show that the reported violations of the adiabatic theorem all arise from resonant transitions between energy levels. We show that as long as a system is not subject to fast driven oscillations the traditional adiabatic theorem holds. Implications for adiabatic quantum computation is discussed.
Phys. Rev. Lett. 102, 220401 (2009)
Geometrical dependence of low frequency noise in superconducting flux qubits
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 systematically varied between qubit designs with strong dependence upon qubit wiring length and wiring width. Furthermore, qubits fabricated above a superconducting ground plane yielded lower noise than qubits without such a layer. These results support the hypothesis that localized magnetic impurities in the vicinity of the qubit wiring are a key source of low frequency flux noise in superconducting devices.
Phys. Rev. B 79, 060509 (2009)
Decoherence in adiabatic quantum computation
We have studied the decoherence properties of adiabatic quantum computation (AQC) in the presence of in general non-Markovian, e.g., low-frequency, noise. The developed description of the incoherent Landau-Zener transitions shows that the global AQC maintains its properties even for decoherence larger than the minimum gap at the anticrossing of the two lowest-energy levels. The more efficient local AQC, however, does not improve scaling of the computation time with the number of qubits n as in the decoherence-free case. The scaling improvement requires phase coherence throughout the computation, limiting the computation time and the problem size n.
Phys. Rev. A 79, 022107 (2009)
Minor-Embedding in Adiabatic Quantum Computation: I. The Parameter Setting Problem
We show that the NP-hard quadratic unconstrained binary optimization (QUBO) problem on a graph
Probing Noise in Flux Qubits via Macroscopic Resonant Tunneling
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 the target well. The rms amplitude of the noise, which is proportional to the dephasing rate 1/
, was observed to be weakly dependent on temperature below 70 mK. Analysis of these results indicates that the dominant source of low energy flux noise in this device is a quantum mechanical environment in thermal equilibrium.
Phys. Rev. Lett. 101, 117003 (2008)
Training a Binary Classifier with the Quantum Adiabatic Algorithm
This paper describes how to make the problem of binary classification amenable to quantum computing. A formulation is employed in which the binary classifier is constructed as a thresholded linear superposition of a set of weak classifiers. The weights in the superposition are optimized in a learning process that strives to minimize the training error as well as the number of weak classifiers used. No efficient solution to this problem is known. To bring it into a format that allows the application of adiabatic quantum computing (AQC), we first show that the bit-precision with which the weights need to be represented only grows logarithmically with the ratio of the number of training examples to the number of weak classifiers. This allows to effectively formulate the training process as a binary optimization problem. Solving it with heuristic solvers such as tabu search, we find that the resulting classifier outperforms a widely used state-of-the-art method, AdaBoost, on a variety of benchmark problems. Moreover, we discovered the interesting fact that bit-constrained learning machines often exhibit lower generalization error rates. Changing the loss function that measures the training error from 0-1 loss to least squares maps the training to quadratic unconstrained binary optimization. This corresponds to the format required by D-Wave’s implementation of AQC. Simulations with heuristic solvers again yield results better than those obtained with boosting approaches. Since the resulting quadratic binary program is NP-hard, additional gains can be expected from applying the actual quantum processor.
Proceedings of NIPS-08 Workshop
arXiv: 0811.0416
Realizable Hamiltonians for Universal Adiabatic Quantum Computers
It has been established that local lattice spin Hamiltonians can be used for universal adiabatic quantum computation. However, the two-local model Hamiltonians used in these proofs are general and hence do not limit the types of interactions required between spins. To address this concern, the present paper provides two simple model Hamiltonians that are of practical interest to experimentalists working toward the realization of a universal adiabatic quantum computer. The model Hamiltonians presented are the simplest known quantum-Merlin-Arthur-complete (QMA-complete) two-local Hamiltonians. The two-local Ising model with one-local transverse field which has been realized using an array of technologies, is perhaps the simplest quantum spin model but is unlikely to be universal for adiabatic quantum computation. We demonstrate that this model can be rendered universal and QMA-complete by adding a tunable two-local transverse 
xx coupling. We also show the universality and QMA-completeness of spin models with only one-local z and x fields and two-local zx interactions.
Macroscopic Resonant Tunneling in the Presence of Low Frequency Noise We develop a theory of macroscopic resonant tunneling of flux in a double-well potential in the presence of realistic flux noise with a significant low-frequency component. The rate of incoherent flux tunneling between the wells exhibits resonant peaks, the shape and position of which reflect qualitative features of the noise, and can thus serve as a diagnostic tool for studying the low-frequency flux noise in SQUID qubits. We show, in particular, that the noise-induced renormalization of the first resonant peak provides direct information on the temperature of the noise source and the strength of its quantum component.
In this paper we explore the use of a quantum optimization algorithm for obtaining low-energy conformations of protein models. We discuss mappings between protein models and optimization variables, which are in turn mapped to a system of coupled quantum bits. General strategies are given for constructing Hamiltonians to be used to solve optimization problems of physical, chemical, or biological interest via quantum computation by adiabatic evolution. As an example, we implement the Hamiltonian corresponding to the hydrophobic-polar model for protein folding. Furthermore, we present an approach to reduce the resulting Hamiltonian to two-body terms gearing toward an experimental realization.On the construction of model Hamiltonians for adiabatic quantum computation and its application to finding low energy conformations of lattice protein models
We present a perturbative method to estimate the spectral gap for adiabatic quantum optimization, based on the structure of the energy levels in the problem Hamiltonian. We show that, for problems that have an exponentially large number of local minima close to the global minimum, the gap becomes exponentially small making the computation time exponentially long. The quantum advantage of adiabatic quantum computation may then be accessed only via the local adiabatic evolution, which requires phase coherence throughout the evolution and knowledge of the spectrum. Such problems, therefore, are not suitable for adiabatic quantum computation. Phys. Rev. Lett. 100 130503 (2008) Effect of Local Minima on Adiabatic Quantum Optimization
Thermally assisted adiabatic quantum computation
We study the effect of a thermal environment on adiabatic quantum computation using the Bloch-Redfield formalism. We show that in certain cases the environment can enhance the performance in two different ways: (i) by introducing a time scale for thermal mixing near the anticrossing that is smaller than the adiabatic time scale, and (ii) by relaxation after the anticrossing. The former can enhance the scaling of computation when the environment is super-Ohmic, while the latter can only provide a prefactor enhancement. We apply our method to the case of adiabatic Grover search and show that performance better than classical is possible with a super-Ohmic environment, with no a priori knowledge of the energy spectrum.
Sign- and Magnitude-Tunable Coupler for Superconducting Flux Qubits
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 in situ. To measure the effective J, the ground state of a coupled two-qubit system has been mapped as a function of the local magnetic fields applied to each qubit. The state of the system is determined by directly reading out the individual qubits while tunneling is suppressed. These measurements demonstrate that J can be tuned from antiferromagnetic through zero to ferromagnetic.
Simulated Quantum Computation of Molecular Energies
The calculation time for the energy of atoms and molecules scales exponentially with system size on a classical computer but polynomially using quantum algorithms. We demonstrate that such algorithms can be applied to problems of chemical interest using modest numbers of quantum bits. Calculations of the water and lithium hydride molecular ground-state energies have been carried out on a quantum computer simulator using a recursive phase-estimation algorithm. The recursive algorithm reduces the number of quantum bits required for the readout register from about 20 to 4. Mappings of the molecular wave function to the quantum bits are described. An adiabatic method for the preparation of a good approximate ground-state wave function is described and demonstrated for a stretched hydrogen molecule. The number of quantum bits required scales linearly with the number of basis functions, and the number of gates required grows polynomially with the number of quantum bits.