AQC 2015

Fourth Conference in Adiabatic Quantum Computing

June 29 to July 2, 2015, ETH Zurich, Switzerland

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On the role of tunneling in quantum annealing
Sergio Boixo


Quantum annealing solver implementation for time-indexed scheduling problems
Davide Venturelli

While part of the attraction of quantum annealing is the possibility of applying the method irrespective of the structure of the binary optimization to be performed, when it comes to design a turnkey quantum annealing solver it is necessary to be mindful of the structure of the problem at hand. Here we show how to solve complex scheduling problems with a quantum annealer, discussing specific programming/running techniques and illustrating them on the D-Wave Two device, taking the Job Shop Scheduling as illustrative problem example. While the proposed strategies are tailored on the device architectural bottlenecks and leverage the algorithmical structure of the problem for useful pre-processing/decomposition, the solver framework can be generalized to arbitrary time-indexed integer linear programming problems.

Solving a refinery planning optimization problem using D-Waves adiabatic quantum computer
Joaquin Ossorio Castillo

The main purpose of this work is to show a possible application of Adiabatic Quantum Computation within the oil and gas industry as a first step to solve real refinery optimization problems by next generation Adiabatic Quantum computers. We present a small-sized refinery planning optimization problem where profit is maximized using as decision variables the number of cargo shipments of each available crude-oil. Using equalities and inequalities, we describe the mass conservation laws associated to the separation and conversion units, and the constraints that have to be accomplished in order to satisfy the demand of refinery products, resulting in an Integer Linear Programming problem. We then replace all inequalities with equalities using slack variables in order to convert it to the standard form and define all integer variables as indicator variables, as shown in the work [C.S. Calude et. al., CDMTCS-473, Nov. 2014]. The resulting 0-1 linear programming problem is then redefined as a QUBO problem following D-Waves documentation, translating the equalities to quadratic penalties.

Finite-Temperature Inference with the D-Wave Machine
Paul Warburton

The D-Wave machine is generally used to find the ground state of the problem Hamiltonian. Here we show experimentally that the excited states also contain useful information which can be exploited in inferential problems. As an example of finite-temperature inference we use the D-Wave machine as a decoder for classical error-correction codes transmitted over noisy communication channels. We show experimentally that decoding by averaging over the ground and excited states at the end of the annealing process can in some circumstances lead to improved bit-error-rates by comparison with ground-state decoding. We further introduce the concept of the spin-sign transition (i.e. a change of sign of the average spin orientation as the magnitude of thermal and/or quantum fluctuations increases) as an analytical tool for characterising Hamiltonians on the D-Wave machine. We have compared the experimentally measured spin-sign transition temperatures on a 3x3 square lattice of 8-bit superspins with those calculated by exact diagonalization. The best fit to the data occurs at a non-zero value of the transverse field, suggesting that our experiments appear to capture remnants of quantum coherence despite the fact that the annealing time exceeds the coherence time. This work was undertaken in collaboration with Nick Chancellor, Szilard Szoke, Walter Vinci, Gabriel Aeppli and Andrew Green. It was supported by Lockheed Martin and EPSRC. We thank the USC Lockheed Martin Quantum Computing Center at the University of Southern Californias Information Sciences Institute for access to their D-Wave Two machine.

Quantum Optimization of Fully-Connected Spin Glasses
Salvatore Mandra

The Sherrington-Kirkpatrick model with random ±1 couplings is programmed on the D-Wave Two annealer featuring 509 qubits interacting on a Chimera-type graph. The performance of the optimizer compares and correlates to simulated annealing. When considering the effect of the static noise, which degrades the performance of the annealer, one can estimate an improvement on the comparative scaling of the two methods in favor of the D-Wave machine. The optimal choice of parameters of the embedding on the Chimera graph is shown to be associated to the emergence of the spin-glass critical temperature of the embedded problem.

Next Generation Quantum Annealing Processor
Mark Johnson

D-Wave's Vesuvius generation processor technology has provided a valuable platform for studying the quantum annealing (QA) algorithm at a non-trivial scale. Experience with this processor has led to the identification of problem Hamiltonian mispecification as a key performance consideration, and this has focused development of the next generation processor on improving the precision of problem specification. In this presentation, I will discuss some of the major development areas within D-Wave directed at improving QA processors. I will review our understanding of the sources of control error, and discuss their mitigation on D-Wave's next generation processor.

Sampling approach for approximating non-Chimera structured problems with the D-Wave processor
Federico Spedalieri

The limited connectivity of the D-Wave processor given by the Chimera graph imposes a strong restriction on the problems that can be solved natively. Some alternatives have been proposed to address this issue, like the use of ferromagnetically coupled chains of qubits to increase the effective connectivity. However, the price paid in qubits and the computational effort to find these embeddings limits the application of this technique to problems with only a few tens of variables. Here we present an alternative approach that aims at exploiting the sampling capabilities of the D-Wave processor to generate approximate solutions to non-Chimera structured problems with a number of variables restricted only by the number of available physical qubits. We will present some benchmarking results for this approach implemented on a D-Wave Two processor running problems with 504 variables.

A Novel Embedding Technique for Optimization Problems of Fully-Connected Integer Variables
Mark Hodson

Several important combinatorial optimization problems involve variables with more than two values, such as financial optimisation problems where positions may be stated in increments of quarter-percentile points {0.00%, 0.25%, 0.50%, 0.75%, …}. An interesting question is how such problems can be effectively embedded in quantum annealing processors with two-valued variables. Finding an embedding of an arbitrary graph onto the D-wave Systems Chimera graph is known to be an NP-hard problem. For optimization problems defined in terms of a fully-connected set of integer, rather than binary, variables, an efficient embedding can be deterministically generated in linear time. This embedding technique leverages the structure of the Chimera by separating the function of intra-cell and inter-cell couplings in an attempt to produce superior results. Integer variables are mapped onto the rows and columns of the Chimera, while the weighted linear terms of the variable are mapped onto qubits within each Chimera cell. We demonstrate this technique and compare it to the D-wave SAPI "find embedding" heuristic using a test set of randomly generated, NP-hard Integer Linear Programming problems with fixed penalties used between members of logical qubit chains. These problems are executed on a D-wave Two quantum annealer with 504 working qubits. We also compare these two techniques with the closed-loop D-wave SAPI "EmbeddingSolver" that seeks to tune the penalties used between members of logical qubit chains for an equivalent total number of anneals. The work illustrates the potential for broadening the class of problems that can be effectively mapped to adiabatic quantum computers.

Domain Walls in 1D: Simple Experiments to Answer Important Questions
Nicholas Chancellor

Even very simple experiments on the D-Wave chip can yield interesting and highly non-trivial results. A simple spin chains with pinned ends, for example, does not yield equipartion of domain wall positions as one would naively expect. Instead the domain walls form U shaped distribution. We demonstrate that the origin of this effect is order-by-disorder related to effective correlations in domain wall energies caused by uncorrelated field control errors. This result is interesting theoretically because it demonstrates that even the Ising spin chain, which is considered to be a well understood system can yield surprising behavior on a real device. It is also interesting experimentally because it allows for a new way to measure the control error which has several advantages over other methods. In the second part of my talk I switch gears to discuss an experimental protocol on the D-Wave device which does not require any hardware modifications but does require access outside of the standard user API. In this protocol initial conditions for the qubits are set by a standard annealing run with only fields, and a transverse field is then turned on with a more complicated Hamiltonian. I show that Redfield simulations predict some non-trivial signatures of tunneling for simple domain wall experiments even with sweep rates no faster than those used on the ISI device. These experiments could also allow access to the schedule dependence of the control errors. I will briefly mention a more long term outlook for using these techniques to simulate 2D particles using a square ice Hamiltonian and the potential advantages of using this type of protocol to explore local state spaces.

Rapidly Mixing Quantum Monte Carlo for 1D Stoquastic Hamiltonians
Elizabeth Crosson

We present a polynomial-time randomized classical algorithm for approximating the partition function as well as the expectation values of observables in the Gibbs state of 1D stoquastic Hamiltonians at any temperatures which is independent of the system size, or at temperatures which decrease at most logarithmically with the system size. The algorithm relies on the rapid mixing of a Markov chain which formalizes the path-integral quantum Monte Carlo method, the proof of rapid mixing is based on the canonical paths method. The class of stoquastic Hamiltonians includes transverse Ising models with arbitrary (bounded) couplings and local fields, which can be highly frustrated, and our analysis shows that in 1D the thermal equilibrium distribution for quantum annealers based on these models can be efficiently approximated on a classical computer.

Bottlenecks of quantum annealing
Sergey Knysh

Quantum annealing of realistic spin glasses is fundamentally limited by the phenomenon of the transverse field chaos. Even if the gap at the critical point is polynomial in system size N (in a system exhibiting continuous phase transition), the spin glass phase may contain additional tunneling bottlenecks. The gaps scale as a stretched exponential and, more surprisingly, their number increases logarithmically with N, requiring large sizes before the effect can be observed. This is shown rigorously for a simple model of Gaussian Hopfield network, extensions to other fully connected spin glass models will be briefly addressed.

Reducing the dimensionality of simulated quantum adiabatic evolution: The case of local noise
Alan Aspuru-Guzik

The gap along quantum adiabatic evolution determines the maximum speed at which one guarantees a substantial probability of remaining in the ground state. Therefore, the gap determines the complexity of solving problems in adiabatic devices. The gap for a family of problem Hamiltonians for which obvious symmetries exist has allowed for the community to reduce the size of the Hilbert space by exploiting these symmetries and therefore get some insights into the power of adiabatic quantum computation. I will discuss a novel, general-purpose reduction method that does not rely on any explicit symmetry and which requires, under certain conditions, only a polynomial amount of classical resources. We use the method to explore the performance of the adiabatic algorithm for a “noisy” Grover search problems. The noise consists of local defects in the Hamiltionian. Our results show that even when this random noise is present, adiabatic quantum computation is potentially faster than any classical algorithm. This is joint with Salvatore Mandrà and Gian Giacomo Guerresci and is supported by the Air Force Office of Scientific Research and the National Science Foundation. The preprint of the work presented is available at

Error correction for quantum annealing
Daniel Lidar

Just like all other paradigms of quantum information processing, quantum annealing requires error correction in order to become scalable. In this talk I will report on our progress in developing quantum annealing correction methods and their implementation using the D-Wave processor at USC.

Mean-field analysis of quantum annealing correction
Shunji Matsuura

Quantum annealing correction is a protocol of error correction for quantum annealing on the chimera graph. It was tested on the D-Wave machine to show excellent performance in comparison with the classical repetition code. In the present talk, results of our analyses of the quantum annealing correction by a mean-field-like method will be explained to show an important role of the penalty qubit to avoid problematic states in the course of quantum annealing.

Asymptotically tight bounds for diabatic errors
Nathan Wiebe

Recent work has shown that understanding the nature of diabatic errors can be used to optimize adiabatic passage as well as enable new classes of adiabatic algorithms that rely on excitation from the ground state. In order to leverage these ideas to their fullest, the structure of the adiabatic approximation must also be well understood. In this talk I will present an intuitive method for analyzing diabatic errors that uses path integrals and apply it to provide upper and lower bounds for the error in the adiabatic approximation. These bounds will be shown to be tight, meaning the upper and lower bounds converge to the true error as the evolution time becomes arbitrarily slow. Further applications of these methods to cases with degenerate ground spaces and where non-Hermitian Hamiltonians are used will also be discussed.

Noncommuting two-local Hamiltonians for quantum error suppression
Eleanor Rieffel

Physical constraints make it challenging to implement and control multi‐,body interactions. Thus, designing quantum information processes with small‐,locality elements is critical, interactions involving no more than 2 bodies are highly preferred. Here, we examine the potential for error suppression in quantum memories using only 2‐,local terms. It has been shown that even single‐,qubit error suppression cannot be obtained by encoding information in the ground state subspace of a Hamiltonian containing only commuting 2‐,local terms [1]. Here, we show that one can get around this no‐,go result by encoding in the ground subspace of a Hamiltonian containing non‐,commuting 2‐,local terms arising in a subsystem code. Specifically, we show how to use a Hamiltonian consisting of sums of gauge generators from Bravyis [[6, 2, 2]] generalized Bacon‐,Shor code [2] to provide error suppression that protects a quantum memory against singlequbit errors. Thus, we show that local noncommuting Hamiltonians have more error‐,suppressing power than local commuting Hamiltonians. They also open up the possibility of finding topological order in the ground subspace of local noncommuting Hamiltonians. [1] I. Marvian and D. A. Lidar, Quantum error suppression with commuting Hamiltonians: Two local is too local, Physical Review Letters 113, 260504 (2014). [2] S. Bravyi, Subsystem codes with spatially local generators,Physical Review A 83, 012320 (2011).

Spin glasses: these extremely touchy people
Victor Martin-Mayor

D-Wave chips are aimed to find low-energy states of (stylized models for) spin-glasses. Interestingly, D-Wave Two performance turns out to be extremely sensitive to a physical effect known by spin-glass practitioners as "temperature chaos" [1]. Temperature chaos is merely one among several fragilities of the spin-glass state: Even tiny changes in temperature, applied magnetic field or couplings constants may have devastating effects. Our understanding of these chaotic effects is still scant. A theoretical picture is emerging, but up to now progress has been limited to temperature instabilities [2]. Salient features include extreme statistical fluctuations and a weird problem-size evolution. In fact, temperature chaos is a real show-stopper for state-of-the-art computations, both classical [3] and quantum [1]. The talk describes our recent understanding of temperature chaos. Under this light, we make some educated guesses regarding magnetic-field and coupling constant instabilities and discuss potential implications for quantum annealers. [1] V. Martin-Mayor and I. Hen, arXiv:1502.02494. [2] L.A. Fernandez, V. Martin-Mayor, G. Parisi and B. Seoane, EPL 103 (2013) 67003. [3] Janus collaboration, J. Stat. Mech. (2010) P06026, J. Stat. Mech. (2014) P05014.

On quantum annealing with limited entanglement
Bela Bauer


Quantum Optimization for Problems with Rugged Energy Landscapes
Hartmut Neven

We study the performance of quantum optimization algorithms for problems with a large number of local minima separated by tall energy barriers. We present the results of two studies, an experimental one on quadratic problems with cluster structure that can be represented natively on D-Wave hardware and a numerical study on optimization problems that require a gate model implementation. For the quadratic problems conforming with current hardware specifications we find a significant advantage in wall clock time relative to simulated annealing. We argue that this advantage can be translated into a computational speedup for annealers with a suitable connectivity graph. An open challenge is to show that problems arising in commercial applications can be mapped to native problems that enjoy this speedup. In the numerical study we focus on the Number Partitioning Problem. The low energy band for number partitioning resembles that of the random energy model. We consider such energy landscapes as representative for very hard optimization problems encountered in practice. We find a consistent speedup for various quantum optimization methods relative to the best known classical algorithms. A resource analysis shows that a gate model quantum computer can be built to run these quantum optimization algorithms. A key open question for this development path is whether error protection protocols can be customized to protect approximate optimization algorithms such that the overhead required for today's general purpose error protection methods is reduced.

Using insights from spin-glass physics to develop hard benchmarks for quantum computing devices
Helmut Katzgraber

There has been considerable progress in the design and construction of quantum annealing devices. However, a conclusive detection of quantum speedup remains elusive. Based on insights from the study of spin glasses, in this talk we present ideas on how to construct hard benchmark problems for optimization devices (as well as novel algorithms) that are tunable and robust to the intrinsic noise found in these devices.

Generating hard problems on the Chimera
Itay Hen

With previous benchmarking tests of the D-Wave chips and other recent studies, it is becoming apparent that a necessary condition for observing a clear separation between quantum and classical scaling behaviors, is the use of problem instances that are hard to solve. In this talk, I will discuss various attempts to generate such hard problems on the Chimera graph, with and without planted solutions.

Universal adiabatic quantum computation via the space time circuit-to-Hamiltonian construction
Barbara Terhal

We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of (fermionic) particles with local quadratic and quartic interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique groundstate by mapping our model onto the ferromagnetic XXZ chain with kink boundary conditions. We discuss how to possibly obtain the required physical interactions of the 2D Hamiltonian.

Universal fault-tolerant adiabatic quantum computing with quantum dots
Andrew Landahl

I will present a design for an adiabatic quantum computer (AQC) that can achieve arbitrarily accurate universal fault-tolerant quantum computations with a constant energy gap and nearest-neighbor interactions. The central approach is to simulate fault-tolerant topological code deformations via sequences of local adiabatic transformations. The construction subverts various no-go theorems for fault-tolerant AQC by utilizing Hamiltonians that access degenerate as well as non-degenerate ground spaces. Our construction requires a richer set of two-qubit interactions than just Ising interactions. To bolster the plausibility of a quantum hardware realization, I will sketch a design for a quantum-dot based AQC architecture that can simulate the requisite interactions. I will further show how this design can also achieve universal quantum computing in the original non-degenerate AQC model. Unfortunately, our interaction simulation method introduces new fault paths that compromise the fault-tolerance of the overall design. I will conclude with a survey of possible mitigation strategies and open research challenges that, if solved, will chart a new and interesting path to realizing universal fault-tolerant quantum computation. The key hardware challenges along this path could be very different than the challenges currently posed by non-adiabatic universal fault-tolerant quantum circuit approaches. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

High-precision threshold of the toric code from spin-glass theory and graph polynomials
Masayuki Ozeki

We propose a duality analysis for determining the optimal error thresholds of the toric code and color code. Our method is based on the computation of exact quenched free energies with periodic and twisted periodic boundary conditions on a finite basis. The precision can be systematically improved by increasing the size of the basis, leading to very fast convergence towards the thermodynamic limit. The similar technique has been proposed in a realm of quantum error correction but is explicitly derived from the duality analysis with real-space renormalization and graph polynomials in context of classical spin system.

A donor/dot surface code insensitive to inter-qubit coupling for parallel fault-tolerant silicon quantum computing
Giuseppe Pica

Entangling two-qubit operations based on the exchange interaction between spins are crucial for universal silicon quantum computing. Scaling such gates to large, practical quantum computers poses strict limitations to the placement of donor atoms, while it is easily achieved with flexible quantum dots. The latter, however, suffer from coherence times several orders of magnitude smaller than those provided by bismuth donors in silicon tuned to clock-transitions. We present a surface code architecture that combines Si:Bi spins hosting measurement qubits (MQ) to MOS quantum dots playing the role of data qubits (DQ). Most of the steps of a generic surface code could be implemented via well established microwave driven ENDOR transitions on the bismuth donors and realistic shuttling of the array of the interface dot electrons with CCD-like gates. A detailed plan is suggested to fill the fundamental gap of how to perform CNOT gates between the MQ and the DQ: rather than pulsing an exchange interaction to generate a dynamical phase, as in previous proposals, the exchange is used to SWAP spin states between the quantum dots and the donors through robust, addressable adiabatic transfer. Most notable is that such SWAP gates are insensitive to even order of magnitude variations in the exchange interaction strength: it is possible to achieve gate fidelities easily tolerated by the surface code error threshold (about 1% per-operation error rate) across almost the entire array. Since all the manipulations proposed here require μ,s operating times, our scheme promises fast, fault-tolerant parallel silicon quantum computing. While other approaches (such as Kane’s quantum computer) require tuning individual qubits in resonance with a global microwave field, our structures only require the control of the SWAP in a site-selective manner, which is accomplished simply with a dc gate voltage that tunes the exchange coupling.

A Quantum Annealing Architecture with All-to-All Connectivity from Local Interactions
Wolfgang Lechner

The working principle of quantum annealing is to encode an optimization problem in the interaction matrix of a spin glass Hamiltonian. The ground state of this Hamiltonian is the solution of the problem which is reached by adiabatic switching. The fundamental challenge in building a universal quantum annealer is the competing requirements of fully programmable all-to-all connectivity and the quasi locality of the interactions between physical qubits. In this talk, I will present a programmable, scalable quantum annealing architecture with full connectivity, which can be implemented with local interactions only. The input of the optimization problem is encoded in local fields acting on an extended set of physical qubits. The output is encoded redundantly in the physical qubits, resulting in an intrinsic fault-tolerance. The architecture can be realized on various platforms with local controllability, including superconducting qubits, NV-centers, quantum dots, as well as atomic systems.

Looking and not looking at error in quantum annealing processors
Andrew King

Efforts to compare the performance of D-Wave quantum annealing processors with classical competition have evolved considerably in the past few years. Competition has gone from tabu and CPLEX to highly optimized and specialized solvers, and selection of input classes has come to include consideration of chaos, degeneracy, and other forms of error sensitivity. In this talk I will discuss the results of some recent benchmarking experiments that aim to limit and to study the effect of error. When precision requirements are limited in frustrated loop constraint satisfaction problems, we see a scaling advantage against thermal and combinatorial algorithms, which highlights the need for careful consideration of these issues.

Quasi-adiabatic quantum computing using the local-field response
Tatsuya Tomaru

I propose a computational method called local-field response, where spins evolve through responding to an effective field consisting of gradually decreasing transverse fields and spin-spin interactions, similar to what is done in adiabatic quantum computing (AQC). This method is partly quantum-mechanical, i.e., spins are treated as classical variables, but the response function of the spins to the effective field is determined a priori by referring to a quantum-mechanical calculation that was done for similar problems. Because the response function includes a quantum effect, the performance of the ground state being maintained in the time evolution is improved compared with the case without a priori information. I numerically checked the performance in an eight-qubit system by solving random-interaction problems of finding their ground states. The false probability decreased by about half as a result of using a priori information. The operation of this method is classical, but it has a quantum-mechanical advantage through a priori information. This method is practically useful because obtaining a complete quantum system is difficult as it stands.

How to find shortcuts to adiabaticity
Kazutaka Takahashi

Shortcuts to adiabaticity (STA) is known as a method accelerating the adiabatic dynamics of quantum systems and has now been under intensive study. We show that the STA can be derived from the quantum br achistochrone equation, which allows us to establish how fast and robust the obtained trajectory is. We also discuss possible deformations of the counterdiabatic Hamiltonian. They can be useful for complicated systems such as many-body ones and are important for practical applications.

On shortcuts to adiabaticity
Adolfo del Campo


Coherent optical Ising machines based on networks of optical parametric oscillators
Peter McMahon

In this contribution, we will present recent results and our future plans for developing a coherent optical Ising machine based on networks of optical parametric oscillators (OPOs). It is possible to engineer mutual couplings in a network of OPOs such that the optical loss of the network as a whole is proportional to the energy given by the classical Ising Hamiltonian on an arbitrary graph, where the problem instance is encoded by the particular choice of couplings between OPOs. It is predicted that such a network will oscillate in a configuration that represents the ground state or one of the low-energy local minima, yielding an approximate solution to the encoded Ising problem. We have recently implemented a proof-of-principle using a network of N = 4 OPOs, and have shown that this system reliably (no errors in 1,000 runs) finds the ground state of an encoded 4-vertex MAX-CUT problem, which has been mapped onto the Ising Hamiltonian [1]. An interesting open question is the extent to which coherent optical Ising machines can compete with the best classical algorithms for finding approximate solutions to NP-hard optimization problems, both in terms of speed and accuracy. While there are continuing efforts to study this question theoretically with both analytical and numerical calculations (e.g., [3, 4]), in this contribution we will primarily discuss our experimental studies. Our current focus is on investigating machine designs that may enable scaling to large numbers of OPOs (N >> 1000), and on trying to understand the operating mechanisms and limitations of this class of annealing machine. Measurement-feedback-based coherent Ising machines [4] seem to be experimentally realizable for N in the range 100-1000, and we will report on our efforts to construct a scalable machine of this type. [1] A. Marandi, et al. Nature Photonics 8, 937-942 (2014). [2] C. Fabre. Nature Photonics 8, 883-884 (2014). [3] Z. Wang, et al. Phys. Rev. A 88, 063853 (2013). [4] Y. Haribara, et al. arXiv:1501.07030

Simulated quantum annealing of multi-well potentials
Sebastiano Pilati

We investigate the performance of the quantum annealing optimisation method in various continuous model potentials with few and with many competing minima. The simulations performed using a projective quantum Monte Carlo (QMC) algorithm are compared with the finite-temperature path-integral QMC technique and with the classical simulated annealing. We show that the projective QMC algorithm is more efficient than the finite-temperature QMC technique, and that both are overwhelmed by classical annealing if this is performed with appropriate long-range moves. However, as the difficulty of the optimisation problem increases, classical annealing looses efficiency, while the projective QMC algorithm keeps stable performance and is finally the most effective optimisation tool. We discuss the implications of our results for the problem of testing the efficiency of adiabatic quantum computers using Monte Carlo simulations performed on classical computers.

Topological adiabatic invariant for discriminating mild versus steep gaps
Edmond Jonckheere

The main point of this presentation is that, depending on the problem, the adiabatic gap could be anywhere between two extremes: the constant gap case where the energy difference E1(s)-E0(s) is constant, all the way to the “super-steep” case where E1(s)-E0(s) abruptly decreases to its near vanishing minimum. Between the two extremes are intermediate cases where E1(s)-E0(s) decreases slowly to its minimum. The difference among the many cases is not numerical—it is morphological. The “super-steep” case can be visually characterized by the two lowest energy level curves having nearby pairs of inflection points occurring simultaneously on both the ground level and the first excited level. Instead of quantitatively characterizing such a situation, it is proposed to characterize it qualitatively—with an easily computable topological invariant that would anticipate such “dangerous” situation. This topological invariant is the number of pairs of transversal roots of E1(s)+E1”(s), where E1”(s) is the second derivative of the first excited level. It is noted that E1”(s) can be computed from a simple recipe that obviates the need for numerical computation of the second derivative. This topological invariant is a refinement of the Legendrian classification of the critical value curves of the numerical range of H0+iH1, where H0, H1 are the initial, final Hamiltonians. A nontrivial invariant implies existence of a short parameter space path that closes the gap in a process that is the reverse of the universal unfolding, such process does not have visual clues and the invariant is the only way to anticipate it. It will be shown that taking H0 to be the classical transverse field together with H1 the Hamming weight plus barrier Hamiltonian generates all gaps from the constant one to the super-steep one as the height of the barrier increases. But the position of the barrier is equally important to get the super-steep gap: it should be positioned such that significant tunneling through the barrier should occur around the end of the adiabatic run.

The flux qubit revisited
William Oliver

We revisit the design and fabrication of the persistent-current flux qubit [1]. By adding a high-Q capacitor, we dramatically improve its reproducibility and coherence times while retaining 800 MHz anharmonicity in the longest lived devices [2]. We first present a systematic study of 20 devices with varying capacitance and T1 values. The measured T1 times are well matched to a single model comprising charge and flux noise. We then discuss in a detail a device with 50 fF capacitance and T1 = 55 us. We identify quasiparticles as causing temporal variability in the T1, and we demonstrate the ability to pump these quasiparticles away [3]. The Hahn echo time T2E = 40 us does not reach the 2T1 limit, as is often observed with transmons coupled to resonators. We demonstrate that this is due to dephasing caused by the shot noise of residual thermal photons in the readout resonator. We use noise spectroscopy techniques to measure the lorentzian noise spectrum of the photon noise, and we then use CPMG dynamical decoupling to recover T2CPMG ~ 2T1 in a manner consistent with the spectrum. [1] W.D. Oliver and P.B. Welander, MRS Bulletin, 38, 816 (2013) [2] F. Yan et al., in preparation (2015). [3] S. Gustavsson et al., in preparation (2015).

On building a better quantum annealing device, and on fast adiabatic qubit gates using only sigma_z control
John Martinis


Experimental realization of adiabatic passage protocols using a superconducting circuit
Sorin Paraoanu

Adiabatic transfer protocols have one important advantage over pi-pulse population transfer, namely that the timing of the control pulses does not need to be precisely controlled. We show that the technique of stimulated Raman adiabatic passage can be implemented in a circuit QED consisting of a three level transmon read via a resonator. We demonstrate the transfering of population from the ground state of the transmon to the second excited state. Using this technique we realize a high fidelity quantum gate which can produce arbitrary superposition states between the ground state and the second excited state. We also study transfer protocols under a time-symmetric sequence of three adiabatic pulses, as well as combination of adiabatic and fast pulses.

Localisation in a model for quantum annealing
Gabriel Aeppli

LiHo1-xYxF4 in a transverse magnetic field was an initial testbed for the concepts of quantum annealing/adiabatic quantum computation AQC(1). Recent experiments where the emergence of many-body localisation effects are probed using spectroscopic hole burning are described here (2). The connection to external thermal baths plays a strong role in determining the visibility of these and other quantum effects (3). There is Fano interference between the internal spin bath and the localised levels, and this interference can be regulated (and even tuned through zero) via either the transverse field or the longitudinal, hole-burning, drive field. 1. Brooke et al, Science 284, 779(1999) and Nature 413, 610(2001) 2. Schmidt et al, PNAS 111, 3689(2014) and unpublished 3. Ghosh et al, Nature 425, 48(2003)