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**On the role of tunneling in quantum annealing**

Sergio Boixo

TBA

**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
http://arxiv.org/abs/1407.7863.

**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

TBA

**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

TBA

**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

TBA

**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)