Itai Arad
National University of Singapore
Local reversibility in ground states of many-body local
Hamiltonians
Gapped ground states define quantum phases of matter at zero temperature
and govern the low-temperature physics of quantum many-body systems. Minimizing
the energy of local interactions, ground states often reflect strong properties
of locality such as the area law for entanglement entropy and the exponential
decay of correlations. In this talk I will present a novel characterization
of locality in quantum states, called `local reversibility'. It characterizes
the type of operations that are needed to reverse the action of a general
disturbance on the state. I will show that unique ground states of gapped
local Hamiltonian are locally reversible and use it to identify new fundamental
features of many-body ground states: exponential bounds on the fluctuations
of local order parameters, a rigorous bound on the quality of mean-field
approximations, and a new general inequality among critical exponents.
Todd Brun
University of Southern California
Quantum measurements by feedback control
The broadest notion of a quantum measurement is the generalized measurement,
defined by a set of measurement operators, and including a wide variety
of quantum operations. Generalized measurements include weak measurements,
where the measurement operators are close to the identity, and where each
measurement disturbs the state very little but also gives little information.
The limit of a suitable sequence of weak measurements is a continuous
measurement. Continuous measurements include such commonly used techniques
as photodetection, homodyne, and heterodyne measurements. It is possible
to decompose any generalized measurement into a continuous measurement
process; however, for most measurements this can only be done using feedback,
in which the weak measurement done depends on the outcomes of the earlier
weak measurements. For a two-outcome measurement, such a process has the
structure of a random walk on a curve in operator space. An important
question then arises: given a particular family of weak measurements that
can be done on a physical system, what set of generalized measurements
does this admit? We consider continuous measurements done by weak interactions
between the system and a sequence of qubit probes. If the interaction
Hamiltonian is fixed, this admits only a very limited class of generalized
measurements (where the measurement operators have only two singular values).
If the interaction Hamiltonian has a set of linear controls, a broader
class of measurements becomes possible; this class is characterized by
the closed Jordan algebras contained in the span of the Hamiltonian terms.
These are nonassociative operator algebras where the multiplication operation
is given by the anticommutator. This algebraic description is surprising,
and is in some ways parallel to the characterization of unitary transformations
in terms of Lie algebras.
Tommaso Calarco
University of Ulm
Controlled quantum many-body dynamics: nonlinearity, reversibility,
complexity
The control of quantum states is an important building block for fundamental
investigations and technological applications of quantum physics. However,
quantum many-body systems exhibit complex behaviors that make them difficult
to manipulate, in particular in the presence of intrinsic dephasing, decoherence
or decay. One strategy to control such quantum states is to implement
operations faster than the characteristic timescales of the prejudicial
processes, using for example optimal control theory (OCT). The speedup
can be exploited to experimentally realize elaborate manipulations, for
instance precisely controlled ultra-fast single electron spin gates using
specially designed microwave fields [1] or a sequence of state transfer
pulses for interferometry [2].
The maximum achievable speedup is influenced non-trivially by inter-particle
interactions, but their effect can be compensated for if many-body nonlinearity
is properly taken into account (see Fig. 1).
Reversibility of quantum dynamics can also be attained experimentally
via optimal control [4]. The bandwidth of the corresponding control pulses
allows for a characterization of quantum many-body processes [5], and
for dynamical discrimination between different level of complexity in
quantum many-body systems.
[1] J. Scheuer, X. Kong, R. Said, J. Chen, A. Kurz, L. Marseglia, J.
Du, P. Hemmer, S. Montangero, T. Calarco, B. Naydenov, F. Jelezko, New
J. Phys. 16, 093022 (2014).
[2] S. van Frank, A. Negretti, T. Berrada, T. Bücker, S. Montangero,
J.-F. Schaff, T. Schumm, T. Calarco, J. Schmiedmayer, Nature Communications
5, 4009 (2014).
[3] I. Brouzos, A. Streltsov, A. Negretti, R. Said, T. Caneva, S. Montangero,
T. Calarco, arXiv:1504.02858.
[4] C. Lovecchio, F. Schäfer, S. Cherukattil, A. K. Murtaza, I. Herrera,
F. Cataliotti, T. Calarco, S. Montangero, F. Caruso, arXiv:1405.6918;
in preparation.
[5] T. Caneva, A. Silva, R. Fazio, S. Lloyd, T. Calarco, S. Montangero,
Phys. Rev. A 89, 042322 (2014); S. Lloyd and S. Montangero, Phys. Rev.
Lett. 113, 010502 (2014).
With images: PDF
Bob Coecke
Oxford University
From quantum foundations to natural language meaning via
string diagrams
Earlier work on an entirely diagrammatic formulation of quantum theory,
which is soon to appear in the form of a textbook, has somewhat surprisingly
guided us towards providing an answer for the following question: how
do we produce the meaning of a sentence given that we understand the meaning
of its words? The correspondence between these seemingly far apart areas
was established in terms of string diagrams. This work has practical applications
in the area of Natural Language Processing.
Jens Eisert
Freie Universität Berlin
Certifying quantum devices
A key task in the study of quantum simulators and devices in quantum
information science is the certification that a device actually functions
in precisely the anticipated fashion. In this talk, I will present several
aspects of this task. We will start from notions of non-commutative compressed
sensing in order to economically perform quantum state tomography of approximately
low-rank states [1-3], as well as notions of quantum field tomography
[4]. We will then turn to elaborating on the question how the correct
state preparation can be achieved yet much more efficiently, and how this
can be done in a rigorous and at the same time experimentally friendly
way [5]. The final theme will be concerned with a make-or-break question
for quantum simulators: Namely, to what extent the functioning of a device
can be certified without the need of being able to efficiently predict
the outcome of a quantum simulation, which is supposedly out of reach
[6].
References:
[1] Phys. Rev. Lett. 105, 150401 (2010).
[2] arXiv:1504.04194 (2015).
[3] In preparation (2015).
[4] Nature Comm. 6, 7663 (2015).
[5] Nature Comm. 7 (2015).
[6] In preparation (2015).
K. Rajibul Islam
Harvard University
Measuring entanglement entropy in Bose-Hubbard systems
In recent years, entanglement has emerged as a central concept in our
understanding of quantum many-body physics. Theoretically, it has been
intensely investigated to characterize quantum phases of matter, and probe
quantum criticality, non-equilibrium dynamics, and topological order.
Experimental measurement of entanglement in spatial degrees of freedom
in itinerant systems of delocalized particles, however, remains an outstanding
challenge. In this talk, I will present experimental results on measuring
entanglement in a Bose-Hubbard system of ultra-cold atoms by preparing
and interfering two copies of a quantum many-body state. This many-body
interference enables us to directly measure the quantum purity, second-order
Renyi entanglement entropy and mutual information without explicitly reconstructing
the quantum state.
Ivette Fuentes
University of Vienna
Relativity in the quantum lab
Quantum experiments are reaching relativistic regimes. Quantum communication
protocols have been demonstrated at long lenghts scales and experiments
are underway to distribute entanglement between Earth and Satellite-based
links. At these regimes the Global Positioning System requieres relativistic
corrections. Therefore, it is necessary to understand how does motion
and gravity will affect long-range quantum experiments. Interestingly,
relativistic effects can also be observed at small lengths scales. Some
effects have been demonstrated in superconducting circuits involving boundary
conditions moving at relativistic speeds and quantum clocks have been
used to measure time dilation in table-top experiments. In this talk I
will present a formalism for the study of relativistic effects on quantum
technologies. This formalism is also applicable in the development of
new quantum technologies that can be used to deepen our understanding
of physics in the overlap of quantum theory and relativity. Examples include
gravimeters, accelerometers and spacetime probes underpinned by quantum
field theory in curved spacetime.
Jay M. Gambetta
IBM TJ Watson Lab USA
Progress in superconducting qubits: Detecting arbitrary single-qubit
errors in a planar sublattice of the surface code
I will review IBM’s current approach towards quantum computing with
superconducting qubits. The goal is to build a system using quantum error
correction
schemes based on rotated surface codes, which has a high error threshold,
requires only nearest-neighbor qubit interactions, and uses simple syndrome
extraction circuits. I will discuss our results on achieving high fidelity
two- and single- quit gates, long coherence times, and our recent experimental
demonstrating the [[2,0,2]] code on a 2x2 square lattice of superconducting
qubits.
Kurt Jacobs
University of Massachusetts
Completing Fermi's Golden Rule: the origin of rate equations in open
quantum systems
Fermi's golden rule is widely used, and the resulting transition rates
are an important part of the thermal behaviour of open quantum systems.
But this rule is curious because it is valid outside the regime in which
it is derived: It is derived only for short times and for off-resonant
transitions but works for all times and for resonant transitions. Here
we show analytically that an interaction with a resonant, dense spectrum
induces a rate equation for all times, giving essentially exact exponential
decay in the appropriate regime. From this analysis we are able to
extract the decay rate, which is indeed the rate of Fermi's golden rule
(with a small correction), the short, non-Markovian time period before
which the rate equation sets in, and determine the parameter regime required
for this behavior. Our analysis provides the start of a more solid foundation
on which to model thermal baths in terms of interactions with dense spectra.
Anthony J.
Leggett
University of Illinois at Urbana-Champaign
The mean-field method in the theory of superconductivity:
is it adequate for quantum-information applications?
For more than fifty years condensed-matter theorists have used for all
but the simplest problems the so-called mean-field (Bogoliubov-de Gennes)
method,which is usually justified by appeal to the concept of spontaneously
broken U(1) symmetry.In recent years this method has in particular been
applied to the analysis of schemes for
the implementation of topologically protected quantum computing,e.g.in
strontium ruthenate.In this talk,using a couple of simple examples,I argue
that the method is untrustworthy as soon as the Cooper pairs have nontrivial
degrees of freedom,and that it may be necessary to re-evaluate the results
obtained using it.
Daniel Lidar
University of Southern California
Quantum annealing and optimization: are we there yet?
In October 2011 USC and Lockheed-Martin jointly founded a quantum computing
center housing the first commercial quantum annealer built by D-Wave Systems.
These programmable processors use superconducting flux qubits and are
designed to minimize the energy of classical spin-glass models with as
many spins as qubits, an NP-hard problem with numerous applications. There
has been much controversy surrounding the D-Wave processors, questioning
whether they offer any advantage over classical computing. I will survey
our recent work on testing the processors for quantum effects, benchmarking
them against highly optimized classical algorithms, and improving their
performance using error correction.
References:
- T. Rønnow et al., “Defining and detecting quantum speedup”
Science 345, 420 (2014).
- S. Boixo et al., “Quantum annealing with more than one hundred
qubits”, Nature Phys. 10, 218 (2014).
- K. Pudenz et al., “Error corrected quantum annealing with hundreds
of qubits”, Nature Commun. 5, 3243 (2014).
- I. Hen et al., “Probing for quantum speedup in spin glass problems
with planted solutions”, arXiv:1502.01663
Klaus Mølmer
Aarhus University
The past state of a monitored quantum system
If a quantum system is monitored continuously in time, its wave function
or density matrix evolves by a combination of unitary and stochastic changes.
While conventional quantum theory accounts for this evolution and provides
the probabilities for the outcome of future measurements, it has been
widely ignored that monitoring of a system also supplements hindsight
knowledge about its earlier evolution.
In the talk I shall present how hindsight knowledge can be formally represented
as a time evolving (past) quantum state, which depends on both earlier
and later monitoring outcomes [1]. I will show examples of its application
to the analysis of real experiments [2,3,4], and I will discuss how some
questions of more foundational character relate to the new state concept
and formalism.
References:
[1] Søren Gammelmark, Brian Julsgaard, and Klaus Mølmer,
Phys. Rev. Lett. 111, 160401 (2013).
[2] P. Campagne-Ibarcq, L. Bretheau, E. Flurin, A. Auffèves,
F. Mallet, and B. Huard, Phys. Rev. Lett. 112, 180402 (2014).
[3] T. Rybarczyk, B. Peaudecerf, M. Penasa, S. Gerlich, B. Julsgaard,
K. Mølmer, S. Gleyzes, M. Brune, J. M. Raimond, S. Haroche, and
I. Dotsenko, Phys. Rev. A 91, 062116 (2015).
[4] D. Tan, S. Weber, I. Siddiqi, K. Mølmer, K. W. Murch, Phys.
Rev. Lett. 114, 090403 (2015).
Bertrand Reulet
Université de Sherbrooke
Generation of Entangled Microwave Radiation by Electron Shot Noise
A classical current in a conductor radiates a classical electromagnetic
field. We explore some properties of the field radiated by a conductor
when electron transport must be described by quantum mechanics, i.e. when
the electron current becomes quantum itself. We have measured the quadratures
of the field generated by a tunnel junction placed at ultra-low temperature
in the presence of ac+dc voltage bias. We demonstrate the existence of
two-mode squeezing as well as entanglement between quadratures at two
different frequencies, thus proving that the electron shot noise generates
a quantum electromagnetic field. We analyze our results by linking the
operators of the (bosonic) electromagnetic field with the (fermionic)
electron current operator. We show a very good agreement between our results
and the appropriate current-current correlator of the electron system.
Terence Rudolph
Imperial College, London
How Einstein and/or Schroedinger should have discovered Bell’s
Theorem
I will present some proofs of Bell’s theorem that are very simple
if one assumes “Einstein locality” as opposed to Bell’s
“local causality”. I will show that the proofs actually rule
out a different class of theories than do proofs based on local causality
and will also connect these proofs to a weakened variant of Spekkens’
notion of generalised contextuality.
Jeffrey H. Shapiro
Research Laboratory of Electronics, Massachusetts Institute of Technology
Quantum Imaging: Is it the future, or does it have a future?
Light is intrinsically quantum mechanical, and photodetection is a quantum
measurement. Consequently, all imaging is really quantum mechanical. It
has long been known, however, that the semiclassical theory of photodetection—in
which light is a classical field and the discreteness of the electron
charge results in photodetection shot noise—predicts measurement
statistics identical to those obtained from quantum theory when the illumination
is in a classical state, namely a Glauber coherent state or a classically-random
mixture of such states, and one of the standard detection paradigms is
employed, i.e., heterodyne, homodyne, or direct detection. (See [1] for
a review of quantum versus semiclassical photodetection.) Thus, because
experiments whose quantitative behavior is correctly predicted by two
disparate theories cannot distinguish between those two theories, it is
entirely appropriate that the term quantum imaging be reserved for imagers
whose quantitative understanding requires the use of quantum theory. (See
[2–4] for how a debate on this point has been settled with regards
to pseudothermal ghost imaging.) This talk will present a broad overview
of quantum imaging that will include—but go well beyond—ghost
imaging to encompass: the quantum limit of the camera; quantum enhancement
in laser-radar imaging; linear optics approaches to sub-Rayleigh imaging;
variations on the theme of optical coherence tomography; first-photon
imaging and related techniques; quantum reading and phase estimation;
and imaging with undetected photons. A recurring theme will be the degree
to which imagers originally developed in the quantum domain have classical
counterparts that can equal or exceed the capabilities of their quantum
predecessors. This quantum-mimetic behavior, as well as the overly-constrained
theoretical scenarios in which some quantum imagers have been shown to
have definite performance gains over their best classical-imaging competitors,
leads to the question posed in the title. It is a question that still
awaits a definitive answer.
References:
1. J. H. Shapiro, “The quantum theory of optical communications,”
IEEE J. Sel. Top. Quantum Electron. 15, 1547–1569 (2009).
2. J. H. Shapiro and R. W. Boyd, “The physics of ghost imaging.,”
Quantum Inf. Process. 11, 949–993 (2012).
3. Y. Shih, “The physics of ghost imaging: nonlocal interference
or local intensity fluctuation correlation?,” Quantum Inf. Process.
11, 995–1001 (2012).
4. J. H. Shapiro and R. W. Boyd, “Response to ‘The physics of
ghost imaging—nonlocal interference or local intensity fluctuation
correlation?’,” Quantum Inf. Process. 11, 1003–1011 (2012).
Irfan Siddiqi
University of California, Berkeley
Unraveling the Quantum Ensemble
We use continuous weak measurements in conjunction with Bayesian statistics
to reconstruct the real-time evolution of the wavefunction describing
a two-state system at the level of individual quantum trajectories. Both
the case of measurement induced collapse as well as driven unitary evolution
are investigated in a cavity coupled superconducting transmon qubit. A
variety of statistical metrics are extracted, including the most probable
path-analogous to the geodesic in space-time-between two points in Hilbert
space. Quantitative agreement with a path integral formalism for the trajectories
and their distribution is achieved, opening the door for new quantum control
protocols. Furthermore, extensions to many-body quantum systems may promise
a route toward more efficient quantum verification and validation of systems
with exponentially increasing complexity.
Rob Spekkens
Perimeter Institute
Experimental tests of noncontextuality without unwarranted
idealizations
To make precise the sense in which nature fails to respect classical
physics, one requires a formal notion of classicality. Ideally, such a
notion should be defined operationally, so that it can be subjected to
a direct experimental test, and it should be applicable in a wide variety
of experimental scenarios, so that it can cover the breadth of phenomena
that are thought to defy classical understanding. Bell's notion of local
causality fulfills the first criterion but not the second. The notion
of noncontextuality fulfills the second criterion, but it is a long-standing
question whether it can be made to fulfill the first. Previous attempts
to experimentally test noncontextuality have all presumed certain idealizations
that do not hold in real experiments, namely, noiseless measurements and
exact operational equivalences. In this talk, I will show how to devise
tests that are free of these idealizations and report on a photonic implementation
of one such test that rules out noncontextual models with high confidence.
Michael Thewalt
Simon Fraser University
28Si - a 'semiconductor vacuum' host for spin qubits
Highly enriched 28Si provides a nuclear spin free host material
into which impurities with electronic and/or nuclear spins having remarkably
long coherence times can be placed and manipulated. It also holds the
promise of inheriting the highly developed Si device nanotechnology to
enable the scalability of a qubit technology. However, 28Si has another
unique property which has nothing directly to do with spin - it has optical
transitions which are much narrower than the already sharp transitions
in natural Si. This provides us with new optical "handles" on
the electronic and nuclear spins of potential qubits in 28Si, including
the shallow donor impurities which have received much recent attention.
This has enabled ensemble measurements of record solid state coherence
times.
Robert Whitney
CNRS Grenoble
Maximum efficiency at given power output in 2 or 3 terminal quantum
thermoelectrics
Carnot efficiency is only achievable at zero power output. So what is
the maximum efficiency at a given finite power output? It appears that
this question is ill-defined in classical thermodynamics, but can be answered
with a quantum theory.
We use the Landauer scattering theory to find this maximum efficiency
for heat engines and refrigerators made of thermoelectric quantum systems.
We find the maximum efficiency at given power output for two-terminal
systems without energy relaxation [1]. This bound scales like the system's
transverse cross-section in units of the Fermi wavelength. For typical
parameters, it means one needs a heat-engine of nearly 1cm across to ensure
a power output of 100 Watts at an efficiency close to that of Carnot.
We use phenomenological models to explore whether this maximum can be
exceeded by two-terminal systems with relaxation [2], or by three-terminal
systems [3]. We have not yet found a system which can do so, although
open questions remain.
