
THE FIELDS
INSTITUTE
FOR RESEARCH IN MATHEMATICAL SCIENCES
20th
ANNIVERSARY
YEAR

CQIQC/Toronto
Quantum Information Seminars
QUINF 201112
held at the Fields Institute , 3rd Floor Stewart Library
Organized
by Hoda HosseinNejad, Yasaman Soudagar

The CQIQC/Toronto
Quantum Information Seminar  QUINF  is held roughly
every two weeks to discuss ongoing work and ideas about
quantum computation, cryptography, teleportation, et cetera.
We hope to bring together interested parties from a variety
of different backgrounds, including math, computer science,
physics, chemistry, and engineering, to share ideas as
well as open questions. 

PAST TALKS

June 29, 2012
11:10 AM

Michael
Revzen (Technion  Israel Institute of Technology)
Classical and Quantum State Reconstruction
Computer assisted tomography (CAT scan) technique for reconstruction
of material density, \rho(x,y), is compared with reconstruction
scheme for physical state the phase space density, \rho(q,p)
of our classical system and the Wigner function for the quantum
one. All require the inversion of the Radon transform. A purely
quantum
approach based on mutual unbiased bases (MUB) bypasses the
Radon transform is also given.
The talk includes accounts of all concepts: State Reconstruction,
CAT scan tomography, Wigner function, and MUB and should be
palatable to graduate physics students.

Monday June 4, 2012 11:10AM
Room MP 606,
60 St. George Street, Toronto
*Please note
nonstandard date and time

Holger Hofmann (University of Hiroshima)
Weak measurements and quasirealities: explaining the paradoxical
statistics of quantum systems
I point out that the complexvalued quantum statistics observed
in weak measurements may be understood as the quantum limit
of classical causality. In this limit, the quantum of action
defines a measure of logical tension between different measurement
contexts that might explain what Bohr meant when he claimed
that there is no quantum reality. It is then possible to explain
the strangeness of quantum effects as a new fundamental relation
between alternative measurement contexts.
[References: NJP 13, 103009 (2011) and NJP 14, 043031 (2012)]

May 18, 2012 11:10AM

Dominic Berry (Macquarie University, Australia)
Universality of the Heisenberg limit / Simulation using
quantum walks
This is a talk in two parts. In the first part I discuss recent
work challenging the Heisenberg limit, and present our results
showing that the Heisenberg limit is universal, provided one
takes into account lack of initial knowledge of the phase.
In the second part I present an approach to simulate Hamiltonian
evolution by using a Szegedy quantum walk. This provides an
improvement in efficiency that seems to be impossible using
a standard TrotterSuzuki approach.

May 3, 2012
2:00 PM

John Rarity (University of Bristol)
Can we make solid state quantum networks
The secure exchanging of cryptographic keys over fibre [1]
or free space [2] is now approaching a commercial reality
through advanced quantum cryptography systems. One key limitation
to all present quantum key distribution systems is the finite
range of a single quantum link and the inability to amplify
the fading signal by classical means. The quantum repeater
[3] has been suggested as a possible solution to this exponential
decrease of bit rate with distance. Ideal repeater schemes
extend the distance using "entanglement swapping"
and "teleportation" and by concatenating short entanglement
swapping subsections it is in principle possible to generate
entangled (correlated) bits over very long distances with
bit rate only limited by the losses in one short section.
If realised this would extend quantum key distribution out
to distances of thousands of kilometres. Each subsection
is linked to the next by an optical circuit which performs
a 'Bell' measurement between photons arriving from each direction.
Proof of principle experiments [4] carried out to date have
been limited to using quantum interference effects at a beamsplitter
to perform a limited Bell measurement with 25% success rate
when photons arrive simultaneously at the beamsplitter. These
quantum 'relays' are extremely inefficient and cannot extend
the range in practical system.

May 4, 2012
11:10 AM

Seth Lloyd (MIT)
Optimizing quantum transport
Photosynthetic systems have attained a high degree of efficiency
in transporting energy. This talk shows how this high efficiency
arises from a sophisticated interplay between quantum
coherence and decoherence. Too little quantum coherence or
too much leads to low efficiency, but at just the right level
of quantum coherence, energy transport becomes highly efficient,
a phenomenon called the `quantum Goldilocks effect.' I present
a simple theory of how biological systems optimize quantum
transport, and show how we can emulate photosynthesis to optimize
quantum transport in man and womanmade systems.

Apr 20, 2012
2:00 PM

Patrick Hayden (McGill University)
http://www.cs.mcgill.ca/~patrick/
Towards the fast scrambling conjecture
The theory of quantum error correction has focused attention
on the relationship between the relaxation timescales of black
holes and their information retention time. Motivated by the
consistency of black hole complementarity, Sekino and Susskind
have conjectured that no physical system can delocalize, or
"scramble", its internal degrees of freedom in time
faster than (1/T) log S, where T is temperature and S the
system's entropy. By considering a number of toy examples
and general LiebRobinsontype causality bounds, I'll explore
the range of validity of the conjecture. Specific toy examples
suggest that logarithmictime information scrambling is indeed
possible, while the adaptation of causality arguments to nonlocal
Hamiltonians excludes faster scrambling under quite general
hypotheses. (Joint work with Nima Lashkari, Douglas Stanford,
Matthew Hastings and Tobias Osborne.)

Feb 17, 2012
11:10 AM

Mackillo (Mack) Kira (PhilippsUniversity, Germany)
Quantum mechanics inevitably implies that only a wavefunction
measurement can provide the ultimate control over matter.
At the same time, the ascent of nanotechnology will eventually
depend on whether or not one can control the wave function
of interacting manybody systems. Yet, it seem nearly impossible
to realize such a "quantumstate tomography" for
interacting manybody systems.
I will overview the latest development in this field and explain
how manybody theory and quantum optics [1] can be systematically
combined to produce a new level of laser spectroscopy. In
particular, I will show why the lightmatter interaction has
an inherent capability to directly excite targeted manybody
states through light source's
quantumoptical fluctuations.[2] This leads to a precise excitation
and characterization of desired manybody states, as the first
steps toward the manybody quantumstate tomography.
To characterize the quantumoptical response experimentally,
one simply needs to collect a massive set of optical responses
[3] to classical laser excitations. The quantumoptical responses
can be projected from the classical data set by applying the
socalled clusterexpansion transformation [4] (CET). As a
proof of principle, I will analyze quantumwell measurements
by CET projecting their
quantumoptical absorption to Schr¨odinger's catstate
sources. The results expose a completely new level of manybody
physics that remains otherwise hidden.[5]
References
[1] M. Kira and S.W. Koch, Semiconductor quantum optics, (Cambridge
University Press, 2011).
[2] M. Kira and S.W. Koch, Phys. Rev. A 73, 013813 (2006);
S.W. Koch, M. Kira, G. Khitrova, and H.M. Gibbs, Nature Mat.
5, 523 (2006); M. Kira and S.W. Koch, Prog. Quantum Electr.
30, 155 (2006).
[3] R.P. Smith, J.K. Wahlstrand, A.C. Funk, R.P. Mirin, S.T.
Cundiff, J.T. Steiner, M. Schafer, M. Kira, and S.W. Koch,
Extraction of manybody configurations from nonlinear absorption
in semiconductor quantum wells, Phys. Rev. Lett. 104, 247401
(2010).
[4] M. Kira and S.W. Koch, Clusterexpansion representation
in quantum optics, Phys. Rev. A 78, 022102 (2008).
[5] M. Kira, S.W. Koch, R.P. Smith, A.E. Hunter, and S.T.
Cundiff, Quantum spectroscopy with Schr¨odingercat states,
Nature Physics 7, 799804 (2011).

Feb10, 2012
11:10 AM

Stefan Trotzky, University of Toronto
Creating, Manipulating and Detecting Entangled Spin Pairs
in Optical Superlattices
Over the past decade, ultracold atoms in optical lattices
have proven to provide versatile grounds for the study of
fundamental condensed matter phenomena. The ever increasing
number of detection and manipulation methods together with
the variety of accessible lattice geometries allows one to
gain deep insight into ground state properties, excitations
and dynamics of interacting manybody systems. On the other
hand, these systems can be seen as arrays of "microlaboratories"
in which few atoms can be controlled in a highly parallel
way.

February 3, 2012
11:10 AM

Keith Lee, University of Pittsburgh
Quantum Algorithms for Quantum Field Theories
Quantum field theory provides the framework for the Standard
Model of particle physics and plays a key role in many areas
of physics. However, calculations are generally computationally
complex and limited to weak interaction strengths. I shall
describe a polynomialtime algorithm for computing, on a quantum
computer, relativistic scattering amplitudes in massive scalar
quantum field
theories. The quantum algorithm applies at both weak and strong
coupling, achieving exponential speedup over known classical
methods at high precision or strong coupling. The study of
such quantum algorithms may also help us learn more about
the nature and foundations of quantum field theory itself.

Jan 27, 2012
10:00 AM
* Please note the nonstandard time

T.C. Ralph, Centre for Quantum Computation and Communication
Technology, University of Queensland.
Advances in Optical Quantum Computing
We will discuss some new ideas and new experiments in optical
quantum computing. In particular, we will present a new experiment
in which a small scale quantum computer calculates the eigenvalues
of an unknown matrix for the first time. Such an operation
has direct relevance to Shor's factoring algorithm. We will
also discuss the Boson Sampling problem, a classically hard
problem, that, in principle, can be emulated efficiently by
a simple optical quantum computer. We will examine the effect
of errors on this problem.

Jan
13, 2012
11:10 AM

David Gosset, Formerly MIT
Quantum Money from Knots
Quantum money is the idea of using quantum states as currency.
The first proposal for a quantum money scheme was developed
by Wiesner and in that scheme the quantum states used as bills
are unforgeable due to the nocloning theorem. However, Wiesner's
scheme requires communication with the bank each time a bill
is spent.
In this talk I will discuss a quantum money scheme where
bills can be spent without communicating with the bank (a
public key quantum money scheme). Our scheme uses the mathematical
theory of knots. This talk is based on joint work with Edward
Farhi, Avinatan Hassidim, Andrew Lutomirski, and Peter Shor.

Dec 02, 2011
1:10 PM

Markus
Muller Perimeter Institute
Undecidability in quantum measurements
A famous result by Alan Turing dating back to 1936 is that a
general algorithm solving the halting problem on a Turing machine
for all possible inputs and programs cannot exist  the halting
problem is undecidable. Formally, an undecidable problem is
a decision problem for which one cannot construct a single algorithm
that will always provide a correct answer in finite time. In
the talk, I show that the problem to determine whether sequentially
used identical measurement devices have outcomes that never
occur is undecidable. This is already true for SternGerlachtype
measurement devices with 9 outcomes. This result shows that
even very natural, apparently simple problems in quantum measurement
theory can be provably undecidable. In contrast, the corresponding
classical problem is decidable, by a reduction to a finite binary
semi group problem.
This is a joint work with Jens Eisert, Christian Gogolin, and
Martin Kliesch. 
Nov 25, 2011
11:10 AM

Damian
Abasto, University of Southern California
"Fidelity Approach to Quantum Phase Transitions"
Over the last 15 years a fruitful collaboration between techniques
and concepts from Quantum Information and Condensed Matter Physics
gave rise to ideas such as Density Matrix Renormalization Group
(DMRG), Topological Entanglement Entropy, Projected Entangled
Pair States (PEPs) and MERA. My talk will focus on one particular
area of interplay between Condensed Matter and Quantum Information,
which has been called Fidelity Approach to Quantum Phase Transitions
(QPTs). Distinguishing between two quantum states is at the
core of many quantum information processing tasks. The fidelity
quantifies such degree of distinguishability and it provides
a useful informationtheoretic framework that encompasses all
critical phenomena.
In this talk I will focus on its applicability to study QPTs
involving topological phases, and describe its advantages
and limitations. Time permitting I will also mention my joint
work with Masoud Mohseni and Seth Lloyd on Quantum Biology.

Nov
16, 2011
12:00 PM
Stewart Library,
Fields Institute
*Please note the nonstandard date and time 
Hari Manoharan Stanford University
Supersymmetric Quantum Nanostructures
Embedded into the topology of our universe lurks a subtle yet
farreaching spectral ambiguity. There exist drumlike manifolds
of different shape that resonate at identical frequencies, making
it impossible to invert a measured spectrum of excitations into
a unique physical reality. An ongoing mathematical quest has
recently compacted this conundrum from higher dimensions to
planar geometries. Inspired by these isospectral domains, we
introduce a class of quantum nanostructures characterized by
matching electronic structure but divergent physical structure.
We perform quantum measurements (scanning tunneling spectroscopy)
on these “quantum drums” (degenerate twodimensional
electrons confined by individually positioned molecules) to
reveal that isospectrality provides an extra topological degree
of freedom enabling the mapping of complete electron wavefunctions—including
all internal quantum phase information normally obscured by
direct quantum measurement.
The robustness of the technique stems from its connection
to supersymmetric quantum mechanics, where inequivalent “superpartner”
Hamiltonians produce equivalent energy spectra. The methods
are general and extensible to other nanostructures and fabrication
techniques, and we have recently used variants of these ideas
to experimentally detect superposition phase and the Berry
phase.
In these experiments we utilize the exciting technology of
atomic and molecular manipulation: a custombuilt scanning
tunneling microscope, operating at low temperature in ultrahigh
vacuum, is used to assemble nanostructures atombyatom to
generate versatile quantum laboratories at the spatial limit
of condensed matter.

Nov 11, 2011
11:10 AM

Robert Spekkens Perimeter Institute
Formulating Quantum Theory as a Causally Neutral Theory
of Bayesian Inference
Quantum theory can be thought of as a noncommutative generalization
of Bayesian probability theory, but for the analogy to be
convincing, it should be possible to describe inferences among
quantum systems in a manner that is independent of the causal
relationship between those systems. In particular, it should
be possible to unify the treatment of two kinds of inferences:
(i) from beliefs about one system to beliefs about another,
for instance, in the EinsteinPodolskyRosen or "quantum
steering" phenomenon, and (ii) from beliefs about a system
at one time to beliefs about that same system at another time,
for instance, in predictions or retrodictions about a system
undergoing dynamical evolution. I will present a formalism
that achieves such a unification by making use of "conditional
quantum states", a noncommutative generalization of conditional
probabilities. Elements of the conventional formalism, such
as sets of states, positive operator valued measures, quantum
operations and quantum instruments become special cases of
conditional states, and familiar formulas, such as Born's
rule, the expression for the ensemble average, the rule for
dynamical evolution, and the nonselective measurementupdate
rule become special cases of belief propagation. (Joint work
with Matthew Leifer)

Nov 4, 2011
1:10 PM

Hector Bombin, Perimeter Institute
By characterizing 2D topological stabilizer codes in terms
of 'lattice groups' on infinite lattices, we show that they
can all be characterized in terms of topological charges and
string operators. This is true either for subspace or subsystem
codes, and it has direct applications for error correction,
for example. Subspace codes are directly connected to topologically
ordered condensed matter systems, and we show that all 2D
topological stabilizer codes are locally equivalent to several
copies of one universal phase: Kitaev's topological code.

Oct 28, 2011
11:10 AM

David Snoke,
University of Pittsburgh
Superfluid Phase Transition of LongLifetime Polaritons
Polaritons are quasiparticles of electronic excitation in
semiconductor structures with extremely light mass, about four
orders of magnitude less than a free electron. Because of this
very light mass, polaritons show Bose quantum effects even at
moderate densities and temperatures from tens of Kelvin up to
room temperature. In the past five years, multiple experiments
have shown effects of polaritons analogous to Bose condensation
of cold atoms, such as a bimodal momentum distribution, quantized
vortices, Bogoliubov excitation spectrum, and spatial condensation
in a trap. In these experiments, though, the lifetime of the
polaritons has been just a little longer than their thermalization
time, which means that nonequilibrium effects play an important
role; in particular, the transition to superfluidity has been
smeared out rather than a sharp transition. In this talk I report
new results with polaritons that have very long lifetime compared
to their thermalization time. We see a discontinuous jump in
the properties of the polariton gas indicative of a true phase
transition, and we see ballistic transport over hundreds of
microns. 
Oct 21, 2011
11:10 AM

Daniel Gottesman, Perimeter Institute
Improving Telescopes With Quantum Repeaters
Interferometry among telescope arrays has become a standard
technique in astronomy, allowing greater resolving power than
would be available to any plausiblysized single telescope.
For radio frequencies, interferometry can be performed robustly
even between telescopes spread across the planet. Interferometry
between telescopes operating at infrared or optical frequencies
is also possible, but fewer photons arrive at these high frequencies,
making interferometry much more difficult. In today's IR and
optical interferometric arrays, photons arriving at different
telescopes must be physically brought together for the interference
measurement, limiting baselines to a few hundred meters at
most because of phase fluctuations and photon loss in the
transmission. I will discuss how to apply quantum repeaters
to the task of optical and infrared interferometry to allow
telescope arrays with much longer baselines than existing
facilities.

Oct 7, 2011
11:10 AM

Daniel Turner, University of Toronto
Measuring Quantum Coherence in Molecules, Semiconductors,
and Proteins using 2D Electronic Spectroscopy
Recent studies using 2D electronic spectroscopy have suggested
that electronic coherence is maintained in lightharvesting
proteins for an exceptionally long time, hundreds of femtoseconds
at physiological temperatures. This leads to speculations
about the presence of quantummechanical effects such as entanglement.
However, the experiment can also excite vibrational wavepackets,
whose signatures are almost identical to electronic coherences.
Here we examine how electronic and vibrational coherences
can be distinguished by careful
investigation of the cross peak oscillations in several different
samples. Our conclusion is that both electronic and vibrational
coherences are present in the lightharvesting protein we
measured.

Sept 20, 2011
11:10 AM

ManDuen Choi, University of Toronto
Positive Linear Maps through Quantum Computers
What on earth does it mean as a REAL quantum computer? We
seek the ways to go through the maze of quantum entanglements,
in the light of the very easy structure of positive linear
maps on matrix algebras.
This is an expository talk, in simple language of linear
algebra, to show some deep aspects of the quantum foundation.

Aug 26, 2011
11:10 AM

Peter Turner, University of Tokyo
Multipartite indistinguishability
The generation of indistinguishable multipartite states of
quantum systems is an important topic  such states are manifest
in all experiments exhibiting quantum interference, and are
the basis for many implementations of quantum information
processors. So far, experiments have been limited to few bosons
 here we investigate the question of how to test and/or
characterise the indistinguishability of many. We adopt a
particle picture for describing multipartite states of N identical
bosons. A distinction must be drawn between 'practical' indistinguishability
imposed by real detectors that are only sensitive to a subset
of the ostensibly complete set of degrees of freedom attributable
to each particle, and 'complete'
indistinguishability where those inaccessible degrees of freedom
are all in the same state. We show that these pictures are
compatible, in that they give rise to the same number of experimentally
accessible measurement outcomes. We will discuss several implications,
such as that informationally complete tomography in a practically
indistinguishable situation does not require exponentially
many measurements, as would be true in the completely distinguishable
case.
The hope is to generate a stimulating informal discussion
about the topic of multipartite indistinguishability and how
it can be understood.

Aug 19, 2011
11:10 AM

Andrew White, University of Queensland
Quantum biology, chemistry, maths and physics
In principle, we can use quantum mechanics to exactly describe
any system of quantum particles  from simple molecules to
unwieldy proteins (and beyond, see figure)  but in practice
this is impossible as the number of equations grows exponentially
with the number of particles. Recognising this, Richard Feynman
suggested that quantum systems be used to model quantum problems
[1]. For example, the fundamental problem faced in quantum
chemistry is the calculation of molecular properties, which
are of practical importance in fields ranging from materials
science to biochemistry. Within chemical precision, the total
energy of a molecule as well as most other properties, can
be calculated by solving the Schrödinger equation. However,
the computational resources required increase exponentially
with the number of atoms involved [1, 2].
In the late 1990's an efficient algorithm was proposed to
enable a quantum processor to calculate molecular energies
using resources that increase only polynomially in the molecular
size [24]. Despite the many different physical architectures
that have been explored experimentally since that time  including
ions, atoms, superconducting circuits, and photons  this
appealing algorithm was not demonstrated until last year.
I will discuss how we have taken advantage of recent advances
in photonic quantum computing [5] to present an optical implementation
of the smallest quantum chemistry problem: obtaining the energies
of H2, the hydrogen molecule, in a minimal basis [6]. We perform
a key algorithmic step  the iterative phase estimation algorithm
[710]  in full, achieving a high level of precision and
robustness to error.
I'll also report on our recent results in simulating quantum
systems in material science  phase transitions in topological
insulators  and in biology  lightharvesting molecules in
photosynthesis. Together this body of work represents early
experimental progress towards the long term goal of exploiting
quantum information to speed up calculations in biology, chemistry
and physics.
[1] R. P. Feynman, International Journal of Theoretical
Physics 21, 467 (1982). [2] S. Lloyd, Science 273, 1073 (1996).
[3] D. Abrams and S. Lloyd, Physical Review Letters 79, 2586
(1997).
[4] C. Zalka, Proceedings of the Royal Society of London A
454, 313 (1998).
[5] B. P. Lanyon, M. Barbieri, M. P. Almeida, et al., Nature
Physics 5,134 (2009).
[6] B. P. Lanyon, J. D. Whitfield, et al., Nature Chemistry
2, 106 (2010).
[7] D. A. Lidar and H. Wang, Physical Review E 59, 2429 (1999).
[8] A. AspuruGuzik, A. Dutoi, et al., Science 309, 1704 (2005).
[9] K. R. Brown, R. J. Clark, and I. L. Chuang, Physical Review
Letters97, 050504 (2006).
[10] C. R. Clark, K. R. Brown, et al., arXiv:0810.5626 (2008).


