SCIENTIFIC PROGRAMS AND ACTIVITIES

December 18, 2014
THE FIELDS INSTITUTE
FOR RESEARCH IN MATHEMATICAL SCIENCES
20th ANNIVERSARY YEAR
CQIQC/Toronto Quantum Information Seminars
QUINF 2011-12

held at the Fields Institute , 3rd Floor Stewart Library

Organized by Hoda Hossein-Nejad, 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) by-passes 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
non-standard date and time

Holger Hofmann (University of Hiroshima)

Weak measurements and quasi-realities: explaining the paradoxical statistics of quantum systems

I point out that the complex-valued 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 Trotter-Suzuki 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 sub-sections 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 sub-section 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 woman-made 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 Lieb-Robinson-type causality bounds, I'll explore the range of validity of the conjecture. Specific toy examples suggest that logarithmic-time 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 (Philipps-University, Germany)

Quantum mechanics inevitably implies that only a wave-function 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 many-body systems. Yet, it seem nearly impossible to realize such a "quantum-state tomography" for interacting many-body systems.

I will overview the latest development in this field and explain how many-body theory and quantum optics [1] can be systematically combined to produce a new level of laser spectroscopy. In particular, I will show why the light-matter interaction has an inherent capability to directly excite targeted many-body states through light source's
quantum-optical fluctuations.[2] This leads to a precise excitation and characterization of desired many-body states, as the first steps toward the many-body quantum-state tomography.

To characterize the quantum-optical response experimentally, one simply needs to collect a massive set of optical responses [3] to classical laser excitations. The quantum-optical responses can be projected from the classical data set by applying the so-called cluster-expansion transformation [4] (CET). As a proof of principle, I will analyze quantum-well measurements by CET projecting their
quantum-optical absorption to Schr¨odinger's cat-state sources. The results expose a completely new level of many-body 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 many-body configurations from nonlinear absorption in semiconductor quantum wells, Phys. Rev. Lett. 104, 247401 (2010).
[4] M. Kira and S.W. Koch, Cluster-expansion 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¨odinger-cat states, Nature Physics 7, 799-804 (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 many-body systems. On the other hand, these systems can be seen as arrays of "micro-laboratories" 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 polynomial-time 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 non-standard 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 no-cloning 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 Stern-Gerlach-type 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 information-theoretic 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 non-standard date and time
Hari Manoharan Stanford University
Supersymmetric Quantum Nanostructures

Embedded into the topology of our universe lurks a subtle yet far-reaching spectral ambiguity. There exist drum-like 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 two-dimensional 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 custom-built scanning tunneling microscope, operating at low temperature in ultrahigh vacuum, is used to assemble nanostructures atom-by-atom 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 Einstein-Podolsky-Rosen 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 measurement-update 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 Long-Lifetime 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 plausibly-sized 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 light-harvesting proteins for an exceptionally long time, hundreds of femtoseconds at physiological temperatures. This leads to speculations about the presence of quantum-mechanical 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 light-harvesting protein we measured.

Sept 20, 2011
11:10 AM

Man-Duen 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 [2-4]. 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 [7-10] - 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 - light-harvesting 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. Aspuru-Guzik, 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).