Speakers


Michael Nielsen

Introduction to Quantum Information
In this sequence of three lectures I introduce the basic principles and notation of quantum mechanics, and illustrate these ideas with some applications to quantum information science. A special topic in the third lecture will be the density matrix formalism, which is widely used in the description of noisy quantum systems.

Alain Tapp

Grover's Algorithm and Applications
In 1996 Lov Grover gave the foundation of an exciting new algorithm for quantum computers. One of the most important classes of problems in computer science is the class NP. Roughly speaking it addresses all the problems that can be stated the following way. We have a function F:{0,1}ⁿ → {0,1} and an efficient classical algorithm that computes it. The problem is to find x such that F(x)=1. Sometimes there is an efficient solution to this problem but in general it is very hard. There are literally hundreds of problems that can be put in this hard class, from areas including optimization, scheduling, cryptography, theorem proving, combinatorics, etc. The most efficient algorithms that can solve this problem have a running time proportional to the number of possible inputs x which is in O(2ⁿ). Grover sketched an algorithm that solves the general problem in a time proportional to the square root of the number of inputs x, which is in O(2^(n/2)). In this talk I will discuss the generalization of Grover's algorithm discussed by Boyer, Brassard, Høyer and Tapp. I will also present the algorithm proposed by Brassard, Høyer, Mosca and Tapp that probabilistically counts the number of solution.

Richard Cleve

Quantum Communication Complexity I & II
We consider how quantum information affects the communication costs of various information processing tasks.

A distributed information processing task is one where two or more physically separated parties each receive some input data and they are required to compute some quantities based on this data. A simple two-party example is where each party receives a binary string and their goal is to determine whether or not the strings are identical. It is clear that this particular task cannot be accomplished without some communication occurring between the parties. In communication complexity, the amount of communication required to perform distributed information processing tasks is quantified.

We shall give examples of information processing tasks that can be accomplished with significant savings in communication when quantum resources are available. These include some intriguing nonlocal effects that were first discovered by John Bell in the 1960s, as well as more recent communication protocols which have connections with quantum algorithms. Taken together, these results complement the well-known fact that bits cannot be compressed by encoding them into qubits.

Daniel Gottesman

Quantum Cryptography
In the first hour, I will give an overview of different types of quantum cryptographic protocols. The most well-known application of quantum cryptography is quantum key distribution (QKD), and I will discuss a number of different protocols for that, including the BB84 protocol and the B92 protocol. I will also discuss two-party secure function computation, and show that quantum bit commitment is impossible. In the second hour, I will give an overview of the Shor-Preskill security proof for BB84.

Martin Rötteler

Quantum Error Correction
Methods for the stabilization of quantum systems against errors are essential for quantum information processing. Quantum error-correcting codes (QECCs) allow to detect and correct errors that are due to decoherence effects. The workhorse of the current theory of QECCs is the so-called stabilizer construction, which was derived by D. Gottesman and in an equivalent formulation by R. Calderbank, E. Rains, P. Shor, and N. Sloane. I will start with some small examples and then give a survey on stabilizer codes. A specific problem which will be addressed is how to construct efficient circuits for the encoding of stabilizer codes. When turning to operations on the encoded quantum information an important issue is how to avoid the propagation of errors since this could possibly derail the whole computation. The basic ideas of the resulting theory of fault-tolerant quantum computing will be presented.

Barry Sanders

Theoretical Quantum Optics
Quantum optics is one of the most promising quantum information technologies due to the following properties: (i) production of nonclassical field states, (ii) rapid and efficient detection schemes, (iii) weak decoherence, and (iv) the capacity for higher-order nonlinear transformations either deterministically or else probabilistically through detection and postselection. Successful quantum optics implementations of quantum information tasks include generation and verification of entangled states, quantum key distribution, quantum teleportation, and sharing quantum secrets, and one of the most exciting proposals for scalable quantum computation is the linear optical quantum computer, which is based on quantum optics technology.

This introduction to theoretical quantum optics will provide a basis for understanding quantum optics as it pertains to quantum information science. We will study the theory underpinning (a) various sources of light, including laser output fields and single photon generators, (b) nonlinear processing of light including parametric down conversion, squeezing, and the optical Kerr nonlinearity, (c) detection schemes including photon counters and homodyne detectors, and (d) quantum information storage with atoms. Both polarization-encoded qubit-based quantum information and amplitude-modulated continuous-variable quantum information will be presented along with important examples of their applications.

A basic knowledge of quantum information is assumed. Background knowledge in physics and knowledge of optics or quantum fields are NOT required.

Juan Pablo Paz

Decoherence
In these lectures I will give review the basic principles behind the process of decoherence. In the first lecture I will concentrate on the implication of decoherence to understand the origin of a classical world from a fundamentally quantum substrate. In the second lecture I will focus on describing the implications of decoherence in the context of quantum information processing.

David DiVincenzo

Solid State Quantum Computation
I will begin with a broad overview of the large variety of different approaches that are being taken to the implemetation of quantum information processing in the solid state. In the remainder of the first lecture, I will consider the particulars of the approach using individual spins in semiconductors. I will emphasize the special problems connected with quantum measurement and with gate implementations in this system, and how these probkems are being solved. In the second lecture I will explain Josephson junction qubits. I will emphasize that this is a novel system from the point of view of quantum control, in that the techniques of control are direct carry-overs of electrical engineering techniques into the quantum domain.

Jonathan Jones

Nuclear Magnetic Resonance
Nuclear magnetic Resonance (NMR) is arguably both the best and the worst technology we have for the implementation of small quantum computers. Its strengths lie in the ease with which arbitrary unitary transformations can be implemented, and the great experimental simplicity arising from the low energy scale and long time scale of radio frequency transitions; its weaknesses lie in the difficulty of implementing essential non-unitary operations, most notably initialisation and measurement. These lectures will explore both the strengths and weaknesses of NMR as a quantum technology, and describe some topics of current interest. This course is based on my lectures at the Les Houches Summer School (2003).

Chris Monroe

Ion Traps
Lecture I: Trapped ion quantum bits and entanglement schemes.
A collection of trapped ions is one of the most attractive hosts for a quantum computer. Appropriate electronic states of trapped ions can form nearly ideal quantum bits, and ions qubits can be entangled through their mutual Coulomb interaction, mediated by applied laser fields. This lecture will cover the rudiments of the trapped ion system, including the initialization and measurement of trapped ion quantum bits, and the discussion of several schemes to entangle trapped ion qubits. Several examples from experiments will be presented.

Lecture II: Scaling the ion trap quantum computer
There are serious challenges in the scaling of the ion trap quantum computer to interesting numbers of qubits. However, there exist proposals to scale this system based on the communication of quantum information between nodes of small numbers of ions, based on the physical shuttling of ions between nodes, and the use of photons to communicate quantum information. These proposals will be discussed, including recent experimental progress.

Posters


Jonathan Baugh

"NMR Quantum Computing in the Solid State"
Solid state NMR can provide a solution to the problems of state initialization and decoherence time that arise in liquid state quantum information processing. In realistic systems, the radio-frequency control should provide decoupling from the environment, in addition to the normal gate operations. We present one proposed method for accomplishing this, and experimental results of its implementation on a three-qubit solid-state system.

Jean Christian Boileau

"Polarization-Based Quantum Key Distribution Protocol Over Noisy Quantum Channel"
Experimentalists attempting to perform QKD over long distances must deal with inherent noise from optical fibers. If we neglect attenuation, the noise in the fiber can be represented as a time-dependent rotation of the photon's polarization states. To overcome this problem, some techniques have been explored: encoding the qubits in the phase of the photons, sending the photon back and forth through the fiber with the help of a Faraday mirror or using an operational system to systematically compensate the error(1). We propose two completely new protocols to cope with this problem, both based on decoherence-free subspace(2). We explain how they can be achieved experimentally using three or four photons per encoded qubit.

(1) Nicolas Gisin, Gregoire Ribordy, Wolfgang Tittel, and Hugo Zbinden, Rev. Mod. Phys. 74, 145 (2002).

(2)J.-C. Boileau, D. Gottesman, R. Laflamme, D. Poulin, and R. W. Spekkens, Phys. Rev. Lett. 92, 017901 (2004).

Kathy-Anne Brickman and Louis Deslauriers

"Trapped Cadmium Ions for Quantum Information Processing"
We report on the ground state laser cooling and the observation of low motional decoherence of ¹¹¹ Cd⁺ ions confined in rf (Paul) traps. Preparing the ion's motion in a pure state is an important requirement for many quantum information applications since the ions intereact through their collective quantum motion. We also discuss the implementation of high fidelity universal logic gates and the demonstration of some non-trivial quantum algorithms in a collection of trapped Cd⁺ ions.

Peter Brooke

"Decoherence Suppressed Subspaces"
We investigate encoding and manipulating a logical qubit constructed from physical qubits, which admit a decoherence-free subspace. This realistic study treats three identical two-level atoms that are coupled via the electric dipole-dipole interaction and the manipulation of the qubit is performed using a sequence of laser pulses. Timing of the pulses is critical---we use quantum trajectories to determine optimal timing of pulses based on the photodetection record. Although we employ an atomic model for creating and transforming a qubit, our results are relevant to generic techniques for exploiting decoherence-free subspaces for qubits.

Donny Cheung

"Improved Bounds for Approximate Quantum Fourier Transforms"
A new analysis of the performance of the approximate quantum Fourier transform (AQFT), leads to an improvement on the current bounds. It was previously established that to use the logarithmic-depth AQFT in a quantum algorithm instead of the regular QFT requires polynomially more applications of the AQFT. This new analysis shows that for sufficiently large n, the n-qubit AQFT effectively becomes a striaght replacement for the QFT altogether, with the approximation improving for the larger n.

Giulio Chiribella

"Efficient use of quantum resources for the transmission of a reference frame."
We introduce a new method for reducing the amount of resources which are needed in the transmission of a Cartesian reference frame using a system of N quantum spins. This method exploits equivalent representations of the rotation group, providing a remarkable improvement with respect to the presently known protocols.

Animesh Datta


The problem of generating classical correlations in a bipartite quantum system is considered. The input resource allowed is a 2 way communication over classical channels of finite capacities. The expression for the maximum attainable correlation is obtained. Its properties are analysed. It is shown to be single letterizable for seperable and pure states with infinite side communication. The trade offs of quantum and classical correlations in a system are also analysed. This is dubbed as the monogamy of entanglement

Ryu Ebisawa

"Quantum-key for quantum information"
Conventional quantum cryptographic protocols allow the secure transmission of classical information by distributing classical keys using quantum states. Once quantum information technology has been developed, secure transmission of quantum information itself will also be required. We propose a new concept, "quantum keys", for secure transmission of quantum information using entanglement. We introduce asymmetric distribution of quantum information, in which quantum information can be extracted by local operation and classical communications (LOCC) at one of the qubits but not at the other. This kind of encoding enables, even for bipartite cases, "unfair" distribution of quantum information such that one party's quantum information can be only used as a key (quantum key) to recover the original quantum information at the other party.

Simon Frederic

"Single Photon Sources for Fibre Based Quantum Cryptography: Semiconductor Quantum Dots in Microcavities"
To ensure the confidentiality of information transferred within many quantum cryptography protocols, a highly efficient source of single or entangled photons is required. At 1550nm, the wavelength of preference for fibre-based implementations, only one such source presently exists; the inherently inefficient faint laser pulse. In the work presented here we will describe our program to construct a highly efficient 1550nm single photon source based on site-selected InAs/InP single quantum dots. InAs/InP quantum dots have been used to demonstrate high quality single dot spectroscopy with emission in the near infrared. The nucleation sites for these quantum dots can be controlled with nanometre precision, without affecting the optical quality, using semiconductor nano-templating techniques. To implement these structures within a single photon emitter it is necessary to construct high finesse microcavities around individual dots. We will describe our latest results for the construction and optical characterisation of these high finesse microcavities.

Kaveh Khodjasteh

"Concatenated Dynamical Decoupling"
In this work we use an analogy between dynamical decoupling and quantum error correction codes to investigate the idea of concatenating dynamical decoupling pulses to obtain further cancellations of the error terms in the system-bath Hamiltonian. To this end we develop a series of renormalized Hamiltonians that are used to estimate the strength of the undesired interactions, after applying each layer of the dynamical decoupling pulse sequence. The sources of these Hamiltonians will be the errors due to the pulse imperfections (including the effects of the pulse width) and the errors due to the evolution of the bath between the application of pulses. We further present a criteria in terms of the system-bath interaction Hamiltonian strength, bath's internal Hamiltonian strength, the time between consecutive pulses, and the pulse width, for the overall usefulness of concatenating dynamical decoupling pulses against decoherence. We also compare these results with the threshold calculations in the quantum error correction literature.

Martin Laforest

"Is time travel a possible answer to the mystery of entanglement?"
Even though they never published the idea, C. Bennett and B. Schumacher came up with a new crazy explanation for the mystery of entanglement. Keeping the standard qubit teleportation circuit in mind, they proposed that the entanglement phenomenon can be seen as information flowing back and forth in time between the sender and the receiver. Although Bennett and Schumacher do not take this idea too seriously by calling this new proposal "recreational quantum mechanics", I have put some solid physical and mathematical footing to it. Suprisingly, I have discovered that this idea is not completely crazy.... Moreover, it can facilitate the understanding of teleportation and can be generalized to a high extent.

Marie Lalire

"Formalizing quantum algorithms and protocols:a process algebraic approach."
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components and assemble them so that they communicate and cooperate. For this purpose, an algebraic notation based on process algebras has been developed, with a formal semantics which transposes the postulates of quantum mechanics into computation and communication primitives.

Paul Lopata


Quantum cloning -- which is only applicable to sets of pairwise orthogonal states -- assumes that the initial states (to be copied) are not entangled with a common "blank state". If this assumption regarding entanglement is removed then it is possible to "copy" sets of states that are not necessarily pairwise orthogonal. This result is demonstrated using a certain natural class of entangled states and a relationship to probabilistic cloning is shown.

David Moehring

"Probabilistic Ion-Photon Entanglement: The best of both quantum worlds."
We report the first direct observation of entanglement between an ideal quantum memory represented by a single trapped atomic ion, and an ideal quantum communication channel carried by a single photon. Coincident quantum state measurements between the ion and its emitted photon directly verify the entanglement and violate Bell's inequality by greater than seven standard deviations. We also discuss our current work on remote ion entanglement and ultrafast two-qubit logic gates.

Osama Moussa

"Numerical Analysis and Experimental Proposal for Heat-bath Algorithmic Cooling"
Algorithmic cooling has been proposed to solve the initialization problem, which is a crucial challenge for scalable NMR quantum computing (QC). We present a numerical analysis, and a study of an experimental realization on a three-qubit system, of the heat-bath algorithmic cooling scheme[1]. In such a scheme, the system is described as a string of bits, in which the last bit is brought to thermal contact with a heat-bath at specific times. In the context of solid-state NMR QC; this system can be realized as a crystal of malonic-acid, in which a dilute fraction of 13C-labeled molecules act as the bit string, the protons throughout the crystal serve as the heat-bath, and thermal contact between one of the carbons and the protons can be achieved by selective cross-polarization. The experiment, which is in the implementation phase, is designed to achieve a polarization on one carbon bit equal to twice the thermal-equilibrium polarization of the proton-bath.

[1] Schulman, L.J. et al., "Physical limits of heat-bath algorithmic cooling", to be published.

Casey Myers

"Linear Optics Quantum Computing: creating the entangled states."
In the basic linear optics quantum computing scheme large entangled states are necessary to boost the teleportation success probability. In this poster we present a method to produce the basic controlled sign state (|CS₁>) from a parametric down converter. This is a proof in principle showing that we can use states accessible in the lab for LOQC.

Camille Negrevergne and Francis-Yan Cyr-Racine

"Quantum simulations with NMR Quantum Information Processors"
Liquid state Nuclear magnetic resonance techniques (NMR) provide ways to initialize, to manipulate and to read the quantum state of a set of coupled spins and have been used to implement small Quantum Information Processors (QIP). We present a method to use such a QIPs to simulate other quantum systems based on indirect measurement algorithms and the mapping of the algebra used to describe those systems into the Pauli operator algebra. We also show experimental results on the simulation of a simple fermionic system based on the Fano-Anderson model with a Trans-crotonic acid based NMR QIP.

Annika Niehage

"Quantum AG Codes over Non-Binary Fields"
Algebaic geometric codes have been studied well in classical coding theory. The advantage of these codes is that they can be decoded efficiently. R. Matsumoto constructed in [1] a sequence of good binary qunatum stabilizer codes without using the CSS construction.

We will present that, in a certain way, his consturction can be generalized to char p > 2 codes using field extensions via hyperelliptic curves, new stabilizer code bases with an inner product different from the standard one, and a down projection from GF(p^m) onto GF(p)^m which is a modified version of that of Ashikhmin and Knill in [2].

[1] R. Matsumoto, "Algebraic geometric construction of a quantum stabilizer code", quant-ph/0107129, August 2001

[2] A. Ashikhmin and E. Knill, "Nonbinary quantum stabilizer codes", IEEE Transactions on Information Theory Vol. 47 No. 7, November 2001

Masaki Owari

"Entanglement convertibility for infinite dimensional pure bipartite states"
It is shown that the order property of pure bipartite states under SLOCC (stochastic local operations and classical communications) changes fundamentally when dimensionality shifts from finite to infinite. In contrast to finite dimensional systems where there is no pure comparable state, the existence of infinitely many mutually SLOCC incomparable states is shown for infinite dimensional systems even under the bounded energy condition. These results show that the effect of the infinite dimensionality of Hilbert space, the "infinite workspace" property, remains even in physically relevant infinite dimensional systems.

Simon Perdrix

"State Transfer instead of Teleportation in Measurement-based Quantum Computation"
Quantum measurement is universal for quantum computation. The model of quantum computation introduced by Nielsen and further developed by Leung relies on a generalized form of teleportation. In order to simulate any n-qubit unitary transformation with this model, 4 auxiliary qubits are required. Moreover Leung exhibited a universal family of observables composed of 4 two-qubit measurements. We introduce a model of quantum computation via measurements only, relying on state transfer: state transfer only retains the part of teleportation which is necessary for computating. In order to simulate any n-qubit unitary transformation with this new model, only one auxiliary qubit is required. Moreover we exhibit a universal family of observables composed of 3 one-qubit measurements and only one two-qubit measurement. This model improves those of Nielsen and Leung in terms of both the number of auxiliary qubits and the number of two-qubit measurements required for quantum universality. In both cases, the minimal amounts of necessary resources are now reached: one auxiliary qubit (because measurement is destructive) and one two-qubit measurement (for creating entanglement).

Colm Ryan

"Fidelity decay as a measure of quantum chaos on an NMR quantum computer"
In classical mechanics, the distinction between regular and chaotic systems is clear - the distance in phase space between two trajectories which initially start close to each other, then grows exponentially in time. However, in quantum mechanics, unitary evolution preserves the distance between two states; so, the conventional definition looses meaning. Fidelity decay(FD), which is the overlap of the same initial state evolving under slightly different unitary evolutions is one measure proposed for measuring chaos in the quantum setting. Poulin et al. (2003) have presented an efficient circuit for measuring the FD which requires only one qubit in a pure state and the rest of the system in the maximally mixed state. Since this is very close to what we start with in NMR, the NMR quantum computer makes an ideal platform for testing this measure of quantum chaos. Simulations of the NMR experiment show we should be able to see a clear difference between regular and chaotic evolution. If successful, this will show that we have an efficient method for testing the sensitivity of systems to perturbations. This would be an important first criterion to test any proposed system for quantum computing.

Krister Shalm

"The Limitations of Quantum Process Tomography"
Can one obtain more information about a quantum system than process tomography allows? Using an interferometric setup, an alternative to process tomography was explored. Various dechorence processes were characterized by placing different decoherence mechanisms in the arms of an interferometer. This technique allows additional information to be obtained about a decoherence process beyond what traditional process tomography yields. Using this technique, it may be possible to develop a decoherence diagnostic tool for quantum systems.

Marcus Silva

"Erasure Thresholds for Efficient Linear Optics Quantum Computing"
Using a error models motivated by the Knill, Laflamme, Milburn[1] proposal for efficient linear optics quantum computing, erasure thresholds for the [[7,1,3]] Steane code are derived and verified through simulation. A novel method -- based on a Markov chain description of the erasure correction procedure -- is developed and used to calculate the recursion relation describing the error rate at different encoding levels from which the threshold is derived, matching threshold predictions by Knill, Laflamme and Milburn[2].

[1] E. Knill, R. Laflamme, and G. Milburn. A scheme for efficient quantum computation with linear optics. Nature, vol 409, pp 46--52, 2001.

[2] E. Knill, R. Laflamme, and G. Milburn. Thresholds for Linear Optics Quantum Computation. arxiv:quant-ph/0006120, 2000.

Prashant Singh

"Analysis of Quantum Dots in Modified Coulomb Potential"
Quantum theory is one of the most successful theories that have influenced the course of scientific progress during the twentieth century. It has presented a new line of scientific thought, predicted entirely inconceivable situations and influenced several domains of modern technologies; in addition to all this it has added a new dimension to the conceptual framework related to the microscopic systems. However, in spite of its enormous success it is baffling even to the hardcore physicists. The very notions of causality, determinism, and measurement need to be redefined and in spite of all this there are almost mysterious situations that are to be faced by anyone familiar with it.

In this paper we are putting forth a radical step in terms of reformulation of Coulomb Potential at low dimensionality to solve the long standing problem of Divergences. This reformulation of Coulomb at low dimensions is further tested by its application to Quantum Dots which are good candidates for testing the validity of the given reformulation. We have calculated energy eigen values and also solved Schroedinger Wave Equation for the modified potential to predict the behaviour of wave function which should be seen in the experiments on Quantum Dots. Hence this paper puts forth a new radical idea in Quantum Dot technology by modification of Coulomb Potential to predict new physics at the nanoscale.

Daniel Stick

"Micron-Scale Ion Traps for Quantum Computation"
Scalable ion trap quantum computing requires smaller and increasingly complex ion trap layouts, and has prompted recent research into new methods of production. Our research on the feasibility of a high aspect ratio trap using semiconductor fabricaion techniques has led us to develop a method of making extremely small ion traps out of GaAs. These offer the ability to make a large number of small traps with great flexibility in the layout. Efforts to test these traps are currently under way.

Muhammad Sabieh Anwar

"Preparing Pure Initial States from Para-Hydrogen"
We discuss the preparation of nearly pure initial states for quantum information processing in liquid NMR. These states are derived from the singlet nuclear spin state of para-hydrogen which is controllably and coherently added to a precursor molecule. Our method circumvents the need for assembling pseudo-pure states in implementing quantum information processing tasks. Our highly polarized system is well above the entanglement threshold, silencing claims that NMR can be explained by a classical model.

Anocha Yimsiriwattana

"Distributed quantum computing: A distributed Shor algorithm"
We present a distributed implementation of Shor's quantum factoring algorithm on a distributed quantum network model. This model provides a means for small capacity quantum computers to work together in such a way as to simulate a large capacity quantum computer. In this paper, entanglement is used as a resource for implementing non-local operations between two or more quantum computers. These non-local operations are used to implement a distributed factoring circuit with polynomially many gates. This distributed version of Shor's algorithm requires an additional overhead of O((log N)²) communication complexity, where N denotes the integer to be factored.