Date: Tuesday, October 4, 2005

Who: Matthew Peacock

Seminar type: Tutorial

Where: Conference Room, Physics Annexe

When: 4-5pm

Abstract:
Modern communications systems are naturally described by linear matrix-vector equations. Essential properties of the system, such as the maximum information throughput and the signal-to-interference ratio of common receivers, are determined by the eigenvalues of the matrices involved. However, the matrices involved are random, which occurs, for example, when the signal from a mobile bounces off trees, buildings, etc., before reaching the base station. Therefore the eigenvalues of the system are also random. Determining the performance of the system is therefore is a complex problem. However, a remarkable thing occurs if you make every parameter (e.g., number of users, number of antennas, etc.) in the system infinitely large, while keeping the ratios of the parameters in proportion: the performance of this asymptotically large system becomes deterministic. Not only that, but the performance of non-infinite sized systems (which are complex to evaluate) is very well approximated by the performance of the infinite sized system.

In these tutorials, I hope to give a brief overview of the main results of random matrix theory which are applicable to communications systems, and show the derivation of a few simple results. I will also give an introduction to free probability theory, and demonstrate some applications of the theory.

Date: Friday, September 30, 2005

Who: Henry Haselgrove

Seminar type: Research

Where: Interaction Room, Physics Annexe

When: 12 Midday

Abstract:
I shall report on efforts to calculate the noise threshold for optical quantum computing. We are considering the recent proposal for combining aspects of the original KLM scheme for optical quantum computation, with the so-called cluster state model of computation. I will describe how one may go about designing an error-correction protocol in this scheme, for resistance to a range of noise types. Numerical threshold results will be given showing the amount of noise permissible for reliable optical quantum computing to occur. See http://www.arxiv.org/abs/quant-ph/0509060 for further details.

Date: Thursday, September 29, 2005

Who: Andrei Lopatenko

Seminar type: Tutorial Seminar

Where: Conference Room, Physics Annexe

When: 4-5pm

Outline

Date: Thursday, 22nd September

Who: Andrei Lopatenko

Seminar type: Tutorial Seminar

Time: 4-5pm

Where: Conference Room

Date: September 22, 2005

Who: Dan Browne

When: 1.00pm

Where: Interaction Room

Seminar type: Research seminar

Abstract:
Recently, the cluster state model of quantum computation has shown to be advantageous for linear optical quantum computation [1] and cavity QED schemes [2]. Cluster state quantum computation has shown to be amenable to fault-tolerant quantum computation techniques [3] using standard error-correcting codes, with an error threshold which competes well with the standard circuit model [4].

In this talk I will describe how the quantum correlations in the cluster states themselves can be used to correct for qubit loss errors, expected to be the dominant source of noise in the above proposals, provided particular tree-like structures are employed [5]. I will discuss numerical results indicating that the resource requirements for the scheme scale in a reasonable manner.

I will also discuss the surprising result that this simple model has an extremely high threshold of up to 50% loss, a limit which is imposed by the no-cloning theorem itself. This is further illustrated by the following observation. A simple modification of the scheme allows the potential for cloning theorem to be circumvented [6], giving protection against arbitrarily high loss rates (unfortunately this scheme is then incompatible with the above cluster state generation proposals!).

Towards the end of the talk I will discuss how these techniques may allow the development of new general error correction schemes.

Suggested reading:

• [1] M.A. Nielsen PRL 93 040503 (2004), D.E. Browne and T. Rudolph PRL 95 10501 (2005)
• [2] See for example, Y.L. Lim et al quant-ph/0508218
• [3] R. Raussendorf, PhD Thesis (Munich), M.A. Nielsen and C.M Dawson, PRA 71, 042323 (2005) , P. Aliferis and D.W. Leung, quant-ph/0503130
• [4] C.M. Dawson, H.L. Haselgrove and M.A. Nielsen, quant-ph/0509060
• [5] M. Varnava, D.E. Browne, T. Rudolph quant-ph/0507036
• [6] T. Stace, private communication

Date: Tuesday, 20 September

Who: Dan Browne

Seminar type: Tutorial Seminar

Time: 4-5pm

Where: Conference Room

Abstract:
Recently, Samson Abramsky and Bob Coecke introduced a “graphical calculus for quantum information” which captures pictorially the flow of quantum information through bi-partite entangling measurements. Beyond a mere pictorial representation, their formulation is a well-defined mathematical language. As well as its formal aspect the picture calculus gives a helpful visualisation of “what is going on” in measurement-based quantum computation.

No knowledge of category theory or measurement based quantum computation will be necessary to follow these talks.

Outline:
In this second tutorial, moving beyond simple teleportation style networks, I will show how additional unitary operations (and general linear maps) can be introduced to the picture calculus. Once this is done, all the tools are in place for a simple pictorial representation of measurement-based quantum computation. I will show how teleportation-based approaches are included almost intrinsically in the formalism, then, with the addition of one simple lemma, I will show how cluster state quantum computation can be explained / derived in this model in a clear and visual way.

References:

• Bob Coecke “Quantum Information-flow, concretely and axiomatically”, quant-ph/0506132
• Samson Abramsky and Bob Coecke “A categorical semantics of quantum protocols”, quant-ph/0402130
• Peter Selinger “Dagger compact closed categories and completely positive maps”, available from his web-site - google “peter
  selinger”.
• A beautifully clear introduction to category theory, written at a level accessible to high school students, is “Conceptual Mathematics” by Lawvere and Schanuel.

Date: September 16, 2005

Time: 12 Midday

Where: Interaction Room

Who: Brendon Lovett

Seminar type: Research seminar

Abstract:
I will describe a number of methods for performing quantum gates in solid-state nanostructures. The qubit is the spin of an extra electron, added to the nanostructure by, for example, n doping. The spin is very robust, with a decoherence time typically on the millisecond scale.

However, its interactions are weak, and so direct two qubit gates are slow. I shall introduce a method for transferring the information carried by the spin to exciton states, which can have mutual interactions of several meV - and then describe a specific protocol for performing a CPHASE gate between a pair of spins in a few picoseconds [1]. If there is time, I shall discuss a method for performing universal quantum computing with spins and excitons, which uses only global control [2, 3].

Suggested reading:

• [1] A. Nazir, B. W. Lovett, T. P. Spiller, S. D. Barrett, G. A. D. Briggs, PRL 93 150502 (2004)
• [2] S. C. Benjamin, B. W. Lovett and J. H. Reina, PRA 70 060305 (2004)
• [3] B. W. Lovett, quant-ph/0508192

Date: Thursday, 15 September

Who: Dan Browne

Seminar type: Tutorial Seminar

Time: 4-5pm

Where: Conference Room

Abstract:
Recently, Samson Abramsky and Bob Coecke introduced a “graphical calculus for quantum information” which captures pictorially the flow of quantum information through bi-partite entangling measurements. Beyond a mere pictorial representation, their formulation is a well-defined mathematical language. As well as its formal aspect the picture calculus gives a helpful visualisation of “what is going on” in measurement-based quantum computation.

No knowledge of category theory or measurement based quantum computation will be necessary to follow these talks.

Outline:
Taking the flow of quantum information in teleportation as a starting point, I will introduce the Abramsky and Coecke’s “graphical calculus” and show how it allows a simple and immediate analysis of complex networks of Bell state measurements. The picture calculus can be more formally described using “category theory”, a comparitively lesser known branch of mathematics which is a language for reasoning about mathematical structures and maps between them in an abstract way. At the end of this first talk I will introduce key concepts of category theory and show how they relate to the picture calculus.

References:

• Bob Coecke “Quantum Information-flow, concretely and axiomatically”, quant-ph/0506132
• Samson Abramsky and Bob Coecke “A categorical semantics of quantum protocols”, quant-ph/0402130
• Peter Selinger “Dagger compact closed categories and completely positive maps”, available from his web-site - google “peter
  selinger”.
• A beautifully clear introduction to category theory, written at a level accessible to high school students, is “Conceptual Mathematics” by Lawvere and Schanuel.

Date: September 13, 2005

Who: Brendon Lovett

Time: 4-5pm

Place: Conference Room, Physics Annexe

Seminar type: Tutorial Seminar

Outline:
Quantum Computing Using Quantum Dots

• the exciton as a qubit
• coherent control of excitons using a laser
• interactions between qubits and two qubit gates

Date: Thursday, 8th September

Who: Brendon Lovett

Seminar type: Tutorial Seminar

Time: 4-5pm

Where: Conference Room

Outline:
Semiconductor Heterostructures

• envelope function model of electronic states
• subband formation
• confined states in 1, 2 and 3 dimensions
• optical selection rules
• excitons