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Dear All

Please make a note of Friday’s research seminar in your diaries. PLEASE NOTE THAT THE TIME AND VENUE ARE DIFFERENT FROM NORMAL – SEE BELOW!

Date: Friday 8th June

Who: Anders Sandvik, Boston University

Seminar type: Research Seminar

Time: 2pm

Where: Physics Annexe, CONFFERENCE ROOM, Room 407

Abstract:

Traditionally, quantum Monte Carlo simulations of spin hamiltonians have been carried out in the basis of the Sz eigenstates. Here Anders will discuss an alternative technique in which the ground state is projected out from a trial state in the valence bond basis. Thanks to the particular properties of the valence basis, this approach enables calculations of some quantities that are difficult to access with standard methods. In particular, triplet excitations at finite momentum can be studied. Their dispersion relation as well as matrix elements corresponding to the single-magnon peak in the dynamic structure factor can be calculated. Anders will present some results for 1D and 2D Heisenberg antiferromagnets.

Date: Friday 4 May

Who: Nick Menicucci

Seminar type: Tutorial

Time: 12pm

Where: Interaction Room

Abstract:
The Bloch representation of qubits is a particularly convenient way to visualize quantum states and their evolutions. Every point on the real three-dimensional Bloch sphere is a pure state, all states within the Bloch ball are valid mixed states, and every rotation corresponds to a Hilbert-space unitary. When generalizing this representation to higher-dimensional systems, none of these properties hold. For this picture to be useful, then, different intuition is needed. This tutorial is an introduction to the Bloch representation of quantum states with D > 2 and will emphasize the similarities and differences with the qubit case.

Date & time: Friday March 9 @ 12pm

Who: Peter Rohde

Seminar type: Research Seminar

Where: Interaction Room

Abstract:
Qubit loss and gate failure are a significant problem in many quantum computing architectures. Most notably this is the case in optical QC where photon loss, inefficient detection, inefficient state preparation, and non-determinsitic gates are a given. To combat these problems several authors have proposed schemes for tolerating qubit loss and/or gate failure. These include Nielsen’s cluster state approach to optical QC, Varnava et al’s ‘horticultural’ approach to loss tolerance, and Ralph et al’s parity encoding scheme. We demonstrate that while such schemes are very effective at tolerating qubit loss, they have the undesirable side-effect that they magnify the effects of other noise types, namely depolarizing noise. We show that there is a tradeoff relationship between the error- and loss-tolerance of such schemes. This places fundamental limitations on the degree of loss tolerance that is achievable in practise.

These observations motivate the question ‘can we say anything about the tradeoff between loss- and error-tolerance in a general scenario, rather than just for these specific protocols?’. We examine this question for the general case of non-degenerate codes, by deriving a generalization of the quantum Hamming bound. We derive the Hamming bound to explicitly include separate parameters for loss and depolarizing errors. From this follows an upper bound on the tradeoff between the number of loss and depolarizing errors a non-degenerate code can correct against.

References:

• Upper bounds on the tradeoff between loss and error rates in non-degenerate quantum error correcting codes, Peter Rohde, quant-ph/0605183
• Error tolerance and tradeoffs in loss- and failure-tolerant quantum computing schemes, Peter Rohde, Timothy Ralph, William Munro, quant-ph/0603130

Date & time: Friday March 9 @ 12pm

Who: Peter Rohde

Seminar type: Research Seminar

Where: Interaction Room

Abstract:
Qubit loss and gate failure are a significant problem in many quantum computing architectures. Most notably this is the case in optical QC where photon loss, inefficient detection, inefficient state preparation, and non-determinsitic gates are a given. To combat these problems several authors have proposed schemes for tolerating qubit loss and/or gate failure. These include Nielsen’s cluster state approach to optical QC, Varnava et al’s ‘horticultural’ approach to loss tolerance, and Ralph et al’s parity encoding scheme. We demonstrate that while such schemes are very effective at tolerating qubit loss, they have the undesirable side-effect that they magnify the effects of other noise types, namely depolarizing noise. We show that there is a tradeoff relationship between the error- and loss-tolerance of such schemes. This places fundamental limitations on the degree of loss tolerance that is achievable in practise.

These observations motivate the question ‘can we say anything about the tradeoff between loss- and error-tolerance in a general scenario, rather than just for these specific protocols?’. We examine this question for the general case of non-degenerate codes, by deriving a generalization of the quantum Hamming bound. We derive the Hamming bound to explicitly include separate parameters for loss and depolarizing errors. From this follows an upper bound on the tradeoff between the number of loss and depolarizing errors a non-degenerate code can correct against.

References:

• Upper bounds on the tradeoff between loss and error rates in non-degenerate quantum error correcting codes, Peter Rohde, quant-ph/0605183
• Error tolerance and tradeoffs in loss- and failure-tolerant quantum computing schemes, Peter Rohde, Timothy Ralph, William Munro, quant-ph/0603130

Date: THURSDAY 25th January

Who: Sean Barrett

Seminar type: Research Seminar

Time: 12 Midday

Where: Interaction Room

Abstract:
Single photon interference effects are of fundamental interest, and are central to many protocols for quantum information processing (QIP). In particular, effects such as photon bunching and ‘which-path’ erasure lie at the heart of many schemes for linear optics quantum computing, and hybrid matter-light QIP. Conventional folklore has that, in order to observe these effects, the photons in question must be identical, in particular that they have the same frequency. Recently, it has been shown that it is possible to observe interference between photons of different frequencies, provided one has photodetectors with sufficiently high temporal resolution. However, this places severe technical constraints on both the sources of these photons, and the detectors.

In this work, we propose a way of observing single photon interference effects between photons of different frequencies, which works even with low resolution detectors. The method is based on carefully controlling the temporal mode shape of the photons, and is roughly analogous to the stroboscopic principle that underlies temporal aliasing, the ‘waggon wheel effect’, and the optical frequency comb that was the subject of the 2005 Nobel prize in physics. The method could allow a much broader range of single photon emitters and matter qubit systems to be used in QIP.

Date: Friday 12th January 2007

Who: Andrew Scott

Seminar type: Research Seminar

Time: 12 Midday

Where: Interaction Room

Abstract:
We introduce a class of informationally complete positive-operator-valued measures which are, in analogy with a tight frame, “as close as possible”
to orthonormal bases for the space of quantum states. These measures are distinguished by an exceptionally simple state-reconstruction formula which allows “painless” quantum state tomography. Complete sets of mutually unbiased bases and symmetric informationally complete positive-operator-valued measures are both members of this class, the latter being the unique minimal rank-one members. Recast as ensembles of pure quantum states, the rank-one members are in fact equivalent to weighted 2-designs in complex projective space. These measures are shown to be optimal for (measurement-based) quantum cloning and quantum state tomography.

Date: Thursday 16 November

Who: Miguel Aguado

Seminar type: Tutorial Seminar

Time: 12-1pm

Where: Interaction Room

Abstract:
After a review of `classical’ techniques from topology (homotopy, homology, cohomology), some applications to QI will be discussed. A model of Quantum Computation based on topological ideas (see M. Freedman et al., quant-ph/0001071, 0001108) will be presented.

Date: Friday 10th November

Who: Lluis Masanes

Seminar type: Research Seminar

Time: 12 Midday

Where: Interaction Room

Abstract:
What is quantum in quantum key distribution (QKD)? All non-signaling theories that predict the violation of a Bell inequality share some features with QM: monogamy of correlations, impossibility of perfect cloning, and potentiality for secret communication. This allows for proving the security of some QKD protocols by only assuming the impossibility of arbitrarily fast signaling. In this framework, all the analysis is made at the level of macroscopic events preparations/measurements), hence, Alice and Bob need not trust their devices as long as they produce the desired classical correlations.
Because our assumptions are weaker we give more power to the Eavesdropper, however, it is still possible to get a rate of one secret bit per singlet, as if we where assuming the whole of QM! As a side result, we obtain a classical exponential De Finetti theorem, which makes the i.i.d. assumption no longer necessary in most of classical information theory applications.

Date: Tuesday 17th October

Who: Animesh Datta

Seminar type: Tutorial Seminar

Time: 4-5pm

Where: Conference Room

Abstract:
Part 2 will deal with the problem of reference frame alignment, which can be seen as an instance of parameter estimation in $\mathrm{SU}(2).$ We will look at some of the methods involved and discuss the results of the analysis. In particular, we will compare the form of the states that achieve the Heisenberg limits in the two problems: clock synchronization and reference frame alignment.

Date: Friday 13th October

Who: Animesh Datta

Seminar type: Research Seminar

Time: 12 Midday

Where: Interaction Room

Abstract:
The “power of one qubit” refers to a computational model that has access to only one pure bit of quantum information, along with n qubits in the totally mixed state. This model, though not as powerful as a pure-state quantum computer, is capable of performing some computational tasks exponentially faster than any known classical algorithm. One such task is to estimate with fixed accuracy the normalized trace of a unitary operator that can be implemented efficiently in a quantum circuit. We show that circuits of this type generally lead to entangled states, and we investigate the amount of entanglement possible in such circuits, as measured by the multiplicative negativity. We show that the multiplicative negativity is bounded by a constant, independent of n , for all bipartite divisions of the n+1 qubits, and so becomes, when n is large, a vanishingly small fraction of the maximum possible multiplicative negativity for roughly equal divisions. This suggests that the global nature of entanglement is a more important resource for quantum computation than the magnitude of the entanglement.