Parallelism for Quantum Computation with Qudits

Robust quantum computation with d-level quantum systems (qudits) poses two requirements: fast, parallel quantum gates and high fidelity two-qudit gates. We first describe how to implement parallel single qudit operations. It is by now well known that any single-qudit unitary can be decomposed into a sequence of Givens rotations on two-dimensional subspaces of the qudit state space. Using a coupling graph to represent physically allowed couplings between pairs of qudit states, we then show that the logical depth of the parallel gate sequence is equal to the height of an associated tree. The implementation of a given unitary can then optimize the tradeoff between gate time and resources used. These ideas are illustrated for qudits encoded in the ground hyperfine states of the atomic alkalies $^{87}$Rb and $^{133}$Cs. Second, we provide a protocol for implementing parallelized non-local two-qudit gates using the assistance of entangled qubit pairs. Because the entangled qubits can be prepared non-deterministically, this offers the possibility of high fidelity two-qudit gates.Comment: 9 pages, 3 figure

Asymptotically Optimal Quantum Circuits for d-level Systems

As a qubit is a two-level quantum system whose state space is spanned by |0>, |1>, so a qudit is a d-level quantum system whose state space is spanned by |0>,...,|d-1>. Quantum computation has stimulated much recent interest in algorithms factoring unitary evolutions of an n-qubit state space into component two-particle unitary evolutions. In the absence of symmetry, Shende, Markov and Bullock use Sard's theorem to prove that at least C 4^n two-qubit unitary evolutions are required, while Vartiainen, Moettoenen, and Salomaa (VMS) use the QR matrix factorization and Gray codes in an optimal order construction involving two-particle evolutions. In this work, we note that Sard's theorem demands C d^{2n} two-qudit unitary evolutions to construct a generic (symmetry-less) n-qudit evolution. However, the VMS result applied to virtual-qubits only recovers optimal order in the case that d is a power of two. We further construct a QR decomposition for d-multi-level quantum logics, proving a sharp asymptotic of Theta(d^{2n}) two-qudit gates and thus closing the complexity question for all d-level systems (d finite.) Gray codes are not required, and the optimal Theta(d^{2n}) asymptotic also applies to gate libraries where two-qudit interactions are restricted by a choice of certain architectures.Comment: 18 pages, 5 figures (very detailed.) MatLab files for factoring qudit unitary into gates in MATLAB directory of source arxiv format. v2: minor change

Isobaric multiplet yrast energies and isospin non-conserving forces

The isovector and isotensor energy differences between yrast states of isobaric multiplets in the lower half of the $pf$ region are quantitatively reproduced in a shell model context. The isospin non-conserving nuclear interactions are found to be at least as important as the Coulomb potential. Their isovector and isotensor channels are dominated by J=2 and J=0 pairing terms, respectively. The results are sensitive to the radii of the states, whose evolution along the yrast band can be accurately followed.Comment: 4 pages, 4 figures. Superseeds second part of nucl-th/010404

Ethical accountability and routine moral stress in SEN professionals

This small-scale interview study considers experiences, difficulties and dilemmas of local SEN (Special Educational Needs) professionals such as SEN Caseworkers, and examines the neglected ethical dimensions of their role. It argues that fostering ‘ethical knowledge’ (Campbell, 2003), rather than an increase in prescriptive guidance, will enable more productive partnerships between professionals, and between parents and professionals respectively. The study demonstrates a SEN professionalism that is able to respond to moral complexity and that is willing to carry significant personal and moral burdens in order to meet the needs of children and young people with SEN. It also highlights experiences of routine moral stress (Cribb, 2011) which are not adequately addressed by either individuals or their organisations

The spirit of sport: the case for criminalisation of doping in the UK

This article examines public perceptions of doping in sport, critically evaluates the effectiveness of current anti-doping sanctions and proposes the criminalisation of doping in sport in the UK as part of a growing global movement towards such criminalisation at national level. Criminalising doping is advanced on two main grounds: as a stigmatic deterrent and as a form of retributive punishment enforced through the criminal justice system. The ‘spirit of sport’ defined by the World Anti-Doping Agency (WADA) as being based on the values of ethics, health and fair-play is identified as being undermined by the ineffectiveness of existing anti-doping policy in the current climate of doping revelations, and is assessed as relevant to public perceptions and the future of sport as a whole. The harm-reductionist approach permitting the use of certain performance enhancing drugs (PEDs) is considered as an alternative to anti-doping, taking into account athlete psychology, the problems encountered in containing doping in sport through anti-doping measures and the effect of these difficulties on the ‘spirit of sport’. This approach is dismissed in favour of criminalising doping in sport based on the offence of fraud. It will be argued that the criminalisation of doping could act as a greater deterrent than existing sanctions imposed by International Federations, and, when used in conjunction with those sanctions, will raise the overall ‘price’ of doping. The revelations of corruption within the existing system of self-governance within sport have contributed to a disbelieving public and it will be argued that the criminalisation of doping in sport could assist in satisfying the public that justice is being done and in turn achieve greater belief in the truth of athletic performances

Proposal for generalised Supersymmetry Les Houches Accord for see-saw models and PDG numbering scheme

The SUSY Les Houches Accord (SLHA) 2 extended the first SLHA to include various generalisations of the Minimal Supersymmetric Standard Model (MSSM) as well as its simplest next-to-minimal version. Here, we propose further extensions to it, to include the most general and well-established see-saw descriptions (types I/II/III, inverse, and linear) in both an effective and a simple gauged extension of the MSSM framework. In addition, we generalise the PDG numbering scheme to reflect the properties of the particles.Comment: 44 pages. Changed titl