Suppressing decoherence of quantum algorithms by jump codes

The stabilizing properties of one-error correcting jump codes are explored under realistic non-ideal conditions. For this purpose the quantum algorithm of the tent-map is decomposed into a universal set of Hamiltonian quantum gates which ensure perfect correction of spontaneous decay processes under ideal circumstances even if they occur during a gate operation. An entanglement gate is presented which is capable of entangling any two logical qubits of different one-error correcting code spaces. With the help of this gate simultaneous spontaneous decay processes affecting physical qubits of different code spaces can be corrected and decoherence can be suppressed significantly

LpL^p-generic cocycles have one-point Lyapunov spectrum

We show the sum of the first $k$ Lyapunov exponents of linear cocycles is an upper semicontinuous function in the $L^p$ topologies, for any $1 \le p \le \infty$ and $k$. This fact, together with a result from Arnold and Cong, implies that the Lyapunov exponents of the $L^p$-generic cocycle, $p<\infty$, are all equal.Comment: 8 pages. A gap in the previous version was correcte

Symmetrised Characterisation of Noisy Quantum Processes

A major goal of developing high-precision control of many-body quantum systems is to realise their potential as quantum computers. Probably the most significant obstacle in this direction is the problem of "decoherence": the extreme fragility of quantum systems to environmental noise and other control limitations. The theory of fault-tolerant quantum error correction has shown that quantum computation is possible even in the presence of decoherence provided that the noise affecting the quantum system satisfies certain well-defined theoretical conditions. However, existing methods for noise characterisation have become intractable already for the systems that are controlled in today's labs. In this paper we introduce a technique based on symmetrisation that enables direct experimental characterisation of key properties of the decoherence affecting a multi-body quantum system. Our method reduces the number of experiments required by existing methods from exponential to polynomial in the number of subsystems. We demonstrate the application of this technique to the optimisation of control over nuclear spins in the solid state.Comment: About 12 pages, 5 figure

Selfsimilarity and growth in Birkhoff sums for the golden rotation

We study Birkhoff sums S(k,a) = g(a)+g(2a)+...+g(ka) at the golden mean rotation number a with periodic continued fraction approximations p(n)/q(n), where g(x) = log(2-2 cos(2 pi x). The summation of such quantities with logarithmic singularity is motivated by critical KAM phenomena. We relate the boundedness of log- averaged Birkhoff sums S(k,a)/log(k) and the convergence of S(q(n),a) with the existence of an experimentally established limit function f(x) = lim S([x q(n)])(p(n+1)/q(n+1))-S([x q(n)])(p(n)/q(n)) for n to infinity on the interval [0,1]. The function f satisfies a functional equation f(ax) + (1-a) f(x)= b(x) with a monotone function b. The limit lim S(q(n),a) for n going to infinity can be expressed in terms of the function f.Comment: 14 pages, 8 figure

The impact of economic information on medical decision making in primary care

Background: Many general practitioners (GPs) are concerned about the increasing dominance of economic issues in major decisions about clinical care, and feel their opinions on economic matters have not been heard. It is unclear whether this information has any impact on everyday clinical practice in a primary care setting. Aim: To investigate GPs' perspectives on the use of economic information in medical decision making. Design of study: Cross-sectional survey. Setting: GP members of the West of Scotland Primary Care Research and Development Network (WestNet). Methods: Questionnaire survey sent to GPs by post and by email. Results: The overall response rate was 44%, favouring postal over email responses. All respondents indicated that economic information has previously influenced them and should be incorporated into their medical decision making. The most common source of this information was generated by local authorities such as health boards, primary care groups and local prescribing advisors – used by 80% of the respondents. However, publications, such as the &lt;i&gt;British Journal of General Practice&lt;/i&gt;, locally produced newsletters and prescribing formularies, and feedback from the General Practice Administration System for Scotland, were used as sources of economic information by 20%, 27% and 33%, respectively. Published materials – in particular, locally specific information and summarized information in leaflet format – were favoured (54%) in comparison to verbally presented material. Conclusions: GPs believe that economic information should be incorporated in medical decision making. The need for precise and summarized information, produced locally, has been highlighted. Better understanding towards the type of economic evidence GPs find useful and comprehensible is required

Zero-dimensional singular continuous spectrum for smooth differential equations on the torus

We study spectral properties of the flow x = 1/F(x,y), y = 1/λF(x,y) on the 2-torus. We show that, in general, the speed of approximation in cyclic approximation gives an upper bound on the Hausdorff dimension of the supports of spectral measures. We use this to prove that for generic pairs (F,λ) the spectrum of the flow on the torus is singular continuous with all spectral measures supported on sets of zero Hausdorff dimension

Experimental requirements for Grover's algorithm in optical quantum computation

The field of linear optical quantum computation (LOQC) will soon need a repertoire of experimental milestones. We make progress in this direction by describing several experiments based on Grover's algorithm. These experiments range from a relatively simple implementation using only a single non-scalable CNOT gate to the most complex, requiring two concatenated scalable CNOT gates, and thus form a useful set of early milestones for LOQC. We also give a complete description of basic LOQC using polarization-encoded qubits, making use of many simplifications to the original scheme of Knill, Laflamme, and Milburn.Comment: 9 pages, 8 figure

Experimentally obtaining the Likeness of Two Unknown Quantum States on an NMR Quantum Information Processor

Recently quantum states discrimination has been frequently studied. In this paper we study them from the other way round, the likeness of two quantum states. The fidelity is used to describe the likeness of two quantum states. Then we presented a scheme to obtain the fidelity of two unknown qubits directly from the integral area of the spectra of the assistant qubit(spin) on an NMR Quantum Information Processor. Finally we demonstrated the scheme on a three-qubit quantum information processor. The experimental data are consistent with the theoretical expectation with an average error of 0.05, which confirms the scheme.Comment: 3 pages, 4 figure