Cyclic Quantum Error-Correcting Codes and Quantum Shift Registers

We transfer the concept of linear feed-back shift registers to quantum circuits. It is shown how to use these quantum linear shift registers for encoding and decoding cyclic quantum error-correcting codes.Comment: 18 pages, 15 figures, submitted to Proc. R. Soc.

The Kinetics of Volatile Lead Compound Formation During Simulated Hazardous Waste Incineration

Air pollution from fine metal-containing particles (and vapors) formed during hazardous waste incineration has attracted less attention than other incinerator emissions. Recently, however, metal pollution has become subject to more stringent regulations. The U.S. Environmental Protection Agency has announced limitations on the emissions of ten toxic metals. Pollution control systems that will effectively remove fine (submicron) metal-containing particles from flue gases are difficult to construct. Incinerators have not been designed or operated to minimize the formation of such particles. Industrial-scale incineration testing has produced anomalous results for air emissions of lead and other metals. To gain a better fundamental understanding of the generation of metal emissions, the kinetics of the formation of volatile pollutants in simulated incinerator kilns were experimentally examined as a function of temperature and acid gas concentration. The chemical reactions between lead oxide, a common toxic metal found in hazardous waste streams, and hydrogen chloride, commonly produced in hazardous waste incineration are the specific focus. Descriptive models were constructed of the kinetics and mass transport of the lead dichloride and oxychloride intermediate compounds that were found to be generated. Fine particulate matter composed of lead dichloride was produced. At temperatures between 260 and 310°C, the hydrochloridation reaction kinetics were measured, and an apparent activation energy of 22 kcal/mol was obtained. At 300°C and apparent reaction rate of 10-7 mol/(cm2.s) was found at 2000 ppm of HCl. At higher temperatures, the formation of lead dichloride was diffusionally controlled, principally in the liquid or solid ash phases, and, until 600°C was reached, changed little from the 10-7 mol/(cm2.s) rate in approximately 30- to 60-min batch hydrochloridation experiments. An interesting phenomenon was found in that at temperatures greater than 590°C, a glassy surface ash phase was formed while at temperatures between 450 and 590°C, distinctly liquid ash phase was formed. The glassy ash phase grew rapidly in thickness and exhibited a lower volatility of lead dichloride than did the liquid phase formed at lower temperatures. This has interesting implications for incineration because this research has revealed a situation in which a higher volatility product is formed at lower temperature, contrary to most expectations and to purely equilibrium considerations

Magnetic qubits as hardware for quantum computers

We propose two potential realisations for quantum bits based on nanometre scale magnetic particles of large spin S and high anisotropy molecular clusters. In case (1) the bit-value basis states |0> and |1> are the ground and first excited spin states Sz = S and S-1, separated by an energy gap given by the ferromagnetic resonance (FMR) frequency. In case (2), when there is significant tunnelling through the anisotropy barrier, the qubit states correspond to the symmetric, |0>, and antisymmetric, |1>, combinations of the two-fold degenerate ground state Sz = +- S. In each case the temperature of operation must be low compared to the energy gap, \Delta, between the states |0> and |1>. The gap \Delta in case (2) can be controlled with an external magnetic field perpendicular to the easy axis of the molecular cluster. The states of different molecular clusters and magnetic particles may be entangled by connecting them by superconducting lines with Josephson switches, leading to the potential for quantum computing hardware.Comment: 17 pages, 3 figure

Correcting for Distortions due to Ionization in the STAR TPC

Physics goals of the STAR Experiment at RHIC in recent (and future) years drive the need to operate the STAR TPC at ever higher luminosities, leading to increased ionization levels in the TPC gas. The resulting ionic space charge introduces field distortions in the detector which impact tracking performance. Further complications arise from ionic charge leakage into the main TPC volume from the high gain anode region. STAR has implemented corrections for these distortions based on measures of luminosity, which we present here. Additionally, we highlight a novel approach to applying the corrections on an event-by-event basis applicable in conditions of rapidly varying ionization sources.Comment: 6 pages, 7 figures, proceedings of the Workshop on Tracking in High Multiplicity Environments (TIME 05) in Zurich, Switzerland, submitted to Nucl. Instr. and Meth.

Sure success partial search

Partial search has been proposed recently for finding the target block containing a target element with fewer queries than the full Grover search algorithm which can locate the target precisely. Since such partial searches will likely be used as subroutines for larger algorithms their success rate is important. We propose a partial search algorithm which achieves success with unit probability

The Optimal Single Copy Measurement for the Hidden Subgroup Problem

The optimization of measurements for the state distinction problem has recently been applied to the theory of quantum algorithms with considerable successes, including efficient new quantum algorithms for the non-abelian hidden subgroup problem. Previous work has identified the optimal single copy measurement for the hidden subgroup problem over abelian groups as well as for the non-abelian problem in the setting where the subgroups are restricted to be all conjugate to each other. Here we describe the optimal single copy measurement for the hidden subgroup problem when all of the subgroups of the group are given with equal a priori probability. The optimal measurement is seen to be a hybrid of the two previously discovered single copy optimal measurements for the hidden subgroup problem.Comment: 8 pages. Error in main proof fixe

Quantum Computing in Molecular Magnets

Shor and Grover demonstrated that a quantum computer can outperform any classical computer in factoring numbers and in searching a database by exploiting the parallelism of quantum mechanics. Whereas Shor's algorithm requires both superposition and entanglement of a many-particle system, the superposition of single-particle quantum states is sufficient for Grover's algorithm. Recently, the latter has been successfully implemented using Rydberg atoms. Here we propose an implementation of Grover's algorithm that uses molecular magnets, which are solid-state systems with a large spin; their spin eigenstates make them natural candidates for single-particle systems. We show theoretically that molecular magnets can be used to build dense and efficient memory devices based on the Grover algorithm. In particular, one single crystal can serve as a storage unit of a dynamic random access memory device. Fast electron spin resonance pulses can be used to decode and read out stored numbers of up to 10^5, with access times as short as 10^{-10} seconds. We show that our proposal should be feasible using the molecular magnets Fe8 and Mn12.Comment: 13 pages, 2 figures, PDF, version published in Nature, typos correcte

Kochen-Specker Theorem for Finite Precision Spin One Measurements

Unsharp spin 1 observables arise from the fact that a residual uncertainty about the actual orientation of the measurement device remains. If the uncertainty is below a certain level, and if the distribution of measurement errors is covariant under rotations, a Kochen-Specker theorem for the unsharp spin observables follows: There are finite sets of directions such that not all the unsharp spin observables in these directions can consistently be assigned approximate truth-values in a non-contextual way.Comment: 4 page

Efficient measurement of quantum gate error by interleaved randomized benchmarking

We describe a scalable experimental protocol for obtaining estimates of the error rate of individual quantum computational gates. This protocol, in which random Clifford gates are interleaved between a gate of interest, provides a bounded estimate of the average error of the gate under test so long as the average variation of the noise affecting the full set of Clifford gates is small. This technique takes into account both state preparation and measurement errors and is scalable in the number of qubits. We apply this protocol to a superconducting qubit system and find gate errors that compare favorably with the gate errors extracted via quantum process tomography.Comment: 5 pages, 2 figures, published versio