Accumulator for shaft encoder

Digital accumulator relies almost entirely on integrated circuitry to process the data derived from the outputs of gyro shaft encoder. After the read command is given, the output register collects and stores the data that are on the set output terminals of the up-down counters

Localization of Two-Dimensional Quantum Walks

The Grover walk, which is related to the Grover's search algorithm on a quantum computer, is one of the typical discrete time quantum walks. However, a localization of the two-dimensional Grover walk starting from a fixed point is striking different from other types of quantum walks. The present paper explains the reason why the walker who moves according to the degree-four Grover's operator can remain at the starting point with a high probability. It is shown that the key factor for the localization is due to the degeneration of eigenvalues of the time evolution operator. In fact, the global time evolution of the quantum walk on a large lattice is mainly determined by the degree of degeneration. The dependence of the localization on the initial state is also considered by calculating the wave function analytically.Comment: 21 pages RevTeX, 4 figures ep

Architectures for a quantum random access memory

A random access memory, or RAM, is a device that, when interrogated, returns the content of a memory location in a memory array. A quantum RAM, or qRAM, allows one to access superpositions of memory sites, which may contain either quantum or classical information. RAMs and qRAMs with n-bit addresses can access 2^n memory sites. Any design for a RAM or qRAM then requires O(2^n) two-bit logic gates. At first sight this requirement might seem to make large scale quantum versions of such devices impractical, due to the difficulty of constructing and operating coherent devices with large numbers of quantum logic gates. Here we analyze two different RAM architectures (the conventional fanout and the "bucket brigade") and propose some proof-of-principle implementations which show that in principle only O(n) two-qubit physical interactions need take place during each qRAM call. That is, although a qRAM needs O(2^n) quantum logic gates, only O(n) need to be activated during a memory call. The resulting decrease in resources could give rise to the construction of large qRAMs that could operate without the need for extensive quantum error correction.Comment: 10 pages, 7 figures. Updated version includes the answers to the Refere

Domestic Support for the U.S. Rice Sector and the WTO: Implications of the 2002 Farm Act

The U.S. rice sector is expected to receive some of the largest relative support under the 2002 Farm Act. USDA's rice baseline model is used to compute marketing loan benefits, while direct payments and counter-cyclical payments are estimated from endogenous prices and exogenous policy parameters. Alternative scenarios of reduced marketing loan benefits suggest that projected annual average sector revenue could decline by 4 to 27 percent.Agricultural and Food Policy,

Complementarity and quantum walks

We show that quantum walks interpolate between a coherent `wave walk' and a random walk depending on how strongly the walker's coin state is measured; i.e., the quantum walk exhibits the quintessentially quantum property of complementarity, which is manifested as a trade-off between knowledge of which path the walker takes vs the sharpness of the interference pattern. A physical implementation of a quantum walk (the quantum quincunx) should thus have an identifiable walker and the capacity to demonstrate the interpolation between wave walk and random walk depending on the strength of measurement.Comment: 7 pages, RevTex, 2 figures; v2 adds references; v3 updated to incorporate feedback and updated references; v4 substantially expanded to clarify presentatio

On the relationship between continuous- and discrete-time quantum walk

Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or discrete time. But whereas a continuous-time random walk can be obtained as the limit of a sequence of discrete-time random walks, the two types of quantum walk appear fundamentally different, owing to the need for extra degrees of freedom in the discrete-time case. In this article, I describe a precise correspondence between continuous- and discrete-time quantum walks on arbitrary graphs. Using this correspondence, I show that continuous-time quantum walk can be obtained as an appropriate limit of discrete-time quantum walks. The correspondence also leads to a new technique for simulating Hamiltonian dynamics, giving efficient simulations even in cases where the Hamiltonian is not sparse. The complexity of the simulation is linear in the total evolution time, an improvement over simulations based on high-order approximations of the Lie product formula. As applications, I describe a continuous-time quantum walk algorithm for element distinctness and show how to optimally simulate continuous-time query algorithms of a certain form in the conventional quantum query model. Finally, I discuss limitations of the method for simulating Hamiltonians with negative matrix elements, and present two problems that motivate attempting to circumvent these limitations.Comment: 22 pages. v2: improved presentation, new section on Hamiltonian oracles; v3: published version, with improved analysis of phase estimatio

Discrimination of unitary transformations in the Deutsch-Jozsa algorithm

We describe a general framework for regarding oracle-assisted quantum algorithms as tools for discriminating between unitary transformations. We apply this to the Deutsch-Jozsa problem and derive all possible quantum algorithms which solve the problem with certainty using oracle unitaries in a particular form. We also use this to show that any quantum algorithm that solves the Deutsch-Jozsa problem starting with a quantum system in a particular class of initial, thermal equilibrium-based states of the type encountered in solution state NMR can only succeed with greater probability than a classical algorithm when the problem size exceeds $n \sim 10^5.$Comment: 7 pages, 1 figur

Hamiltonian Oracles

Hamiltonian oracles are the continuum limit of the standard unitary quantum oracles. In this limit, the problem of finding the optimal query algorithm can be mapped into the problem of finding shortest paths on a manifold. The study of these shortest paths leads to lower bounds of the original unitary oracle problem. A number of example Hamiltonian oracles are studied in this paper, including oracle interrogation and the problem of computing the XOR of the hidden bits. Both of these problems are related to the study of geodesics on spheres with non-round metrics. For the case of two hidden bits a complete description of the geodesics is given. For n hidden bits a simple lower bound is proven that shows the problems require a query time proportional to n, even in the continuum limit. Finally, the problem of continuous Grover search is reexamined leading to a modest improvement to the protocol of Farhi and Gutmann.Comment: 16 pages, REVTeX 4 (minor corrections in v2

Generic quantum walk using a coin-embedded shift operator

The study of quantum walk processes has been widely divided into two standard variants, the discrete-time quantum walk (DTQW) and the continuous-time quantum walk (CTQW). The connection between the two variants has been established by considering the limiting value of the coin operation parameter in the DTQW, and the coin degree of freedom was shown to be unnecessary [26]. But the coin degree of freedom is an additional resource which can be exploited to control the dynamics of the QW process. In this paper we present a generic quantum walk model using a quantum coin-embedded unitary shift operation $U_{C}$. The standard version of the DTQW and the CTQW can be conveniently retrieved from this generic model, retaining the features of the coin degree of freedom in both variants.Comment: 5 pages, 1 figure, Publishe

Quantum walk on a line for a trapped ion

We show that a multi-step quantum walk can be realized for a single trapped ion with interpolation between quantum and random walk achieved by randomizing the generalized Hadamard coin flip phase. The signature of the quantum walk is manifested not only in the ion's position but also its phonon number, which makes an ion trap implementation of the quantum walk feasible.Comment: 5 pages, 3 figure