4 research outputs found
Quantum Computation with Coherent Spin States and the Close Hadamard Problem
We study a model of quantum computation based on the
continuously-parameterized yet finite-dimensional Hilbert space of a spin
system. We explore the computational powers of this model by analyzing a pilot
problem we refer to as the close Hadamard problem. We prove that the close
Hadamard problem can be solved in the spin system model with arbitrarily small
error probability in a constant number of oracle queries. We conclude that this
model of quantum computation is suitable for solving certain types of problems.
The model is effective for problems where symmetries between the structure of
the information associated with the problem and the structure of the unitary
operators employed in the quantum algorithm can be exploited.Comment: RevTeX4, 13 pages with 8 figures. Accepted for publication in Quantum
Information Processing. Article number: s11128-015-1229-
Gaussian quantum computation with oracle-decision problems
We study a simple-harmonic-oscillator quantum computer solving oracle
decision problems. We show that such computers can perform better by using
nonorthogonal Gaussian wave functions rather than orthogonal top-hat wave
functions as input to the information encoding process. Using the Deutsch-Jozsa
problem as an example, we demonstrate that Gaussian modulation with optimized
width parameter results in a lower error rate than for the top-hat encoding. We
conclude that Gaussian modulation can allow for an improved trade-off between
encoding, processing and measurement of the information.Comment: RevTeX4, 10 pages with 4 figure
Asymptotically Improved Grover's Algorithm in any Dimensional Quantum System with Novel Decomposed -qudit Toffoli Gate
As the development of Quantum computers becomes reality, the implementation
of quantum algorithms is accelerating in a great pace. Grover's algorithm in a
binary quantum system is one such quantum algorithm which solves search
problems with numeric speed-ups than the conventional classical computers.
Further, Grover's algorithm is extended to a -ary quantum system for
utilizing the advantage of larger state space. In qudit or -ary quantum
system n-qudit Toffoli gate plays a significant role in the accurate
implementation of Grover's algorithm. In this paper, a generalized -qudit
Toffoli gate has been realized using qudits to attain a logarithmic depth
decomposition without ancilla qudit. Further, the circuit for Grover's
algorithm has been designed for any d-ary quantum system, where d >= 2, with
the proposed -qudit Toffoli gate so as to get optimized depth as compared to
state-of-the-art approaches. This technique for decomposing an n-qudit Toffoli
gate requires access to higher energy levels, making the design susceptible to
leakage error. Therefore, the performance of this decomposition for the unitary
and erasure models of leakage noise has been studied as well