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Journal of Experimental and Theoretical Physics Letters

Realization of the quantum Fourier transform and simulation of a wave function on a quantum computer with fixed continuous interaction

Yu. I. Ozhigov

Published Nov 1, 2002• 0 citations
Publisher

Abstract

A model of a quantum computer with diagonal continuous interaction between qubits is proposed. Such a computer is controlled only by short single-qubit operations. The realization of quantum Fourier transform and simulation of the wave function of a many-particle problem with linear and quadratic potentials on this quantum computer are discussed. This method applies to a wide class of diagonal interactions and to the case, where the interactions of different qubits are different.

DOI
10.1134/1.1541053

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A model of a quantum computer with diagonal continuous interaction between qubits is proposed. Such a computer is controlled only by short single-qubit operations. The realization of quantum Fourier transform and simulation of the wave function of a many-particle problem with linear and quadratic potentials on this quantum computer are discussed. This method applies to a wide class of diagonal interactions and to the case, where the interactions of different qubits are different.
The effect of off-diagonal interactions between quantum bits is studied in a simple quantum computer algorithm designed to calculate the sum of two n-bit numbers. Scaling laws are derived numerically for the dependence of the error on the number n of bits, the strength of the interaction, and the calculation time. The case of diagonal interactions, previously studied in the context of the quantum Fourier transform algorithm, is also considered. No substantial differences are found between the off-diagonal and diagonal forms of the interaction: in both cases, the errors accumulate almost coherently, despite the fact that the system's free evolution is constantly being interrupted by the logical gates, which scramble the coefficients of the wave function. Some comments on the possibility of using ``field-insensitive'' atomic states in ion-chain quantum computers are also given.
At present, it is one of various effective approaches for quantum algorithm to using the nuclear magnetic resonance (NMR) experiment technology. NMR uses radio frequency (RF) electromagnetic pulses to rotate the spins. By tuning the frequency of the RF-field to the precession frequency of a particular spin, the power of the applied pulse controls how much the spin will rotate. The axis of the rotation is determined by the direction of the applied RF-field. By selecting the appropriate RF pulses, arbitrary single-spin rotation can be carried out. In other words, using RF pulses we can perform any single-qubit operation. Communication between the qubits is accomplished through the spin-spin interaction in model. A simulation approach in this paper is described to realize quantum Fourier transform algorithm (QFT).
For discussing the solving methods of NP problems in classical computers and studying the circuit model which is the most representative in quantum computing to simulate the compute processes, this article discussed how to simulate the quantum Fourier transform by using the quantum logic gates, implemented the quantum Fourier transform and constructed the quantum information and compute simulation platform. The experiment introduced the quantum register structure to be the storage medium, which is better than the form of matrix in space. The operation processes adopted the bit manipulation to avoid the mass time for matrix multiplications. The results presented the changes of quantum amplitudes and probabilities of quantum states according to the quantum effect and compared with the approximate quantum Fourier transform. The experimental platform provided a groundwork for the further simulations of other important quantum algorithms and quantum circuits.
We describe an architecture based on a processing "core," where multiple qubits interact perpetually, and a separate "store," where qubits exist in isolation. Computation consists of single qubit operations, swaps between the store and the core, and free evolution of the core. This enables computation using physical systems where the entangling interactions are "always on." Alternatively, for switchable systems, our model constitutes a prescription for optimizing many-qubit gates. We discuss implementations of the quantum Fourier transform, Hamiltonian simulation, and quantum error correction.