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Fluctuation and Noise Letters

LSI-BASED EFFICIENT EMULATION OVERCOMING ALGORITHMIC RESTRICTIONS INHERENT IN QUANTUM COMPUTERS

Minoru Fujishima

Published Dec 1, 2003• 1 citation
Publisher

Abstract

Quantum computers are believed to perform high-speed calculations, compared with conventional computers. However, the quantum computer solves NP (non-deterministic polynomial) problems at a high speed only when a periodic function can be used in the process of calculation. To overcome the restrictions stemming from the quantum algorithm, we are studying the emulation by a LSI (large scale integrated circuit). In this report, first, it is explained why a periodic function is required for the algorithm of a quantum computer. Then, it is shown that the LSI emulator can solve NP problems at a high speed without using a periodic function.

DOI
10.1142/s0219477503001476

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Quantum computers are believed to perform high-speed calculations, compared with conventional computers. However, the quantum computer solves NP (non-deterministic polynomial) problems at a high speed only when a periodic function can be used in the process of calculation. To overcome the restrictions stemming from the quantum algorithm, we are studying the emulation by a LSI (large scale integrated circuit). In this report, first, it is explained why a periodic function is required for the algorithm of a quantum computer. Then, it is shown that the LSI emulator can solve NP problems at a high speed without using a periodic function.
Quantum computers are believed to perform high-speed calculations, compared with conventional computers. However, the quantum computer has inherent issues. Firstly, it solves NP (non-deterministic polynomial) problems at a high speed only when a periodic function can be used in the process of calculation. Secondly, it is extremely difficult to increase the problem scale to be solved, which is determined by the number of quantum bits. To overcome the restrictions stemming from the quantum algorithm, we are studying the emulation by a FPGA (field programmable gate array). In this paper, first, it is explained why a periodic function is required for the algorithm of a quantum computer. Then, it is shown that the hardware emulator can solve NP problems at a high speed without using a periodic function.
A quantum computer is highly promising and widely studied since it enables a much higher calculation speed than current computers. Due to physical limitations, however, the current quantum computer can only solve much smaller scale problems than conventional computers. In order to process a large-scale problem at high speed, we have been studying a quantum computing emulator utilizing semiconductor memories. As a result, we have realized a dedicated processor that solves search problems, such as the satisfiability problem, at much higher speed than current computers. Consequently, without using "quantum process," the possibility of a quantum computer executing a large-scale problem is shown.
Quantum computing has attracted many research studies to solve non-deterministic polynomial (NP) problems at high speed. However, large-scale quantum computing has not been realized yet. In this study, a new emulation method is proposed, where qubits are replaced with classical bits that use unitary macro-operations, which are a combination of quantum operations at the principal stage of the quantum computing process for executing several-hundred-qubit operations in a large-scale emulation. As a result, a quantum computing emulator has been successfully fabricated, and a 64-bit factorization was demonstrated with only 40 kbits of classical memory, where 320 qubits are required with Shor's algorithm in a quantum computer.
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A high-speed and large-scale processor dedicated to quantum computing is proposed, which has the minimum operation function needed for execution of a quantum algorithm. In this processor, the probability amplitudes determined by the states of the quantum bits in the quantum computer are described using only one bit, and we named it a logic quantum processor. It is found that for this processor an execution speed 275 times higher than that of a software simulation is obtained when the processor executing the quantum algorithm for 16 qubit has been implemented in a FPGA. As an example application, it is shown that the processor can solve the satisfiability problem and that it can also simulate the decoherence in the quantum computer at high speed.
A 16-qubit quantum-computing emulator executing quantum algorithms at high speed is proposed. By limiting the command of the quantum computing emulator to the minimum function required with the quantum algorithm, probability amplitudes are expressed with one bit and the functions of many qubits are integrated on a field programmable gate array (FPGA). As a result of implementing the emulator in the FPGA, it is found that the emulator has a 250 times higher-speed as compared with a software simulation by a general-purpose processor.