Implementation and Analysis of Quantum Fourier Transform Gates Over FPGA Framework

Vladimir V. Arsoski

Ivan V. Murashko, Constantine C. Korikov

Tin Moe Aye, Masahiro Iwahashi

Since the emergence of the Shor's factoring algorithm, the research over Quantum Fourier Transform (QFT) has motivated the broad attention in the dilemma of the efficient quantum computation. For the purpose of exploring the sizable extent for their exponential growth and the massive computational steps, this paper confers the Field Programmable Gate Arrays (FPGA) implementation of the QFT and, investigate the association between the logic density, complexity and power consumption. In this context, reusability as well as compensating resource utilization is discussed together with the observing issues.

Valerii Hlukhov

Quantum computers are analog and probabilistic computers and, in fact, they play the role of coprocessors in relation to classical computers. The components of quantum coprocessors are called qubits. Their behavior should be described by a wave function. In particular, qubits can be discrete objects - finite states machines. Such qubits will be called digital. Quantum coprocessors and quantum computers built on their basis will also be called digital. External influences on digital qubits are fed through digital quantum gates. So a digital qubit is a unique chain of digital quantum gates. Digital quantum coprocessor can be implemented in FPGA as several chains of digital quantum.The article explores FPGA-based digital quantum coprocessor. It consists of 32 qubits. The structures of digital quantum gates, digital qubits, and a digital quantum coprocessor capable of performing the quantum Fourier transform are presented. Digital qubits were implemented for the case of real amplitudes of the wave functions.The results of the quantum Fourier transform of a 32-qubit digital quantum coprocessor implemented on one FPGA are presented.The execution time of one quantum Fourier transform does not depend on the number of qubits in the digital quantum coprocessor and is commensurate with the time of electron spin change (near 10 ns). But the time complexity of the quantum Fourier transform is probabilistic polynomial in time. The measured ratio of correct results for a 32-qubit coprocessor is approximately 1700 ppm.

Nagendra Singh, Abhishek Tiwari, K. Bhagirath +1 more

Madiha Khalid, Umar Mujahid, Atif Raza Jafri +2 more