Duality and Recycling Computing in Quantum Computers

TL;DR

This paper explores the concept of duality and recycling modes in quantum computers, demonstrating how duality can enhance computational power and proposing new modes for algorithm design, including a search algorithm for unsorted databases.

Contribution

It introduces the duality mode in quantum computing, models duality computers with standard qubits, and proposes recycling computing mode for improved algorithm efficiency.

Findings

Duality mode links classical and quantum computing.

A duality computer can perform non-unitary operations.

Recycling mode enables continuous computation until results are obtained.

Abstract

Quantum computer possesses quantum parallelism and offers great computing power over classical computer \cite{er1,er2}. As is well-know, a moving quantum object passing through a double-slit exhibits particle wave duality. A quantum computer is static and lacks this duality property. The recently proposed duality computer has exploited this particle wave duality property, and it may offer additional computing power \cite{r1}. Simply put it, a duality computer is a moving quantum computer passing through a double-slit. A duality computer offers the capability to perform separate operations on the sub-waves coming out of the different slits, in the so-called duality parallelism. Here we show that an $n$-dubit duality computer can be modeled by an $(n+1)$-qubit quantum computer. In a duality mode, computing operations are not necessarily unitary. A $n$-qubit quantum computer can be used as an $n$-bit reversible classical computer and is energy efficient. Our result further enables a $(n+1)$-qubit quantum computer to run classical algorithms in a $O(2^n)$-bit classical computer. The duality mode provides a natural link between classical computing and quantum computing. Here we also propose a recycling computing mode in which a quantum computer will continue to compute until the result is obtained. These two modes provide new tool for algorithm design. A search algorithm for the unsorted database search problem is designed.