Quantum Computing with Qubits

D. R. Sypher, Ian M. Brereton, Howard M. Wiseman +2 more

Read-only-memory-based (ROM-based) quantum computation (QC) is an alternative to oracle-based QC. It has the advantages of being less ``magical,'' and being more suited to implementing space-efficient computation (i.e., computation using the minimum number of writable qubits). Here we consider a number of small (one- and two-qubit) quantum algorithms illustrating different aspects of ROM-based QC. They are: (a) a one-qubit algorithm to solve the Deutsch problem; (b) a one-qubit binary multiplication algorithm; (c) a two-qubit controlled binary multiplication algorithm; and (d) a two-qubit ROM-based version of the Deutsch-Jozsa algorithm. For each algorithm we present experimental verification using nuclear magnetic resonance ensemble QC. The average fidelities for the implementation were in the ranges 0.9--0.97 for the one-qubit algorithms, and 0.84--0.94 for the two-qubit algorithms. We conclude with a discussion of future prospects for ROM-based quantum computation. We propose a four-qubit algorithm, using Grover's iterate, for solving a miniature ``real-world'' problem relating to the lengths of paths in a network.

Qichun Liu, Shuai-Peng Wang, Yulong Liu +4 more

It is expected that a useful quantum computing (QC) system would require millions of qubits within one system. The state-of-the-arts QC systems contain hundreds of qubits, which is still several orders of magnitude away from the ultimate goal. To scale the QC system, namely, to increase the number of qubits and QC circuit layers, and also to improve the performance such as fidelity, robustness, etc., we need to develop scalable techniques including high-density qubit devices, ultra-low power qubit interfacing circuits, 3D interconnection and packaging etc. This article will review the recent reported device, circuit and system-level techniques that contribute to the QC system scaling and may ultimately lead to a fully functional quantum computer.

Pieter Kok, S. D. Barrett

Chao Lu, Zhao Hui Hu, Bei Xie +1 more

Abstract In this paper, computational heat transfer (CHT) equations were solved using the state-of-art quantum computing (QC) technology. The CHT equations can be discretized into a linear equation set, which can be possibly solved by a QC system. The linear system can be characterized by Ax = b. The A matrix in this linear system is a Hermitian matrix. The linear system is then solved by using the HHL algorithm, which is a quantum algorithm to solve a linear system. The quantum circuit requires an Ancilla qubit, clock qubits, qubits for b and a classical bit to record the result. The process of the HHL algorithm can be described as follows. Firstly, the qubit for b is initialized into the phase as desire. Secondly, the quantum phase estimation (QPE) is used to determine the eigenvalues of A and the eigenvalues are stored in clock qubits. Thirdly, a Rotation gate is used to rotate the inversion of eigenvalues and information is passed to the Ancilla bit to do Pauli Y-rotation operation. Fourthly, revert the whole processes to untangle qubits and measure all of the qubits to output the final results for x. From the existing literature, a few 2 × 2 matrices were successfully solved with QC technology, proving the possibility of QC on linear systems [1]. In this paper, a quantum circuit is designed to solve a CHT problem. A simple 2 by 2 linear equation is modeled for the CHT problem and is solved by using the quantum computing. The result is compared with the analytical result. This result could initiate future studies on determining the quantum phase parameters for more complicated QC linear systems for CHT applications.