On Quantum Computing with Macroscopic Josephson Qubits Jie Han and Pieter Jonker Pattern Recognition Group, Faculty of Applied Sciences, Delft University of Technology. Lorentzweg 1, 2628 CJ, Delft, The Netherlands. {jie, pieter}@ph.tn.tudelft.nl Abstract — The achievements of quantum computation theory, e.g. Shor’s factoring algorithm, motivate efforts to realize quantum computers. Among systems proposed for quantum computing macroscopic superconducting circuits of Josephson junctions appear promising for integration in electronic circuits and large-scale applications. Recently, a superconducting tunnel junction circuit was designed and a sufficiently high quality factor of quantum coherence has been obtained. This indicates that decoherence need not be among the obstacles in building quantum computers with macroscopic Josephson circuits. In this paper we present the setup of some elementary quantum logic with macroscopic Josephson qubits, strengthened by some simulation work, and then study the feasibility of implementing Shor’s quantum factoring algorithm on them. It is shown that it would be eventually possible to build a 2-Dimensional Josephson qubit array, possibly accompanied by classical computing components, capable of performing useful quantum computations. I. INTRODUCTION Current computer systems are based on Boolean logic, which operates on two distinguishable states – False or True, or simply 0 or 1. As the size of microelectronics shrinks, quantum physics becomes increasingly important. Quantum mechanics tells us that if a bit can be in one or the other of two distinguishable states, then it can also exist in coherent superpositions of these states. A single bit of information by such a two-state quantum system is known as a qubit or quantum bit. A qubit exists as a superposition of two distinct states 0 and 1 . With two or more qubits, we can consider quantum logical gate operations, which are the building blocks of a quantum computer. Because of the quantum mechanical superpositions of qubits, a quantum computer would have more freedom in computation than classical computers using conventional Boolean operations. In 1994 Shor discovered a quantum algorithm for factorization that is exponentially faster than any known classical algorithm [1]. It was then realized that quantum computers could perform certain hard tasks that are intractable for any classical computers. The achievements of quantum computation theory motivate efforts to realize quantum computers. Various physical systems were proposed for quantum information processing. Among those macroscopic superconducting circuits of Josephson junctions appear promising for integration in electronic circuits and large-scale applications. The quantum superposition of two macroscopic persistent-current states on superconducting Josephson circuits have been detected and measured [2]. The proposed Josephson Persistent- Current (PC) qubit, which consists of a micrometer-sized loop with three Josephson junctions, is therefore possible to be brought into quantum coherence to perform quantum computing. The macroscopic qubits with Josephson junctions can be produced by modern lithography. They can also be easily initiated, precisely manipulated, individually addressed by conventional techniques. However, macroscopic quantum systems may easily suffer from the problem of decoherence, which destroys quantum coherent superpositions by any irreversible interaction with environments. Recently, a superconducting tunnel junction circuit has been designed and measured, and a sufficiently high quality factor of quantum coherence has been obtained [3]. This result shows that decoherence need not be among the obstacles in building quantum computers with macroscopic Josephson circuits [4]. Any quantum computation can be defined as a unitary evolution of quantum network that takes its initial state into some final state [5]. A quantum network is a computing device consisting of quantum logic gates, and each quantum logic gate is a unitary operation on one or more qubits. Quantum computations are then always accomplished by building up quantum logic circuits out of many quantum logic gates. Since a unitary transformation is reversible, quantum gates need to be reversible and cannot be directly deduced from their classical counterparts. In this paper, we discuss the setup of elementary quantum gates with macroscopic Josephson qubits, and study the feasibility of implementing Shor’s quantum factoring algorithm on them. The structure of the paper is as follows. In section II we present a close look at a Josephson PC qubit and focus on the properties we are interested in. In section III the setup of some elementary quantum logic is discussed and some simulation work is presented. In section IV we present the implementation of Shor’s factoring algorithm on the arrays of superconducting Josephson qubits. Section V concludes the paper.