Implementing Shor's algorithm on Josephson Charge Qubits

Abstract

We investigate the physical implementation of Shor's factorization algorithm on a Josephson charge qubit register. While we pursue a universal method to factor a composite integer of any size, the scheme is demonstrated for the number 21. We consider both the physical and algorithmic requirements for an optimal implementation when only a small number of qubits is available. These aspects of quantum computation are usually the topics of separate research communities; we present a unifying discussion of both of these fundamental features bridging Shor's algorithm to its physical realization using Josephson junction qubits. In order to meet the stringent requirements set by a short decoherence time, we accelerate the algorithm by decomposing the quantum circuit into tailored two- and three-qubit gates and we find their physical realizations through numerical optimization.

12 pages, submitted to Phys. Rev. A

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• Universal set of scalable dynamically corrected gates for quantum error correction with always-on qubit couplings
• Non-Adiabatic Universal Holonomic Quantum Gates Based on Abelian Holonomies
• Demonstrating quantum algorithm acceleration with NMR quantum computer
• Dynamically corrected gates for qubits with always-on Ising couplings: Error model and fault-tolerance with the toric code
• Implementation of Grover search algorithm with Josephson charge qubits
• Dynamics of Bloch vectors and the channel capacity of a non identical charged qubit pair
• Recursive encoding and decoding of the noiseless subsystem for qudits
• Acceleration of quantum algorithms using three-qubit gates