Optimising Matrix Product State Simulations of Shor's Algorithm

We detail techniques to optimise high-level classical simulations of Shor's quantum factoring algorithm. Chief among these is to examine the entangling properties of the circuit and to effectively map it across the one-dimensional structure of a matrix product state. Compared to previous approaches whose space requirements depend on $r$, the solution to the underlying order-finding problem of Shor's algorithm, our approach depends on its factors. We performed a matrix product state simulation of a 60-qubit instance of Shor's algorithm that would otherwise be infeasible to complete without an optimised entanglement mapping.Comment: 8 pages, 2 figures, 2 tables. v2 using PDFLaTeX compiler. v3 to include extra references. v4 for publication in Quantu

A multiplexed single electron transistor for application in scalable solid-state quantum computing

Single Electron Transistors (SETs) are nanoscale electrometers of unprecedented sensitivity, and as such have been proposed as read-out devices in a number of quantum computer architectures. We show that the functionality of a standard SET can be multiplexed so as to operate as both read-out device and control gate for a solid-state qubit. Multiplexing in this way may be critical in lowering overall gate densities in scalable quantum computer architectures.Comment: 3 pages 3 figure

Quantum information transport to multiple receivers

The importance of transporting quantum information and entanglement with high fidelity cannot be overemphasized. We present a scheme based on adiabatic passage that allows for transportation of a qubit, operator measurements and entanglement, using a 1-D array of quantum sites with a single sender (Alice) and multiple receivers (Bobs). Alice need not know which Bob is the receiver, and if several Bobs try to receive the signal, they obtain a superposition state which can be used to realize two-qubit operator measurements for the generation of maximally entangled states.Comment: Modified in view of referee's comments, new author added, natural scheme for operator measurements identified, hence W state preparation replaced with GHZ state preparation via operator measurements. 4 pages, 3 figure

Quantum gate for Q switching in monolithic photonic bandgap cavities containing two-level atoms

Photonic bandgap cavities are prime solid-state systems to investigate light-matter interactions in the strong coupling regime. However, as the cavity is defined by the geometry of the periodic dielectric pattern, cavity control in a monolithic structure can be problematic. Thus, either the state coherence is limited by the read-out channel, or in a high Q cavity, it is nearly decoupled from the external world, making measurement of the state extremely challenging. We present here a method for ameliorating these difficulties by using a coupled cavity arrangement, where one cavity acts as a switch for the other cavity, tuned by control of the atomic transition.Comment: 6 pages, 5 figures, 1 tabl

Single atom-scale diamond defect allows large Aharonov-Casher phase

We propose an experiment that would produce and measure a large Aharonov-Casher (A-C) phase in a solid-state system under macroscopic motion. A diamond crystal is mounted on a spinning disk in the presence of a uniform electric field. Internal magnetic states of a single NV defect, replacing interferometer trajectories, are coherently controlled by microwave pulses. The A-C phase shift is manifested as a relative phase, of up to 17 radians, between components of a superposition of magnetic substates, which is two orders of magnitude larger than that measured in any other atom-scale quantum system.Comment: 5 pages, 2 figure

Quantum computing with nearest neighbor interactions and error rates over 1%

Large-scale quantum computation will only be achieved if experimentally implementable quantum error correction procedures are devised that can tolerate experimentally achievable error rates. We describe a quantum error correction procedure that requires only a 2-D square lattice of qubits that can interact with their nearest neighbors, yet can tolerate quantum gate error rates over 1%. The precise maximum tolerable error rate depends on the error model, and we calculate values in the range 1.1--1.4% for various physically reasonable models. Even the lowest value represents the highest threshold error rate calculated to date in a geometrically constrained setting, and a 50% improvement over the previous record.Comment: 4 pages, 8 figure