Designing short robust NOT gates for quantum computation

Composite pulses, originally developed in Nuclear Magnetic Resonance (NMR), have found widespread use in experimental quantum information processing (QIP) to reduce the effects of systematic errors. Most pulses used so far have simply been adapted from existing NMR designs, and while techniques have been developed for designing composite pulses with arbitrary precision the results have been quite complicated and have found little application. Here I describe techniques for designing short but effective composite pulses to implement robust NOT gates, bringing together existing insights from NMR and QIP, and present some novel composite pulses.Comment: 12 pages RevTex including 7 figures; in press at Phys Rev

Robust quantum information processing with techniques from liquid state NMR

While Nuclear Magnetic Resonance (NMR) techniques are unlikely to lead to a large scale quantum computer they are well suited to investigating basic phenomena and developing new techniques. Indeed it is likely that many existing NMR techniques will find uses in quantum information processing. Here I describe how the composite rotation (composite pulse) method can be used to develop quantum logic gates which are robust against systematic errors.Comment: 11 pages including 4 figures in rspublic format. Article submitted for proceeding of the Discussion Meeting on Practical Realisations of Quantum Information Processing, held at the Royal Society, Nov. 13-14, 200

Efficient Hamiltonian programming in qubit arrays with nearest-neighbour couplings

We consider the problem of selectively controlling couplings in a practical quantum processor with always-on interactions that are diagonal in the computational basis, using sequences of local NOT gates. This methodology is well-known in NMR implementations, but previous approaches do not scale efficiently for the general fully-connected Hamiltonian, where the complexity of finding time-optimal solutions makes them only practical up to a few tens of qubits. Given the rapid growth in the number of qubits in cutting-edge quantum processors, it is of interest to investigate the applicability of this control scheme to much larger scale systems with realistic restrictions on connectivity. Here we present an efficient scheme to find near time-optimal solutions that can be applied to engineered qubit arrays with local connectivity for any number of qubits, indicating the potential for practical quantum computing in such systems.Comment: 5 pages, 5 figures. Shortened and clarified from previous versio

Witnesses of non-classicality for simulated hybrid quantum systems

The task of testing whether quantum theory applies to all physical systems and all scales requires considering situations where a quantum probe interacts with another system that need not obey quantum theory in full. Important examples include the cases where a quantum mass probes the gravitational field, for which a unique quantum theory of gravity does not yet exist, or a quantum field, such as light, interacts with a macroscopic system, such as a biological molecule, which may or may not obey unitary quantum theory. In this context a class of experiments has recently been proposed, where the non-classicality of a physical system that need not obey quantum theory (the gravitational field) can be tested indirectly by detecting whether or not the system is capable of entangling two quantum probes. Here we illustrate some of the subtleties of the argument, to do with the role of locality of interactions and of non-classicality, and perform proof-of-principle experiments illustrating the logic of the proposals, using a Nuclear Magnetic Resonance quantum computational platform with four qubits.Comment: Revised and extende

Controlling NMR spin systems for quantum computation

Nuclear magnetic resonance is arguably both the best available quantum technology for implementing simple quantum computing experiments and the worst technology for building large scale quantum computers that has ever been seriously put forward. After a few years of rapid growth, leading to an implementation of Shor's quantum factoring algorithm in a seven-spin system, the field started to reach its natural limits and further progress became challenging. Rather than pursuing more complex algorithms on larger systems, interest has now largely moved into developing techniques for the precise and efficient manipulation of spin states with the aim of developing methods that can be applied in other more scalable technologies and within conventional NMR. However, the user friendliness of NMR implementations means that they remain popular for proof-of-principle demonstrations of simple quantum information protocols

Quantum Computing with NMR

A review of progress in NMR quantum computing and a brief survey of the literatureComment: Commissioned by Progress in NMR Spectroscopy (95 pages, no figures

Preparing pseudo-pure states with controlled-transfer gates

The preparation of pseudo-pure states plays a central role in the implementation of quantum information processing in high temperature ensemble systems, such as nuclear magnetic resonance. Here we describe a simple approach based on controlled-transfer gates which permits pseudo-pure states to be prepared efficiently using spatial averaging techniques.Comment: Significantly revised and extended: now 7 pages including 3 figures; Phys. Rev. A (in press

Quantum Information Processing with Delocalized Qubits under Global Control

Any technology for quantum information processing (QIP) must embody within it quantum bits (qubits) and maintain control of their key quantum properties of superposition and entanglement. Typical QIP schemes envisage an array of physical systems, such as electrons or nuclei, with each system representing a given qubit. For adequate control, systems must be distinguishable either by physical separation or unique frequencies, and their mutual interactions must be individually manipulable. These difficult requirements exclude many nanoscale technologies where systems are densely packed and continuously interacting. Here we demonstrate a new paradigm: restricting ourselves to global control pulses we permit systems to interact freely and continuously, with the consequence that qubits can become delocalized over the entire device. We realize this using NMR studies of three carbon-13 nuclei in alanine, demonstrating all the key aspects including a quantum mirror, one- and two-qubit gates, permutation of densely packed qubits and Deutsch algorithms.Comment: 4 pages, 5 figure

Robust Logic Gates and Realistic Quantum Computation

The composite rotation approach has been used to develop a range of robust quantum logic gates, including single qubit gates and two qubit gates, which are resistant to systematic errors in their implementation. Single qubit gates based on the BB1 family of composite rotations have been experimentally demonstrated in a variety of systems, but little study has been made of their application in extended computations, and there has been no experimental study of the corresponding robust two qubit gates to date. Here we describe an application of robust gates to Nuclear Magnetic Resonance (NMR) studies of approximate quantum counting. We find that the BB1 family of robust gates is indeed useful, but that the related NB1, PB1, B4 and P4 families of tailored logic gates are less useful than initially expected.Comment: 6 pages RevTex4 including 5 figures (3 low quality to save space). Revised at request of referee and incorporting minor corrections and updates. Now in press at Phys Rev