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QUANTUM ALGORITHMS

 

Program Manager:
Prof Ray Offen - Macquarie University

Participating Macquarie University Researchers:
Prof Barry Sanders
A/Prof Igor Shparlinski
Dr James Cresser
A/Prof Bernard Mans
Dr Manas Patra
Dr Ron Steinfeld
Mr Peter Brooke (PhD)

Program Description
The quantum algorithms work commenced with Igor Shparlinski's collaboration with Alex Russell of the University of Connecticut, as they developed a new algorithm for recovering a "hidden" polynomial over a finite field. This algorithm applies for the case that a black box evaluation of the quadratic character is provided at the values of the polynomial. This new algorithm steers away from Shor's method and exploits tensor products of states, which works with states that are not perfectly orthogonal. Since this project, Russell and Shparlinski have continued to collaborate on quantum algorithms, with particular efforts on quantum noisy rational function reconstruction.

Research in Physics, in the group of Barry Sanders, focussed on two areas of theoretical quantum information science: (i) "Resources and Equivalences" and (ii) "Quantum Information Protocols". This research was undertaken with minimal expenditure of Centre funding in order to provide substantial support to attract Macquarie University's new Chair of Quantum Information Science, who, as of July 2003, joined the faculty at the University of Calgary but is seconded back to Macquarie University for 20% of each year as an Adjunct Professor.

The first of the two Physics projects, "Resources and equivalences", is important because this research addresses questions about the best way to perform quantum computation. Some operations like controlled not gates may be easy and generating entanglement may be hard so how many controlled not operations can substitute for a specific amount of entanglement makes these assessments possible. Another equivalence might involve relating a measurable quantity, such as the degree of squeezing, to a fundamental resource, such as the degree of entanglement - we can measure one quantity to infer the other.

Research has concentrated on equivalence relations for entropy, entanglement and squeezing. Equivalences between entanglement and squeezing are important to establish means for measuring degrees of entanglement at the macroscopic scale. Connections between entropy and entanglement have been explored, and the employment of relatively-easy-to-calculate entropies to determine other entropies has been established. We have also established strong relations between spin squeezing measurements, which are amenable to laboratory-scale measurements, and entanglement within the system, which may present a resource for quantum computation.

The second Physics project, on "Quantum Information Protocols", is important because it focusses on new protocols for quantum information processing, which will be required as tasks in quantum computers, particulary for quantum computers realised as distributed networks, as well as providing tests and benchmarks for quantum computer performance.
For example, quantum teleportation and sharing quantum secrets are important quantum information protocols that are useful in certain quantum computation implementations. These protocols are worth developing in their own right but also allow tests of few-qubit protocols. Such few-qubit protocols are relevant to medium term quantum computation development because they enable testing and performance benchmarking for few-qubit systems.

The two protocols under investigation have been quantum walks in a cavity quantum electrodynamics setting and the sharing of quantum secrets. In a collaboration with Imperial College, Bartlett and Sanders introduced a realization of quantum walks in a microwave cavity that is considered to be experimentally feasible and allows controlled decoherence to recover the classical walk. Sharing of quantum secrets, which is important for distributing quantum states to nodes of a network that cannot be trusted (error-prone) has been realised in a collaboration between Sanders and Ping Koy Lam's experimental quantum optics group at the Australian National University.


In relation to quantum information protocols, Berry and Sanders have been collaborating with researchers at Imperial College, London, and at the University of Waterloo, Canada, on how to process single photons produced by a source with some given efficiency p<1; this processing is performed by sending single photons into a multiport interferometer and using a linear optics and photodetection, produce single photons in the output with higher efficiency p than in the input states. Limitations and potential gains by this method have been discovered, which will have an impact on future development of single photon sources for linear optics quantum computation. In addition, Bartlett and Sanders have collaborated with Stanford University researchers to push the limits of photon counters to detect nonclassicality of light directly by photon counting instead of indirectly by homodyne tomography. This work on producing single photons and counting photons is important for all linear optics quantum information protocols.

 

 


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