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LINEAR-OPTICAL QUANTUM COMPUTATION - THEORY

Program Manager
A/Prof Timothy Ralph - University of Queensland

Linear Optics Quantum Computation Researchers
Students
Ms Agatha Branczyk (honours), Mr Alex Hayes (PhD), Mr Austin Lund (PhD),
Mr Peter Rohde (PhD)

Staff
Dr Kenneth Pregnell
Dr Hyunseok Jeong
Dr Alexei Gilchrist

Collaborating Centre Researchers
Mr Nathan Langford - University of Queensland
Dr Geoff Pryde - University of Queensland
Dr Jeremy O'Brien - University of Queensland
A/Prof Andrew White - University of Queensland
Prof Gerard Milburn - University of Queensland

Other Collaborators
Dr Jennifer Dodd & Prof Michael Nielson - University of Queensland
Dr Steven Bartlett - University of Sydney
Dr William Munro, Dr Pieter Kok - Hewlett Packard, UK
Prof Myungshik Kim - Queens University Belfast, UK
Mr Scott Glancy & Ms Hilma Vasconcelos - University of Notre Dame, USA
Prof Jon Dowling - Jet Propulsion Laboratory, USA
Mr Oliver Gloeckl, Dr Ulrik Anderson, Prof Norbert Lutkenhaus, Prof Gerd Leuchs - Erlangen University, Germany
Mr Casey Myers - University of Waterloo, Canada
Dr Christine Silberhorn, Prof Ian Walmsley - Oxford University, UK
Prof Helmut Ritsch - University of Innsbruck, Austria

Program Description
Linear optics is an incredibly precise technology. As such it is a natural candidate for quantum information processing. However quantum computation gates require non-linearities. Non-linear optics is not so precise. The idea of linear optical quantum computing (LOQC) is to do all the qubit manipulations with linear optics and apply non-linearities via the introduction and measurement of special ancilla quantum states, as described by E.Knill, R.Laflamme and G.J.Milburn, Nature 409, 46 (2001) (KLM). At the basic level KLM describes a tractable way to build non-deterministic, 2-qubit quantum gates in optics. By non-deterministic we mean the gates do not always work, but successful attempts can be unambiguously identified. At its highest level KLM delivers an in principle recipe for the construction of an optical quantum computer.

The LOQC theory program addresses a broad range of issues associated with optical quantum computation from; close collaborations on experimental demonstrations to; alternative architectures to; fundamental issues of scaling. Below we illustrate some current research directions and key papers.

Figure 1: Circuit for performing encoded Controlled-NOT (CNOT) via incremental encoding. The input qubits are parity encoded over four physical qubits each (shown as red lines). A CNOT is performed between one of the control qubits and one of the target qubits. The control qubit is then re-encoded into a new parity qubit, using more CNOTs, and the old qubits are measured in the computational basis (triangles). Bit flip corrections may need to be made as a function of the measurement results (blue lines). For non-deterministic LOQC gates the resource usage for this scheme is considerably less than for the concatenated scheme proposed in KLM. See: A.J.F.Hayes, A.Gilchrist, C.R. Myers, T.C. Ralph, J. Opt. B: Quantum Semiclass. Opt. 6, 533 (2004). quant-ph/0408098 and; T.C. Ralph, A.J.F. Hayes, Alexei Gilchrist, to appear in Physical Review Letters (2005). quant-ph/0501184.


Figure 2: Quantum interference effects, which drive LOQC circuits, depend on the photons being indistinguishable. This schematic depicts the effect of timing mismatch of two single photon states arriving at a beam-splitter. From most events the origin of the photons cannot be determined. However if a photon is detected arriving very early or very late it can be identified as coming from one or other input beam. This leads to a reduction in the visibility of the interference. We have investigated the effect of photon indistinguishability both in current experimental circuits and on future scalable circuits. See: P.P. Rohde and T.C. Ralph, Phys. Rev. A 71, 032320 (2005) and; P.P. Rohde, G.J. Pryde, J.L. O'Brien and T.C. Ralph, to appear Physical Review A (2005) quant-ph/0411144.

Figure 3: The quasi-probability distribution (Wigner-function) of a superposition of two coherent states (sometimes called a cat state) with amplitudes plus and minus two. The Gaussian mounds are the coherent states whilst the fringes are caused by interference between them. If this was just a mixture of two coherent states only the Gaussian mounds would be present. We have shown that such states can be used as a resource for a resource efficient linear optical quantum computation scheme based on coherent qubit states. See: T.C. Ralph, A. Gilchrist, G.J. Milburn, W.J. Munro and S. Glancy, Physical Review A 68, 042319 (2003) and; S. Glancy, H. Vasconcelos, and T.C.Ralph, Physical Review A 70, 022317 (2004).

Figure 4: Scheme for producing large cat states from small cat states. Two identical, small cat states are mixed on a beam-splitter. One of the outputs is mixed with a coherent state on another beam-splitter and photon counters are placed at the outputs. If photons are counted at both outputs the event is successful and a cat state with twice the average intensity of the originals is produced. Detector efficiency does not affect the quality of the cat state produced. Small cat states can be produced from standard sources. Cat states of a useful size for quantum computation can then be produced via this scheme. See: A.P. Lund, H. Jeong, T.C. Ralph and M.S. Kim, Physical Review A (R) 70, 020101 (2004) and; A.P. Lund and T.C. Ralph, Physical Review A 71, 032305 (2005).

Figure 5: Schematic of proposed optical circuit for demonstrating a simple cluster state qubit evolution. All beamsplitters have a reflectivity of 1/3 except those labelled "1/2''. An arbitrary qubit is prepared in the uppermost modes whilst ancilla qubits prepared in logical "1" states are injected into the other modes. By making measurements in particular bases, diagonal and a phase rotated basis (for example circular), any single qubit x-rotation can be applied. If constructed from a sequence of 2-photon CNOTs this circuit would work with probability 1/81. This construction works with probability 1/27. See: T.C. Ralph, Physical Review A 70, 012312 (2004).

 

 


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