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
Mr Till Weinhold - 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
Prof Howard Wiseman - Griffith University
Dr Elanor Huntington - UNSW@ADFA

Other Collaborators
Prof Michael Nielson - University of Queensland, Australia
Dr Kevin Resch - University of Queensland, Australia
Dr Jennifer Dodd - University of Queensland, Australia
Dr Steven Bartlett - University of Sydney, Australia
Dr Charles Harb - Australian National University
Dr William Munro - Hewlett Packard, UK
Prof Myungshik Kim - Queens University Belfast, UK
Prof Jon Dowling - Louisiana State University, USA
Dr Christine Silberhorn - Erlangen University, Germany
Prof Gerd Leuchs - Erlangen University, Germany
Mr Casey Myers - University of Waterloo, Canada
Prof Norbert Lutkenhaus - University of Waterloo, Canada
Prof Ian Walmsley - Oxford University, UK
Dr Pieter Kok - Oxford University, UK
A/Prof Kae Nemoto - National Institute of Informatics, Japan
Dr N.B. An - Korean Institute for Advanced Study

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 nondeterministic 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 and fundamental issues of scaling. We are supported by ARC, US Government (DTO) and Queensland State Government funding. This year 15 papers by group members were published including 3 Physical Review Letters. We have 12 more papers submitted, 7 of which are in press. In the following we briefly discuss some of the highlights.

1. Reduced Overheads and Loss Tolerance
To be practical any potential quantum computing architecture must have reasonable requirements on the overheads and precision needed to implement a universal set of gates in a scaleable way. Although “reasonable” is a somewhat subjective term, it is fair to say that the original KLM scheme did not pass this test, with overheads of tens of thousands of operations per gate and efficiencies of greater than 99% required for all elements.

This year we continued our study of a new approach to LOQC based on an incremental parity encoding. Parity encoding was used in the original KLM proposal to protect against teleporter failures, i.e. the non-determinism of the gates. In “Efficient Parity Encoded Optical Quantum Computing”, Alexei Gilchrist, A.J.F. Hayes, T.C. Ralph, quantph/ 0505125 we show that by using parity encoding, but re-encoding via the “fusion” technique, we obtain a major reduction in overheads, similar to that achieved for “cluster states”.

Figure 1 A model for quantum optical memory that is tolerant of losses. The logical qubit is a 10 photon parity plus redundancy code. The logical qubit is held in memory for some time. When released an attempt is made to re-encode off one of the parity qubits (P2). If this attempt succeeds, see (a), the other parity qubit (P1) is disentangled and the newly re-encoded state is placed back in memory. If the re-encoding attempt fails, see (b), then P2 is disentangled and re-encoding is carried out on P1, which is then placed back in memory. This scheme can correct up to one loss event per round. As indicated, loss may arise not only from scattering in the memory, but also due to finite detector and source efficiency in the re-encoding.

Figure 2 If the loss tolerant memory scheme of Figure 1 is scaled up to larger and larger codes it can achieve higher and higher probabilities of success provided the loss rates do not exceed a certain threshold. This is demonstrated in this figure where efficiency (of the detectors, sources and memory, all taken = η) and code size (code size ≈ n3) are plotted against success probability, PE. We observe that provided the efficiency is greater than about 83% the code can in principle succeed with arbitrarily high probability of success.

We have also shown how efficient codes can be designed, based on the parity state approach, that are fault tolerant to loss. Although loss is present in all the elements, i.e. inefficient detectors, sources and optical memories, the coding prevents the loss from propagating and destroying the computation (see Figure 1). The threshold value for the greatest amount of loss that can be tolerated (in all the elements) was found to be ≈17% (see Figure 2); an error level much higher than those previously obtained and thought to be optimal. This work was published as “Loss Tolerant Optical Qubits”, T.C.Ralph, A.J.F.Hayes, Alexei Gilchrist, Phys. Rev.Lett. 95, 100501 (2005)

2. Photon and Photon Counting Characteristics in LOQC
Typically linear optical quantum computing (LOQC) models assume that all input photons are completely indistinguishable. However photons have a spatio-temporal “structure” that can introduce a degree of distinguishability between them and as a result can compromise LOQC algorithms. This year we have investigated the question: what spatiotemporal structure is most resilient to small “distinguishability producing” imperfections (i.e. mode-mismatch) in the optical circuits. We show that Gaussian distributed photons with large bandwidth are optimal. The result is general and holds for arbitrary linear optical circuits, including ones which allow for post-selection and classical feed-forward. The results have been published as “Optimal photons for quantum information processing”, P.P.Rohde, T.C.Ralph, M.A.Nielsen, Phys. Rev. A 72, 052332 (2005).

Photon detection plays a fundamental role in LOQC. Often theoretical treatments of photon detectors are highly idealized and fail to consider many important physical effects. This year we proposed a physically motivated model for photon detectors which includes the effects
of finite resolution, bandwidth and efficiency, as well as dark-counts and dead-time. We apply our model to two simple well known applications, which illustrates the significance of these characteristics. This work will appear in J.Mod.Opt as “Modelling Photo-Detectors in Quantum Optics”, P.P.Rohde and T.C.Ralph, quant-ph/0511099.
Entanglement purification protocols play an important role in the distribution of entangled systems, a necessity for various quantum information processing applications. This year we studied the effects of photon detector efficiency and bandwidth, channel loss and modemismatch on the operation of a particular optical entanglement purification protocol.
We derived necessary detector and modematching requirements to facilitate practical operation of such a scheme, without having to resort to destructive coincidence type demonstrations. This work will appear as a Rapid Communication in Phys.Rev. A as “Practical limitations in optical entanglement purification”, Peter P. Rohde, Timothy C. Ralph, William J. Munro, quantph/ 0511268.

3. Coherent State LOQC
A quite different version of the LOQC paradigm involves encoding the quantum information in multi-photon coherent states, rather than single photon states [T.C.Ralph, A.Gilchrist, G.J.Milburn, W.J.Munro and S.Glancy, Phys. Rev. A 68, 042319 (2003)]. We have continued to explore the practicalities and long term benefits of such an approach.

A new version of the coherent state scheme based upon adaptive photon counting measurements was proposed this year. The adaptive measurement can be configured in such a way as to perform specified projections onto any two orthogonal basis states that are in the space spanned by the two coherent states that define the qubits. In particular we considered projections onto the states . We showed that it is possible to perform the universal gate set; arbitrary Z rotation, controlled-Z gate and Hadamard using this projective adaptive measurement. In general the resource requirements are significantly reduced. Most gates become near-deterministic, thus also reducing the memory requirements. This work will appear as “Quantum Processing with Schrödinger Cat States”, H.Jeong and T.C.Ralph, to appear in Quantum Information with Continuous Variables of Atoms and Light, Ed. N.Cerf (2006). On going studies are focussed on the error properties of these new gates and ultimately seek to find fault tolerant protocols for their implementation.

An important near term goal for coherent state LOQC is to propose practical tests of the basic principles of the scheme. This year we outlined such a scheme using sophisticated but not unrealistic quantum states. The major resource required to demonstrate coherent state quantum gates are states diagonal to the basis states i.e. superpositions of coherent states. We used our recent observation that a squeezed single photon state approximates well an odd superposition of coherent states to address the diagonal resource problem. Using these approximate states we model experimental demonstrations and show that the basic properties of teleportation and a Hadamard gate could be demonstrated in this way. This work has been published as “Coherent State LOQC gates using Simplified Diagonal Superposition Resource States”, A.P.Lund and T.C.Ralph, Phys. Rev. A 71, 032305 (2005).

4. Weak Non-linearities
Strong nonlinear effects, if available, could be very useful for the generation of nonclassical states and quantum information processing in optical systems. However, nonlinear effects in currently available nonlinear media are extremely weak compared with the required level for the non-classical state generation and quantum information processing. Recently, the idea of using weak nonlinearities combined with strong coherent fields has been developed for various applications including the generation of macroscopic quantum states and quantum computation. The basic idea of the weak-nonlinearity-based approach is that the weak strength of a nonlinearity can be compensated by using a strong coherent field as an ancillary state. However, it is unclear whether the weak-nonlinearity-based approach can overcome decoherence effects in nonlinear media. Decoherence is one of the main obstacles to the observation of quantum phenomena and the realization of quantum computation. Remarkably, we have found that the weak-nonlinearitybased approach can naturally overcome decoherence effects in nonlinear media.
Decoherence can be made arbitrarily small simply by using arbitrarily strong ancillary fields in the macroscopic quantum state generation and also in quantum computation if the ancillary field measurement is properly chosen. Our results suggest that the weaknonlinearity- based approach can be a good cadidate for the observation of macroscopic quantum phenomena and the realization of quantum computation. This work has been published as H. Jeong, Phys. Rev. A 72, 034305 (2005).

5. Measuring Quantum Gate Metrics
In the context of quantum communication and computing protocols, measures such as purity, entropy, entanglement and fidelity are essential in characterising the performance and non-classical resources of a physical experiment. While these quantities are usually easy to calculate from a theoretical model (or a complete reconstructed state), a simple experimental technique to directly and efficiently measure these quantities in practice has remained illusive. This year we have investigated this problem. We have proposed an experimental technique to directly measure any so-called non-linear functional, Tr[ρ1k ρ2l ρ3j …] of a given set of density matrices ρ1, ρs, ρ3,…, for integer k, l and j. Remarkably, the scheme, tailored specifically for systems of harmonic oscillators such as optical modes, requires only linear interactions and local energy measurements. Since quantities such as purity, entropy etc are specific examples of these functionals, this proposal is of importance to experimental efforts in quantum information and computing
protocols. Most importantly, the proposal is already within the reach of current
technology with linear optics. This work was published in Physical Review Letters as ``Measuring non-linear functionals of quantum harmonic oscillator states’’, K. L. Pregnell, Phys. Rev. Lett. 96, 060501 (2006).

6. Super-Phase Resolution via Retrodiction
Common wisdom holds that entangled states are a necessary resource for many protocols in quantum information, ranging across quantum communication, quantum computation and quantum metrology. One feature of entangled states is that they can exhibit phase super-resolution, where the interference oscillation occurs over a phase N-times smaller than one cycle of classical light (see Figure 3). In some cases this gives rise to phase super-sensitivity, a reduction of phase uncertainty.

This year we proposed an experiment to demonstrate phase super-resolution in the absence of prepared entangled states, allowing a significant reduction in experimental complexity. The key insight is to use the inherent time-reversal symmetry (retrodiction) of quantum mechanics: we measure, as opposed to prepare, an entangled state. An experiment was performed in collaboration with the LOQC experimental group at UQ that demonstrated phase super-resolution with 3, 4, and 6 photons. The six-photon experiment demonstrated the highest phase superresolution yet reported. The paper has been submitted as “Time-reversal and super-resolving phase measurements”, K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, A. G. White, quant-ph/0511214.

Figure 3 Phase oscillations of entangled states of 1 to 6 photons showing the increased phase resolution.