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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum computation based on linear optics

Timothy C. Ralph, William J. Munro, Gerard J Milburn

Published Sep 11, 2002• 33 citations
Publisher

Abstract

We review recent theoretical progress in finding ways to do quantum processing with linear optics, non-classical input states and conditional measurements. We focus on a dual rail photonic scheme and a single rail coherent state scheme.
DOI
10.1117/12.483016

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Photon counting induces an effective non-linear optical phase shift in certain states derived by linear optics from single photons. Although this non-linearity is non-deterministic, it is sufficient in principle to allow scalable linear optics quantum computation (LOQC). The most obvious way to encode a qubit optically is as a superposition of the vacuum and a single photon in one mode—so-called ‘single-rail’ logic. Until now this approach was thought to be prohibitively expensive (in resources) compared to ‘dual-rail’ logic where a qubit is stored by a photon across two modes. Here we attack this problem with real-time feedback control, which can realize a quantum-limited phase measurement on a single mode, as has been recently demonstrated experimentally. We show that with this added measurement resource, the resource requirements for single-rail LOQC are not substantially different from those of dual-rail LOQC. In particular, with adaptive phase measurements an arbitrary qubit state can be prepared deterministically .
We demonstrate manipulation of a photonic qubit, encoded in a dual-rail basis, by a plasmonic metamaterial absorber. The metamaterial is designed in a way to transmit a single photon, occupying anti-symmetric superposition of two spatial modes, without losses and to absorb its symmetric superposition completely. Thus, whatever the input state of the dual-rail photon, it can leave the absorber in anti-symmetric state only. Probability to pass through the absorber is defined by the amplitude of the anti-symmetric part in the input photon state. To verify this phenomenon, we assembled actively stabilized in-fibre quantum network containing fully-fiberized metamaterial package. By altering the input state of the photon propagating in the network and passing through metamaterial, we measure the output state of the photon and show that it is coherent and does not depend on the input state of the photon. By varying the input state, we also affect the probability of the photon to pass through the absorber. All the results are in a good agreement with the above discussion. We notice, that absorber can be designed in an opposite way: to transmit symmetric state and to absorb anti-symmetric one. Proposed devices can be employed in quantum computation schemes with dual-rail encoding as well as in other protocols of quantum information, operating with single photons or weak coherent states.
We show how to convert between partially coherent superpositions of a single photon with the vacuum by using linear optics and postselection based on homodyne measurements. We introduce a generalized quantum efficiency for such states and show that any conversion that decreases this quantity is possible. We also prove that our scheme is optimal by showing that no linear optical scheme with generalized conditional measurements, and with one single-rail qubit input, can improve the generalized efficiency.