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arXiv:quant-ph/0201047 · Physical Review A

Imperfect detectors in linear optical quantum computers

Scott Glancy, John M. LoSecco, H. M. Vasconcelos, Carol E. Tanner

Published Jun 14, 2002• 26 citations
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Abstract

We discuss the effects of imperfect photon detectors suffering from loss and noise on the reliability of linear optical quantum computers. We show that for a given detector efficiency there is a maximum achievable success probability, and that increasing the number of ancillary photons and detectors used for one controlled sign flip gate beyond a critical point will decrease the probability that the computer will function correctly. We have also performed simulations of some small logic gates and estimate the efficiency and noise levels required for the linear optical quantum computer to function properly. We find that the construction of a $99%$ reliable controlled sign flip gate would require photon detectors with an efficiency greater than 0.999987.

DOI
10.1103/physreva.65.062317

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We discuss the effects of imperfect photon detectors suffering from loss and noise on the reliability of linear optical quantum computers. We show that for a given detector efficiency there is a maximum achievable success probability, and that increasing the number of ancillary photons and detectors used for one controlled sign flip gate beyond a critical point will decrease the probability that the computer will function correctly. We have also performed simulations of some small logic gates and estimate the efficiency and noise levels required for the linear optical quantum computer to function properly. We find that the construction of a 9999%99 reliable controlled sign flip gate would require photon detectors with an efficiency greater than 0.999987.
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One of the main problems that optical quantum computing has to overcome is the efficient construction of two-photon gates. Theoretically these gates can be realized using Kerr-nonlinearities, but the techniques involved are experimentally very difficult. We therefore employ linear optics with projective measurements to generate these non-linearities. The downside is that the measurement-induced nonlinearities achieved with linear optics are less versatile and the success rate can be quite low. This project is mainly the result of a literature study but also a theoretical work on the physics behind quantum optical multiports which is essential for realizing two-photon gates. By applying different postcorrection techniques we increase the probability of success in a modifed non-linear sign shift gate which is foundational for the two photon controlled-NOT gate. We prove that it's not possible to correct the states by only using a single beam splitter. We show that it might be possible to increase the probability of success using a more complex setup with at least two error-correcting beam splitters.
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Recently it was realized that linear optics and photodetectors with feedback can be used for theoretically efficient quantum information processing. The first of three steps toward efficient linear optics quantum computation is to design a simple postselected gate that implements a nonlinear phase shift on one mode. Here a computational strategy is given for finding postselected gates for bosonic qubits with helper photons. A more efficient conditional sign flip gate is obtained. What is the maximum efficiency for such gates? This question is posed and it is shown that the probability of success cannot be 1.
Optical quantum computation was limited to a few photon applications such as quantum cryptography and partial teleportation until 2001. Then the possibility of performing arbitrary logic conditional on certain detection outcomes was introduced by Knill, Laflamme and Milburn ( Nature 2001 409 46). Simple circuits consisting of single photon sources, entangled pair sources, linear optical elements and high efficiency photon counting detectors can be used to develop probabilistic two-photon logic gates. Initially such gates show a low probability of success but can approach the success rate of deterministic (non-linear) logic at the cost of added complexity. These developments have led to the emergence of a novel field of research aimed at improving the efficiency of linear logic and developing the efficient sources and detectors for its implementation. This topical issue of Journal of Optics B: Quantum and Semiclassical Optics is devoted to recent advances in this field. Key to all linear optics gates is the interference effect between separate photons that have no previous history. In this issue we include the first experiment to show such an effect (Rarity et al ), on which many later experiments are based. These interference effects can then be used to entangle separate pairs of particles into higher order entangled states (Zou et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 119–121) and also to establish entanglement between matter qubits (Kok et al ). Quantum dot single photon sources suitable for linear optics quantum logic are discussed in the paper by Unitt et al while a waveguide source of pair photons is presented by Ducci et al . The difficulties in scaling linear optics quantum computing arise from the low success probabilities of the gates. Introducing a small amount of non-linearity could allow unit efficiency gates to be designed (Munro et al ) while large non-linearities generated by the collective effects in EIT could be used to implement a wide variety of quantum logic functions (Petrosyan). The development of algorithms suitable for optical implementation is addressed by Ellinas et al . Key contributors to this issue are collaborating in the project IST:38864 RAMBOQ which has a primary goal of developing linear optics computation tools and techniques.