Quantum computation using photons is reviewed. In the first part, the basic idea of optical quantum gates using linear optical element, and the principle to enhance the success probability of the gate, with recent progress of one-way optical quantum computation using cluster state, is explained. In the second part, the effort to develop highly-efficient optical quantum gates realizing strong non-linear interaction between photons is reviewed.
Quantum computation using photons is reviewed. In the first part, the basic idea of optical quantum gates using linear optical element, and the principle to enhance the success probability of the gate, with recent progress of one-way optical quantum computation using cluster state, is explained. In the second part, the effort to develop highly-efficient optical quantum gates realizing strong non-linear interaction between photons is reviewed.
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.
Scalable quantum computation with linear optics was considered to be impossible due to the lack of efficient two-qubit logic gates, despite its ease of implementation of one-qubit gates. Two-qubit gates necessarily need a nonlinear interaction between the two photons, and the efficiency of this nonlinear interaction is typically very tiny in bulk materials. However, we recently have shown that this barrier can be circumvented with effective nonlinearities produced by projective measurements, and with this work linear-optical quantum computing becomes a new possibility of scalable quantum computation. We review several issues concerning its principles and requirements.
In the previous chapter we developed some of the basic aspects of quantum information processing with single photons as qubits. Apart from noting the obvious benefit of using light for quantum communication, we identified some difficulties in manipulating quantum information that is encoded in photons. In particular, it is difficult to construct two-qubit gates for photonic qubits. In this chapter we will have to face this difficulty head-on in our discussion of quantum computation with single photons and linear-optical elements. The possibility of a quantum computer based on single photons, linear optics, and photon counting was demonstrated in a landmark paper by Knill, Laflamme, and Milburn in 2001. Their protocol is commonly referred to as the ‘ klm protocol’. In subsequent years, the klm protocol has been dramatically slimmed down in terms of complexity and the necessary resources to create the universal set of quantum gates. For pedagogical reasons we give the streamlined version here, and we briefly describe the original klm protocol in Appendix 2. We will make extensive use of the results in Section 1.4 about mode transformations, and Section 2.3 about cluster-state quantum computing. We start this chapter, however, with a description of linear-optical networks, and how they fail as deterministic quantum computers. In Section 6.2 we discuss the principle of post-selection, and how this can be used to create probabilistic gates with deterministic feed-forward control.
Quantum states of two photons simultaneously entangled in polarization and linear momentum, namely hyper-entangled or cluster states, allow to operate in a larger Hilbert space, since we can associate four qubits to two photons. We describe how these states are generated, characterized and manipulated by linear optics technique. Some recent results verifying that the ratio between the quantum and classical prediction grows with the size of the Hilbert space are also presented in this work. Finally, we show the efficient realization of a C-NOT gate by using two photon cluster states operating in the one-way model of quantum computation.
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.
This Spotlight aims to provide a general introduction to linear and nonlinear optical components that are frequently used to implement the protocols for quantum computation and communication. The role of each optical element is described briefly, and it is shown that these optical elements can be combined to constitute quantum circuits for performing various quantum computing and communication tasks. Present challenges and future scopes are also mentioned briefly. Specifically, after introducing the qubit, it is stated that a quantum gate is a device that transforms a quantum state into another quantum state. Thus, most of the optical components (e.g., a beamsplitter, a wave plate, a mirror, a polarizing beamsplitter) can be viewed as quantum gates because each of these optical elements can transform a quantum state into another quantum state. This fact is the basis for constructing useful quantum circuits using optical elements. Finally, a few proposals for optical realizations of schemes for quantum communication and computation are described.
In classical computation and communication, we use classical gates and bits. Similarly, in quantum computation and communication, we use their quantum analogs, i.e., quantum gates and qubit(s) [quantum bit(s)]. We have already mentioned that a bit can be realized in various ways. In the same way, a qubit can also be realized in various ways, and accordingly, corresponding quantum gates that would operate on qubits can also be realized in various ways. Here, we focus on a specific implementation: optical implementation, where qubits are realized using photons and quantum gates, and circuits are realized using various optical components. Specific merits of this realization lie in the following facts: (i) in quantum communication we need to transmit qubits from one location to the other, and transmission of photons is easier than any other realization of qubits; (ii) the effect of the environment (e.g., external electric and magnetic fields) on photons is less compared to any other implementations of qubits; and (iii) integrated optics are already a well-developed field. Keeping these points in mind, this Spotlight describes basic optical elements and how to use those elements to implement various schemes of quantum computation and communication. We will mostly describe realizations using bulk optics. However, in most cases, it is not difficult to transform these bulk-optics-based realizations into integrated optics. To begin with, in Section 1.1, we formally define a qubit and describe two alternative ways of realizing a qubit using a photon.