We model an optical implementation of a controlled-SIGN gate that makes use of the quantum Zeno effect [Franson et al., Phys. Rev. A 70, 062302 (2004)] in the presence of photon loss. Gate operation is severely affected. However, we show that by using photon loss codes proposed for linear optical quantum computation (LOQC), performance is greatly enhanced, outperforming LOQC equivalents. The technique can be applied to other types of nonlinearities, making the implementation of nonlinear optical gates much more attractive.
Quantum information science has shown that computers which exploit the quantum nature of particles, namely quantum computers, can outperform contemporary computers in some computational tasks. The fundamental building blocks of a quantum computer are quantum logical gates and quantum bits (qubits). Previous research has shown that the optical approach to quantum computing is promising. However, linear optical quantum computing (LOQC) schemes require a huge amount of resource, which makes large scale LOQC impractical, and hence there have been renewed interests in nonlinear optical quantum computing schemes, where less resource is required. The performance of these quantum gates depends on the properties of the nonlinear media. However, requirements on some of the properties for high performance quantum gates are not fully known. This thesis intends to bridge this gap of knowledge and examines the necessary conditions on several types optical nonlinearities that are common in two-qubit quantum gates schemes. These types of nonlinearities are, namely two-photon absorption,
χ(2) nonlinearity and
χ(3) cross-Kerr nonlinearity. The two-photon absorption based quantum Zeno gate is modeled in this thesis. It is shown that for practical absorbers, the photon loss significantly lowers the quantum fidelity of the Zeno gate. Nevertheless, this thesis proposes to use the Zeno gate for fusing optical cluster states. With the best theoretical estimate of single photon loss in the absorbers, the Zeno gate can outperform linear optical schemes. This thesis also proposes to embed the Zeno gate in the teleportation-type of two-qubit gate, namely GC-Zeno gate, such that the success rate of the gate can be traded off for higher gate fidelity. The effect of some mode matching error and detector inefficiency on the GC-Zeno gate are also considered here. It is shown that the photon loss requirement as well as the mode matching requirement are both stringent for having a fault tolerant GC-Zeno gate. This thesis models some of the properties of a
χ(3) optical medium and explores how they affect the fidelity of the cross-Kerr nonlinearity based quantum gate. This thesis shows that for a cross-Kerr medium with fast time response but negligible wave dispersion, the medium would induce spectral entanglement between the input photons and this significantly lowers the fidelity of the quantum gate. Nevertheless, when the dispersion has a stronger effect than the time response, and if phase noise is negligible, it is possible to achieve a quantum gate with high fidelity. However, the noise is actually significant, and this thesis suggests that spectral filtering can be applied to prohibit the occurrence of the noise. The requirements on employing optical
χ(2) nonlinearity for quantum computing are also examined. This study models the spectral effects of a
χ(2) medium on its efficiency. It is shown in this thesis that since the Hamiltonian of the medium does not commute at different times, the unitary operation should be modeled by a Dyson series, which leads to undesired spectral entanglement that lowers the efficiency of the medium. However, in the case of periodical poling, the unitary operation can be modeled by a Taylor series, where under some phase matching conditions, the medium can have a high efficiency. Furthermore, this thesis proposes a Bell measurement scheme and a quantum gate scheme based on
χ(2) nonlinearity that can always outperform linear optics even when the nonlinearity strength is weak. In the case of sufficiently strong nonlinearity, a quantum gate with high success rate can be achieved. In summary, this thesis models some of the properties of two-photon absorbers,
χ(2) nonlinearity and
χ(3) nonlinearity, and shows that it is possible to achieve the conditions required for high performance quantum gates, however these conditions are experimentally challenging to meet.
We have modeled the Zeno effect controlled-sign gate of Franson et al. [Phys. Rev. A 70, 062302 (2004)] and shown that high two-photon to one-photon absorption ratios, $\ensuremath{\kappa}$, are needed for high fidelity free-standing operation. Hence we instead employ this gate for cluster state fusion, where the requirement for $\ensuremath{\kappa}$ is less restrictive. With the help of partially offline one-photon and two-photon distillations, we can achieve a fusion gate with unity fidelity but nonunit probability of success. We conclude that for $\ensuremath{\kappa}>2200$, the Zeno fusion gate will out perform the equivalent linear optics gate.
Quantum logic gates for photonic qubits can be implemented using the quantum Zeno effect based on strong two-photon absorption. The fidelity of quantum Zeno gates of this kind may be substantially reduced by photon loss. Heralding on those outcomes in which both of the logical qubits emerge from the Zeno gate can increase the fidelity at the expense of a limited success rate (P.M. Leung et al., Phys. Rev. A 74, 062325 (2006)). We analyze the performance of heralded quantum Zeno gates by solving Schrodinger's equation for a system of photons coupled to three-level atoms. This approach identifies several potential error sources that are not described by earlier models that assumed a fixed rate of single-photon loss and two-photon absorption.
The use of photons as qubits is a promising implementation for quantum computation. The inability of photons to interact, especially with the environment, makes them an ideal physical candidate. However, this also makes them a difficult system to perform two qubit gates on. Recent breakthroughs in photonic quantum computing have shown methods around the requirement of direct photon-photon interaction. In this thesis we study three recently discovered schemes for optical quantum computation. \n \n We first investigate the so called linear optical quantum computing (LOQC) scheme, exploring a method to improve the original proposal by constructing a photon-number QND detector that succeeds with a high probability. In doing this we present a new type of LOQC teleporter, one that can detect the presence of a single photon in an arbitrary polarisation state when the input state is a sum of vacuum and multi-photon terms. This new type of teleporter is an improvement on the original scheme in that the entangled states required can be made offline with fewer entangling operations. \n \n We next investigate the so called quantum bus (qubus) scheme for photonic quantum computing. We show a scheme to measure the party of n qubit states by using a single qubus mode, controlled rotations and displacements. This allows for the syndrome measurements of any stabilizer quantum error correcting code. We extend these results to a fault tolerant scheme to measure an arbitrary Pauli operator of weight n, incorporating so called single bit teleportations. We investigate the construction of a Toffoli gate by using a single qubus mode, controlled rotations and displacements that works with a success probability of at least 25%. We also investigate the use of single bit teleportations to construct a universal set of gates on coherent state type logic and in the construction of cluster states. \n \nWe finally investigate the optical Zeno gate, a gate that uses the Zeno effect in the form of two photon absorbers to induce a CSIGN. We model realistic two photon absorption and include realistic single photon loss for this gate, examining the use of encoding to overcome the single photon loss, showing that our results are competitive with the leading equivalent LOQC scheme.
Reliable entangling gates for qubits encoded in single-photon states represent a major challenge on the road to scalable quantum computing architectures based on linear optics. In this work, we present two approaches to develop high-fidelity, near-deterministic controlled-sign-shift gates based on the techniques of quantum gate teleportation. On the one hand, teleportation in a discrete-variable setting, i.e., for qubits, offers unit-fidelity operations but suffers from low success probabilities. Here, we apply recent results on advanced linear optical Bell measurements to reach a near-deterministic regime. On the other hand, in the setting of continuous variables, associated with coherent states, squeezing, and, typically, Gaussian states, teleportation can be performed in a deterministic fashion, but the finite amount of squeezing implies an inevitable deformation of a teleported single-mode state. Using a new generalized form of the nonlinear-sign-shift gate for gate teleportation, we are able to achieve fidelities of the resulting controlled-sign gate above
90. A special focus is also put on a comparison of the two approaches, not only with respect to fidelity and success probability, but also in terms of resource consumption.