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arXiv:0804.4344 · Physical Review A

Computation with coherent states via teleportations to and from a quantum bus

Marcus Palmer Da Silva, Casey R. Myers

Published Dec 5, 2008• 11 citations
arXivHTMLPDF

Abstract

In this paper, we present results illustrating the power and flexibility of one-bit teleportations in quantum bus computation. We first show a scheme to perform a universal set of gates on continuous variable modes, which we call a quantum bus or qubus, using controlled phase-space rotations, homodyne detection, ancilla qubits, and single-qubit measurement. Within our comparison criteria, the resource usage for this scheme is lower than any previous scheme to date. We then illustrate how one-bit teleportations into a qubus can be used to encode qubit states into a quantum repetition code, which in turn can be used as an efficient method for producing Greenberger-Horne-Zeilinger states that can be used to create large cluster states. Each of these schemes can be modified so that teleportation measurements are post-selected to yield outputs with higher fidelity without changing the physical parameters of the system.

DOI
10.1103/physreva.78.062314

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In this paper, we present results illustrating the power and flexibility of one-bit teleportations in quantum bus computation. We first show a scheme to perform a universal set of gates on continuous variable modes, which we call a quantum bus or qubus, using controlled phase-space rotations, homodyne detection, ancilla qubits, and single-qubit measurement. Within our comparison criteria, the resource usage for this scheme is lower than any previous scheme to date. We then illustrate how one-bit teleportations into a qubus can be used to encode qubit states into a quantum repetition code, which in turn can be used as an efficient method for producing Greenberger-Horne-Zeilinger states that can be used to create large cluster states. Each of these schemes can be modified so that teleportation measurements are post-selected to yield outputs with higher fidelity without changing the physical parameters of the system.
There are numerous proposals for the physical realization of a quantum computer.However, distributed approaches, making use both of flying and stationary qubits, seem to constitute the most promising route towards a truly scalable device.Such systems guarantee extendibility, they incorporate the interface with communication applications and relax the physical realization of the device, allowing for defect tolerance.Flying qubits are included in the more general concept of a quantum bus, a mediating system which can be of higher dimension.Such a quantum bus can be used in the straightforward preparation of a standard multi-qubit resource enabling measurement based quantum computation, the cluster state.This constitutes the framework for the results presented in this thesis.We begin by investigating the effects of dissipation in the continuous variable bus scheme known as the qubus scheme.By considering loss in the bus as it mediates interactions between the stationary qubits, we obtain analytical results for the effective action of the induced quantum gate.We find that a particular two-qubit gate operates with high fidelity in the presence of moderate loss and give a simple iteration scheme to simplify the effects of loss on the qubits.We then attempt to reduce these effects by preparing the bus in more elaborate state, however no improvements are observed.We then apply the qubus scheme to the probabilistic generation of cluster states and develop an entangling gate working with high success probability.This allows us to produce cluster states far more efficiently than other proposals.Investigating new methods to analyze the performance of different generation strategies constitutes the second part of this set of results.We begin by making the large flow approximation, used in queuing theory, to obtain the optimal strategy in a regime with large resources.After what we take the other more familiar limit of single cluster growth and introduce absorbing Markov chains as a key mathematical tool.Finally we look at the transmission of composite quantum systems via a single higher dimensional bus.We provide generalized protocols and interactions guaranteeing a full transfer of the information from one composite system to another.These protocols can also serve information processing tasks, as useful logical operations can be applied to the data as it is transfered.We notice lastly that the qubus scheme constitutes a potential physical realization.
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.
We present here a new approach to scalable quantum computing—a 'qubus computer'—which realizes qubit measurement and quantum gates through interacting qubits with a quantum communication bus mode. The qubits could be 'static' matter qubits or 'flying' optical qubits, but the scheme we focus on here is particularly suited to matter qubits. There is no requirement for direct interaction between the qubits. Universal two-qubit quantum gates may be effected by schemes which involve measurement of the bus mode, or by schemes where the bus disentangles automatically and no measurement is needed. In effect, the approach integrates together qubit degrees of freedom for computation with quantum continuous variables for communication and interaction.
We investigate experiments of continuous-variable quantum information processing based on the teleportation scheme. Quantum teleportation, which is realized by a two-mode squeezed vacuum state and measurement-and-feedforward, is considered as an elementary quantum circuit as well as quantum communication. By modifying ancilla states or measurement-and-feedforwards, we can realize various quantum circuits which suffice for universal quantum computation. In order to realize the teleportation-based computation we improve the level of squeezing, and fidelity of teleportation. With a high-fidelity teleporter we demonstrate some advanced teleportation experiments, i.e., teleportation of a squeezed state and sequential teleportation of a coherent state. Moreover, as an example of the teleportation-based computation, we build a QND interaction gate which is a continuous-variable analog of a CNOT gate. A QND interaction gate is constructed only with ancillary squeezed vacuum states and measurement-and-feedforwards. We also create continuous-variable four mode cluster type entanglement for further application, namely, one-way quantum computation.
Processing information quantum mechanically is known to enable new communication and computational scenarios that cannot be accessed with conventional information technology (IT). We present here a new approach to scalable quantum computing---a "qubus computer"---which realizes qubit measurement and quantum gates through interacting qubits with a quantum communication bus mode. The qubits could be "static" matter qubits or "flying" optical qubits, but the scheme we focus on here is particularly suited to matter qubits. Universal two-qubit quantum gates may be effected by schemes which involve measurement of the bus mode, or by schemes where the bus disentangles automatically and no measurement is needed. This approach enables a parity gate between qubits, mediated by a bus, enabling near-deterministic Bell state measurement and entangling gates. Our approach is therefore the basis for very efficient, scalable QIP, and provides a natural method for distributing such processing, combining it with quantum communication.
We propose a hybrid quantum computing scheme where qubit degrees of freedom for computation are combined with quantum continuous variables for communication. In particular, universal two-qubit gates can be implemented deterministically through qubit-qubit communication, mediated by a continuous-variable bus mode (``qubus''), without direct interaction between the qubits and without any measurement of the qubus. The key ingredients are controlled rotations of the qubus and unconditional qubus displacements. The controlled rotations are realizable through typical atom-light interactions in quantum optics. For such interactions, our scheme is universal and works in any regime, including the limits of weak and strong nonlinearities.