Quantum information can be protected from decoherence and other errors, but only if these errors are sufficiently rare. For quantum computation to become a scalable technology, practical schemes for quantum error correction that can tolerate realistically high error rates will be necessary. In some physical systems, errors may exhibit a characteristic structure that can be carefully exploited to improve the efficacy of error correction. Here, we describe a scheme for topological quantum error correction to protect quantum information from a dephasing-biased error model, where we combine a repetition code with a topological cluster state. We find that the scheme tolerates error rates of up to 1.37%-1.83% per gate, requiring only short-range interactions in a two-dimensional array.
Quantum information processing and its associated technologies has reached an interesting and timely stage in their development where many different experiments have been performed establishing the basic building blocks. The challenge moving forward is to scale up to larger sized quantum machines capable of performing tasks not possible today. This raises a number of interesting questions like: How big will these machines need to be? how many resources will they consume? This needs to be urgently addressed. Here we estimate the resources required to execute Shors factoring algorithm on a distributed atom-optics quantum computer architecture. We determine the runtime and requisite size of the quantum computer as a function of the problem size and physical error rate. Our results suggest that once experimental accuracy reaches levels below the fault-tolerant threshold, further optimisation of computational performance and resources is largely an issue of how the algorithm and circuits are implemented, rather than the physical quantum hardware
In this paper we introduce a design for an optical topological cluster state computer constructed exclusively from a single quantum component. Unlike previous efforts we eliminate the need for on demand, high fidelity photon sources and detectors and replace them with the same device utilised to create photon/photon entanglement. This introduces highly probabilistic elements into the optical architecture while maintaining complete specificity of the structure and operation for a large scale computer. Photons in this system are continually recycled back into the preparation network, allowing for a arbitrarily deep 3D cluster to be prepared using a comparatively small number of photonic qubits and consequently the elimination of high frequency, deterministic photon sources.
Dynamic coupling of cavities to a quantum network is of major interest to distributed quantum information processing schemes based on cavity quantum electrodynamics. This can be achieved by active tuning a mediating atom-cavity system. In particular, we consider the dynamic coupling between two coupled cavities, each interacting with a two-level atom, realized by tuning one of the atoms. One atom-field system can be controlled to become maximally and minimally coupled with its counterpart, allowing high fidelity excitation confinement, Q-switching and reversible state transport. As an application, we first show that simple tuning can lead to emission of near-Gaussian single-photon pulses that is significantly different from the usual exponential decay in a passive cavity-based system. The influences of cavity loss and atomic spontaneous emission are studied in detailed numerical simulations, showing the practicality of these schemes within the reach of current experimental technology in solid-state environment. We then show that when the technique is employed to an extended coupled-cavity scheme involving a multi-level atom, arbitrary temporal superposition of single photons can be engineered in a deterministic way.
Cavity quantum electrodynamic schemes for quantum gates are amongst the earliest quantum computing proposals. Despite continued progress, and the dramatic recent demonstration of photon blockade, there are still issues with optimal coupling and gate operation involving high-quality cavities. Here we show dynamic control techniques that allow scalable cavity-QED based quantum gates, that use the full bandwidth of the cavities. When applied to quantum gates, these techniques allow an order of magnitude increase in operating speed, and two orders of magnitude reduction in cavity Q, over passive cavity-QED architectures. Our methods exploit Stark shift based Q-switching, and are ideally suited to solid-state integrated optical approaches to quantum computing.
According to idealized models, a strong Kerr non-linearity may be used to build optical quantum gates for optical quantum information processing by inducing conditional phase shifts on quantum states. Recently, Shapiro (PRA 73, 062305 (2006)) argued that for a Kerr medium with non-instantaneous but fast response, essentially no phase shift is induced on two-single-photon input states, and thus a quantum gate build from such a medium cannot work. Here we show that a fast response Kerr medium induces some but very little phase shifts on a two-single-photon input state, and it is insufficient for high fidelity quantum computation. We point out that this is caused by the medium imparting spectral entanglement to the input photons. We further show that a way to circumvent this problem and achieve a high fidelity gate, is to engineer the dispersion properties of the medium to give a dominant spectral effect over the non-instantaneous response, in addition to satisfying a phase matching condition.
Optical $chi^{(2)}$ non-linearity can be used for parametric amplification and producing down-converted entangled photon pairs that have broad applications. It is known that weak non-linear media exhibit dispersion and produce a frequency response. It is therefore of interest to know how spectral effects of a strong $chi^{(2)}$ crystal affect the performance. Here we model the spectral effects of the dispersion of a strong $chi^{(2)}$ crystal and illustrate how this affects its ability to perform Bell measurements and influence the performance of a quantum gates that employ such a Bell measurement. We show that a Dyson series expansion of the unitary operator is necessary in general, leading to unwanted spectral entanglement. We identify a limiting situation employing periodic poling, in which a Taylor series expansion is a good approximation and this entanglement can be removed.
