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arXiv:cond-mat/0412114

Fault-tolerant quantum computing with spins using the conditional Faraday rotation

Michael Niklaus Leuenberger

Published Dec 6, 2004• 0 citations
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Abstract

We propose a fault-tolerant scheme for deterministic quantum computing with spins that is based on a quantum teleportation scheme using the conditional Faraday rotation. The phase gate between two sets of noninteracting quantum dots, embedded in microcavities inside a photonic crystal, is mediated by single photons, which yields a Faraday rotation rate high enough for gate operation times of 100 ps. Using sets of quantum dots and error correction codes makes our scheme fault-tolerant. Single-qubit operations on encoded qubits can be implemented by means of the optical Stark effect combined with the optical RKKY interaction.

DOI
10.48550/arxiv.cond-mat/0412114

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We propose a fault-tolerant scheme for deterministic quantum computing with spins that is based on a quantum teleportation scheme using the conditional Faraday rotation. The phase gate between two sets of noninteracting quantum dots, embedded in microcavities inside a photonic crystal, is mediated by single photons, which yields a Faraday rotation rate high enough for gate operation times of 100 ps. Using sets of quantum dots and error correction codes makes our scheme fault-tolerant. Single-qubit operations on encoded qubits can be implemented by means of the optical Stark effect combined with the optical RKKY interaction.
We propose a scalable fault-tolerant scheme for deterministic quantum computing with spins that is based on a three-particle entanglement produced by the conditional Faraday rotation of the polarization of single photons due to the nonresonant interaction with spins of quantum dots, embedded in microcavities inside a photonic crystal. The resulting conditional phase gate yields switching times of 50ps50\phantom{\rule{0.3em}{0ex}}\mathrm{ps}50ps. We show that it acts fault-tolerantly not only on the Calderbank-Shor-Steane quantum error correction codes, but also on Shor's code in a single shot. Single-qubit operations on Shor's logical qubits can be implemented by means of the optical Stark effect combined with the optical Ruderman-Kittel-Kasuya-Yosida interaction in a single shot.
We present some compact quantum circuits for a deterministic quantum computing on electron-spin qubits assisted by quantum dots inside single-side optical microcavities, including the CNOT, Toffoli, and Fredkin gates. They are constructed by exploiting the giant optical Faraday rotation induced by a single-electron spin in a quantum dot inside a single-side optical microcavity as a result of cavity quantum electrodynamics. Our universal quantum gates have some advantages. First, all the gates are accomplished with a success probability of 100% in principle. Second, our schemes require no additional electron-spin qubits and they are achieved by some input-output processes of a single photon. Third, our circuits for these gates are simple and economic. Moreover, our devices for these gates work in both the weak coupling and the strong coupling regimes, and they are feasible in experiment.
We construct a fault-tolerant quantum error-correcting protocol based on a qubit encoded in a large spin qudit using a spin-cat code, analogous to the continuous-variable cat encoding. With this, we can correct the dominant error sources, namely processes that can be expressed as error operators that are linear or quadratic in the components of angular momentum. Such codes tailored to dominant error sources can exhibit superior thresholds and lower resource overheads when compared to those designed for unstructured noise models. A key component is the gate that preserves the rank of spherical tensor operators. Categorizing the dominant errors as phase and amplitude errors, we demonstrate how phase errors, analogous to phase-flip errors for qubits, can be effectively corrected. Furthermore, we propose a measurement-free error-correction scheme to address amplitude errors without relying on syndrome measurements. Through an in-depth analysis of logical gate errors, we establish that the fault-tolerant threshold for error correction in the spin-cat encoding surpasses that of standard qubit-based encodings. We consider a specific implementation based on neutral-atom quantum computing, with qudits encoded in the nuclear spin of 87 Sr , and show how to generate the universal gate set, including the rank-preserving gate, using quantum control and the Rydberg blockade. These findings pave the way for encoding a qubit in a large spin with the potential to achieve fault tolerance, high threshold, and reduced resource overhead in quantum information processing. Published by the American Physical Society 2024
Using linear optical manipulation, single photons, entangled photon pairs, photon measurement, and classical communication, we propose a scheme for a two-spin-qubit phase gate and the teleportation of a controlled-not gate between two electron spins from acting on local qubits to acting on remote qubits using quantum dots in optical microcavities. The scheme is based on spin selective photon reflection from the cavity and is achieved in a deterministic way by the sequential detection of photons and the single-qubit rotations of a single electron spin in a self-assembled GaAs-InAs quantum dot. The feasibility of the scheme is assessed showing that high average fidelities of the gates are achievable in the weak-coupling regime when the side leakage and cavity loss are low. The scheme opens promising possibilities for long-distance quantum communication, distributed quantum computation, and construction of remote quantum-information-processing networks.
In this article, we propose an experimental scheme for implementing quantum teleportation of tripartite GHZ-Like state under the control of the controller. Due to the entanglement produced by the interaction between quantum dots embedded in microcavities and a single photon, the controlled quantum teleportation scheme of tripartite GHZ-Like state encoded in the electron spins in quantum dots can be realized in terms of theory via the conditional Faraday rotation of the polarization of single photons, single photons detection, and electron spin orientation measurement. By choosing the appropriate Faraday rotation angle for the switchable microcavities, the success probability of controlled quantum teleportation can reach 1. The similar controlled quantum teleportation procedure discussed here can be generalized to the quantum teleportation of multipartite GHZ-Like state.
We propose a teleportation scheme that relies only on single-photon measurements and Faraday rotation, for teleportation of many-qubit entangled states stored in the electron spins of a quantum dot system. The interaction between a photon and the two electron spins, via Faraday rotation in microcavities, establishes Greenberger-Horne-Zeilinger entanglement in the spin-photon-spin system. The appropriate single-qubit measurements, and the communication of two classical bits, produce teleportation. This scheme provides the essential link between spintronic and photonic quantum information devices by permitting quantum information to be exchanged between them.