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Scientific Reports

Hybrid Toffoli gate on photons and quantum spins

Ming-Xing Luo, Song-Ya Ma, Xiu‐Bo Chen, Xiaojun Wang

Published Nov 16, 2015• 11 citations
Publisher

Abstract

Quantum computation offers potential advantages in solving a number of interesting and difficult problems. Several controlled logic gates, the elemental building blocks of quantum computer, have been realized with various physical systems. A general technique was recently proposed that significantly reduces the realization complexity of multiple-control logic gates by harnessing multi-level information carriers. We present implementations of a key quantum circuit: the three-qubit Toffoli gate. By exploring the optical selection rules of one-sided optical microcavities, a Toffoli gate may be realized on all combinations of photon and quantum spins in the QD-cavity. The three general controlled-NOT gates are involved using an auxiliary photon with two degrees of freedom. Our results show that photons and quantum spins may be used alternatively in quantum information processing.

DOI
10.1038/srep16716

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Quantum computation offers potential advantages in solving a number of interesting and difficult problems. Several controlled logic gates, the elemental building blocks of quantum computer, have been realized with various physical systems. A general technique was recently proposed that significantly reduces the realization complexity of multiple-control logic gates by harnessing multi-level information carriers. We present implementations of a key quantum circuit: the three-qubit Toffoli gate. By exploring the optical selection rules of one-sided optical microcavities, a Toffoli gate may be realized on all combinations of photon and quantum spins in the QD-cavity. The three general controlled-NOT gates are involved using an auxiliary photon with two degrees of freedom. Our results show that photons and quantum spins may be used alternatively in quantum information processing.
Abstract Although universal quantum computation can be realized with two-qubit controlled-not (CNOT) gates and single-qubit rotations, it would be convenient to have resource-efficient and robust multiqubit quantum gates in practical quantum information processing. Here we present two new schemes to determinately implement three-qubit Toffoli gate and Fredkin gate on photon systems with two degrees of freedom (DOFs), assisted by charged quantum dots (QDs) inside single-sided optical microcavities. In contrast to the traditional Toffoli and Fredkin gates operating in photonic one DOF, the gates presented here with two DOFs can reduce the photon numbers required to implement the gate operations. Compared with the ones synthesized by CNOT and single-qubit gates, the present gates can reduce the complexity in experiment. Our schemes exploit the robust giant circular birefringence induced by a single-electron spin in a QD-cavity system, which do not require photon indistinguishability or photon interference as demanded by other schemes using linear optics. Moreover, additional ancillary photons are not required in the schemes. We discuss the feasibility of our schemes, concluding that they can be realized with current or near-future technologies.
High-efficiency quantum information processing is equivalent to the fewest quantum resources and the simplest operations by means of logic qubit gates. Based on the reflection geometry of a single photon interacting with a three-level ΛΛΛ-typle atom-cavity system, we present some refined protocols for realizing controlled-not (CNOT), Fredkin, and Toffoli gates on hybrid systems. The first control qubit of our gates is encoded on a flying photon, and the rest qubits are encoded on the atoms in optical cavity. Moreover, these quantum gates can be extended to the optimal synthesis of multi-qubit CNOT, Fredkin and Toffoli gates with O(n) optical elements without auxiliary photons or atoms. Further, the simplest single-qubit operations are applied to the photon only, which make these logic gates experimentally feasible with current technology.
Abstract High‐efficiency quantum information processing is equivalent to the fewest quantum resources and simplest operations by means of logic qubit gates. Based on the reflection geometry of a single photon interacting with a three‐level Λ‐type atom‐cavity system, the authors present some refined protocols for realizing controlled‐not (CNOT), Fredkin, and Toffoli gates on hybrid systems. The first control qubit of gates is encoded on a flying photon, and the remaining qubits are encoded on the atoms in the optical cavity. Moreover, these quantum gates can be extended to the optimal synthesis of multi‐qubit CNOT, Fredkin, and Toffoli gates with optical elements without auxiliary photons or atoms. Further, the simplest single‐qubit operations are applied to the photon only, which make these logic gates experimentally feasible with current technology.
Minimizing the number of necessary two-qubit gates is an important task in quantum information processing. By introducing non-computational quantum states in auxiliary spaces, we construct effective circuits for the controlled-NOT (CNOT) gate and the n-control-qubit Toffoli gate with (2n-1) qubit-qudit gates and (2n-2) single-qudit gates. We propose the polarization CNOT and Toffoli gates based on the designed quantum circuits in linear optics by operating on the spatial-mode degree of freedom of photons. Our optical schemes can be achieved with a higher success probability and no extra auxiliary photons are needed.
Quantum state joining has been recently experimentally demonstrated [C. Vitelli et al., Nat. Photon. 7, 521 (2013)] which can transfer two input photonic qubits into a photonic ququart. Here, we revisit these processes from a hybrid point of view. By exploring the giant optical circular birefringence induced by quantum-dot spins in one-sided optical microcavities, we introduce some deterministic joining schemes including two quantum-dot spin joining, hybrid photon and quantum-dot spin joining, and two-photon joining. The input quantum information is represented by one photon with polarization and spatial mode degrees of freedom (DOFs). These schemes are also adapted to the inverse processes called quantum state splitting because all the joining procedures are unitary and do not require projection and feed-forward steps. The fused photon is convenient for realizing elementary logic gates such as the controlled-not (cnot) gate, swap gate, and Toffoli gate. These hybrid fusion and splitting schemes provide flexible synthesis of the quantum-dot spin and photon in quantum applications. The transmission superiority of photons and storage superiority of the quantum-dot spin may be combined for quantum network communication or quantum computations.
High-fidelity quantum logic gates are essential in quantum computation, and both photons and electron spins in quantum dots (QDs) have their own unique advantages in implementing quantum computation. It is of critical significance to achieve high-fidelity quantum gates for photon-QD hybrid systems. Here, we propose two schemes for implementing high-fidelity universal quantum gates including Toffoli gate and Fredkin gate for photon-QD hybrid systems, utilizing the practical scattering of a single photon off a QD-cavity system. The computation errors from the imperfections involved in the practical scattering are detected and prevented from arising in the final results of the two gates. Accordingly, the unity fidelity of each quantum gate is obtained in the nearly realistic condition, and the requirement for experimental realization is relaxed. Furthermore, the quantum circuits for the two gates are compact and no auxiliary qubits are required, which would also be the advantages regarding their experimental feasibility. These features indicate that our schemes may be useful in the practical quantum computation tasks.