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Advances in Photonics of Quantum Computing, Memory, and Communication

Deterministic two-photon controlled phase gate by exploiting nonlinear pi-phase shift in photonic molecule generations

Zihao Chen, Yao Zhou, Jung‐Tsung Shen

Published Mar 4, 2019• 1 citation
Publisher

Abstract

To resolve the intrinsic trade-off between the deterministic nature and scalability of controlled phase gate implementation in the linear optics regime, we propose a novel deterministic two-photon controlled phase gate scheme in chiral quantum nanophotonics. The essential ingredient here is that, a non-linear π-phase shift is imprinted during the photonic molecule generations. On one hand, the gate operates in a deterministic way without the assistance of probabilistic ancilla qubit measurement. On the other hand, the gate implementation is of low complexity to be highly scalable. To date, the chiral coupling is readily underpinned by the advent of directional emission technique. Potential implementation platforms include QD, superconducting qubit, Rydberg atom, or N-V center that is coupled to a PhC waveguide, transmission line, or optical fiber.

DOI
10.1117/12.2517035

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To resolve the intrinsic trade-off between the deterministic nature and scalability of controlled phase gate implementation in the linear optics regime, we propose a novel deterministic two-photon controlled phase gate scheme in chiral quantum nanophotonics. The essential ingredient here is that, a non-linear π-phase shift is imprinted during the photonic molecule generations. On one hand, the gate operates in a deterministic way without the assistance of probabilistic ancilla qubit measurement. On the other hand, the gate implementation is of low complexity to be highly scalable. To date, the chiral coupling is readily underpinned by the advent of directional emission technique. Potential implementation platforms include QD, superconducting qubit, Rydberg atom, or N-V center that is coupled to a PhC waveguide, transmission line, or optical fiber.
Deterministic Two-photon Controlled-phase Gate Enabled by Induced π\piπ -phase Shift in Photonic Molecule Generations
We propose a novel deterministic two-photon controlled-phase gate scheme enabled by a nonlinear π\piπ -phase shift imprinted during photonic molecule generations, which serves as a vital building block for scalable photon-based quantum computing network. © 2019 The Author(s)
Photons are appealing as flying quantum bits due to their low-noise, long coherence times, light-speed transmission, and ease of manipulation at the single-qubit level using standard optical components such as beam splitters and waveguides. The challenge in optical quantum information processing has been the realization of two-qubit gates for photonic qubits due to the lack of highly efficient optical Kerr nonlinearities at the single-photon level. To date, only probabilistic two-qubit photonic controlled-phase gates based on linear optics and projective measurement using photon detectors have been demonstrated. Here we show that a high-fidelity frequency-encoded deterministic two-photon controlled-phase gate can be achieved by exploiting the strong photon-photon correlation enabled by photonic dimers, and the unique nonreciprocal photonic propagation in chiral quantum nanophotonic systems.
Engineering deterministic photonic gates with simple resources is one of the long-standing challenges in photonic quantum computing. Here, we design a passive conditional gate between copropagating photons using an array of only two-level emitters. The key resource is to harness the effective photon-photon interaction induced by the chiral coupling of the emitter array to two waveguide modes with different resonant momenta at the emitter’s transition frequency. By studying the system’s multiphoton scattering response, we demonstrate that, in certain limits, this configuration induces a nonlinear π -phase shift between the polariton eigenstates of the system without distorting spectrally the wave packets. Then, we show how to harness this nonlinear phase shift to engineer a conditional, deterministic photonic gate in different qubit encodings, with a fidelity arbitrarily close to 1 in the limit of large number of emitters and coupling efficiency. Our configuration can be implemented in topological photonic setups with multiple chiral-edge modes, opening their use for quantum information processing, or in other setups where such chiral light-matter couplings can be effectively obtained, such as optical fibers or photonic-crystal optical and microwave waveguides.
Photon-based quantum logic gate has substantial advantages over conventional atom-based designs as a result of a longer coherence time and an inherent compatibility with quantum communication protocol of flying qubits, photons. As a vital logic gate for universal quantum computing, the two-photon controlled-phase gate demands a few-photon nonlinearity, which historically suffers from either an indeterministic nature in the linear optics regime, or a weak nonlinearity within naturally-occurring materials in the nonlinear optics regime. It is intriguing yet challenging to deliver a logic gate design by exploiting a genuine fewphoton nonlinearity. In this dissertation, we study a particular one-dimensional quantum nanophotonic system that offers the desired few-photon nonlinearity through light-matter interactions in the quantum limit (i.e., between light quanta of photons and individual material formation of atoms). Towards this end, we study the exotic photonic trimer state generation to frst demonstrate few-photon nonlinearity. Then we report the breakdown of the non-Hermitian Hamiltonian for correlated multi-photon process to unveil the non-trivial effects of few-photon nonlinearity. Finally by exploiting such a nonlinearity, we present a deterministic two-photon controlled-phase gate proposal, and further showcase universal quantum logic gate designs in quantum nanophotonic systems.
The quantum logic between single photons lies at the foundation of deterministic, scalable quantum information processing. However, practical implementation suffers from weak optical nonlinearity, and gate fidelity is intrinsically limited by phase noise and spectral mixing. The authors address these concerns by utilizing an ultrahigh-QQQ photonic microcavity with ${\ensuremath{\chi}}^{2}$ nonlinearity. Two-photon spontaneous emission is thoroughly suppressed by shutting off the coupling channels between this artificial atom and the continuum states of a waveguide. This promising scheme for room-temperature operation is almost within reach of current experiments, and can be generalized to other systems.
We present a scheme for implementing a high-fidelity non-linear phase shift on a photonic state. The scheme is based on repeated scattering off a two-level quantum emitter embedded in a chiral or one-sided waveguide. The waveguide is equipped with elements inducing second-order dispersion and temporal phase shifts, which effectively form a harmonic trap and confine the photon pulses to a Gaussian shape. The same quantum emitter can be used for each scattering, and thus, only one quantum emitter is needed in this scheme. To illustrate the application of our scheme for photonic quantum computing and quantum communication, we analyze the implementation of a control-Z gate and a deterministic Bell-state analyzer for photonic qubits. Through numerical optimization, we show that we can reach a control-Z gate fidelity of F∼99.2%\mathcal{F} \sim 99.2\%F∼99.2% (F∼96%\mathcal{F} \sim 96\%F∼96%) and a success probability of Ps∼99.6%P_s \sim 99.6 \%Ps​∼99.6% (Ps∼98%P_s\sim 98 \%Ps​∼98%) for a Bell-state measurement with N=17N=17N=17 (N=5N=5N=5) scatterings.