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IEEE Journal of Selected Topics in Quantum Electronics

Interaction-Free Quantum Optical Fredkin Gates in $\chi^{(2)}$ Microdisks

Yuping Huang, Prem Kumar

Published Apr 7, 2011• 29 citations
Publisher

Abstract

We present novel “interaction-free” realizations of quantum optical Fredkin gates that do not rely on direct physical coupling between the target light (signal) and the control light (pump). The interaction-free feature of such gates allow to overcome the fundamental limits of photon loss and quantum-state decoherence imposed by the signal-pump coupling. This advantage, together with the low inherent quantum-noise level in χ(2)microdisks, gives rise to substantially improved performance over the existing Fredkin-gate designs. Explicitly using lithium-niobate mircrodisks, we present two kinds of interaction-free Fredkin gates, a phase gate and an optical-path gate, both of which are designed with telecom-band applications in mind. For both gates, the threshold pump peak power to achieve a gate contrast >;100 and a signal loss <;10% is hundreds of microwatts for practical parameters of the devices.

DOI
10.1109/jstqe.2011.2116111

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Interaction-Free Quantum Optical Fredkin Gates in χ(2)\chi^{(2)}χ(2) Microdisks
We present novel “interaction-free” realizations of quantum optical Fredkin gates that do not rely on direct physical coupling between the target light (signal) and the control light (pump). The interaction-free feature of such gates allow to overcome the fundamental limits of photon loss and quantum-state decoherence imposed by the signal-pump coupling. This advantage, together with the low inherent quantum-noise level in χ(2)microdisks, gives rise to substantially improved performance over the existing Fredkin-gate designs. Explicitly using lithium-niobate mircrodisks, we present two kinds of interaction-free Fredkin gates, a phase gate and an optical-path gate, both of which are designed with telecom-band applications in mind. For both gates, the threshold pump peak power to achieve a gate contrast >;100 and a signal loss <;10% is hundreds of microwatts for practical parameters of the devices.
We propose an interaction-free scheme for all-optical switching which does not rely on the physical coupling between signal and control waves. The interaction-free nature of the scheme allows it to overcome the fundamental photon-loss limit imposed by the signal-pump coupling. The same phenomenon protects photonic-signal states from decoherence, making devices based on this scheme suitable for quantum applications. Focusing on $\ensuremath{\chi}{}^{(2)}$ waveguides, we provide device designs for traveling-wave and Fabry-Perot switches. In both designs, the performance is optimal when the signal switching is induced by coherent dynamical evolution. In contrast, when the switching is induced by a rapid dissipation channel, it is less efficient.
The quantum optical Fredkin gate is an indispensable resource for networkable quantum applications. Its performance in practical implementations, however, is limited fundamentally by the inherent quantum fluctuations of the pump waves. We demonstrate a method to overcome this drawback by exploiting stimulated Raman scattering in fiber-based implementations. Using a Sagnac fiber-loop switch as a specific example, we show that high switching contrast can be maintained even in the presence of significant pump fluctuations. This unique feature of self-stabilization, together with high-speed and low-loss performance of such devices, point to a viable technology for practical quantum communications.
We present an all-optical control device in which coupling a weak control optical field into a high-QQQ lithium niobate whispering-gallery-mode microcavity decouples it from a signal field due to nonlinear optical interactions. This results in switching and modulation of the signal with low-power control pulses. In the quantum limit, the underlying nonlinear-optical process corresponds to the quantum Zeno blockade. Its ``interaction-free'' nature effectively alleviates loss and decoherence for the signal waves. This work therefore presents experimental progress towards acquiring large phase shifts with few photons or even at the single-photon level.
The decoherence effect caused by the coupling between the system and the environment undoubtedly leads to the errors in efficient implementations of two (or three) qubit logical gates in quantum information processing. Fortunately, decoherence-free subspace (DFS) introduced can effectively decrease the influence of decoherence effect. In this paper, we propose some schemes for setting up a family of quantum control gates, including controlled-NOT (CNOT), Toffoli, and Fredkin gates for two or three logical qubits by means of cross-Kerr nonlinearities in DFS. These three logical gates require neither complicated quantum computational circuits nor auxiliary photons (or entangled states). The success probabilities of three logical gates are approximate 1 by performing the corresponding classical feed-forward operations based on the different measuring results of the X-homodyne detectors, and their fidelities are robust against the photon loss with the current technology. The proposed logical gates rely on only simple linear-optics elements, available single-qubit operations, and mature measurement methods, making our proposed gates be feasible and efficient in practical applications.
One of the greatest challenges in modern science is the realisation of quantum computers which, as their scale increases, will allow enhanced performance of tasks across many areas of quantum information processing. Quantum logic gates play a vital role in realising these applications by carrying out the elementary operations on the qubits; a key aim is minimising the resources needed to build these gates into useful circuits. While the salient features of a quantum computer have been shown in proof-of-principle experiments, e.g., single- and two-qubit gates, difficulties in scaling quantum systems to encode and manipulate multiple qubits has hindered demonstrations of more complex operations. This is exemplified by the classical Fredkin (or controlled-SWAP) gate [1] for which, despite many theoretical proposals [2,3] relying on concatenating multiple two-qubit gates, a quantum analogue has yet to be realised. Here, by directly adding control to a two-qubit SWAP unitary [4], we use photonic qubit logic to report the first experimental demonstration of a quantum Fredkin gate [5]. Our scheme uses linear optics and improves on the overall probability of success by an order of magnitude over previous proposals [2,3]. This optical approach allows us to add control an arbitrary black-box unitary which is otherwise forbidden in the standard circuit model [6]. Additionally, the action of our gate exhibits quantum coherence allowing the generation of the highest fidelity three-photon GHZ states to date. The quantum Fredkin gate has many applications in quantum computing, quantum measurements [7] and cryptography [8,9]. Using our scheme, we apply the Fredkin gate to the task of direct measurements of the purity and state overlap of a quantum system [7] without recourse to quantum state tomography.