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arXiv:2003.04473 · Physical Review Applied

Quantum Process Tomography of a Controlled-Phase Gate for Time-Bin Qubits

Hsin-Pin Lo, Takuya Ikuta, Nobuyuki Matsuda, Toshimori Honjo, William J. Munro, Hiroki Takesue

Published Mar 4, 2020• 25 citations
arXivHTMLPDF

Abstract

Time-bin qubits, where information is encoded in a single photon at different times, have been widely used in optical-fiber- and waveguide-based quantum communications. With the recent developments in distributed quantum computation, it is logical to ask whether time-bin encoded qubits may be useful in that context. We have recently realized a time-bin qubit controlled-phase (C-phase) gate using a $2\ifmmode\times\else\texttimes\fi{}2$ optical switch based on a lithium-niobate waveguide, with which we demonstrated the generation of an entangled state. However, the experiment was performed with only a pair of input states and thus the functionality of the C-phase gate was not fully verified. In this research, we use quantum process tomography to establish a process fidelity of $97.1\mathrm{%}$. Furthermore, we demonstrate the controlled-not gate operation with a process fidelity greater than $94\mathrm{%}$. This study confirms that typical two-qubit logic gates used in quantum computational circuits can be implemented with time-bin qubits and thus it is a significant step forward for the realization of distributed quantum computation based on time-bin qubits.

DOI
10.1103/physrevapplied.13.034013

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•Nov 19, 2019•9 citations
Time-bin qubits, where information is encoded in a single photon at different times, have been widely used in optical-fiber- and waveguide-based quantum communications. With the recent developments in distributed quantum computation, it is logical to ask whether time-bin encoded qubits may be useful in that context. We have recently realized a time-bin qubit controlled-phase (C-phase) gate using a 2\ifmmode×\else\texttimes\fi22\ifmmode\times\else\texttimes\fi{}22\ifmmode×\else\texttimes\fi2 optical switch based on a lithium-niobate waveguide, with which we demonstrated the generation of an entangled state. However, the experiment was performed with only a pair of input states and thus the functionality of the C-phase gate was not fully verified. In this research, we use quantum process tomography to establish a process fidelity of 97.1\mathrm{%}. Furthermore, we demonstrate the controlled-not gate operation with a process fidelity greater than 94\mathrm{%}. This study confirms that typical two-qubit logic gates used in quantum computational circuits can be implemented with time-bin qubits and thus it is a significant step forward for the realization of distributed quantum computation based on time-bin qubits.
Quantum logic gates are important for quantum computation and quantum information processing in numerous physical systems. Although time-bin qubits are suitable for quantum communication over optical fiber, many essential quantum logic gates for them have not yet been realized. Here, we demonstrated a controlled-phase (C-Phase) gate for time-bin qubits that uses a 2 × 2 optical switch based on an electro-optic modulator. A Hong–Ou–Mandel interference measurement showed that the switch could work as a time-dependent beam splitter with a variable splitting ratio. We confirmed that two independent time-bin qubits were entangled as a result of C-Phase gate operation with the switch.
Quantum computers comprise elementary logic gates that initialize, control and measure delicate quantum states. One of the most important gates is the controlled-NOT, which is widely used to prepare two-qubit entangled states. The controlled-NOT gate for single photon qubits is normally realized as a six-mode network of individual beamsplitters. This architecture however, utilizes only a small fraction of the circuit for the quantum operation with the majority of the footprint dedicated to routing waveguides. Quantum walks are an alternative photonics platform that use arrays of coupled waveguides with a continuous interaction region instead of discrete gates. While quantum walks have been successful for investigating condensed matter physics, applying the multi-mode interference for logical quantum operations is yet to be shown. Here, we experimentally demonstrate a two-qubit controlled-NOT gate in an array of lithium niobate-on-insulator waveguides. We engineer the tight-binding Hamiltonian of the six evanescently-coupled single-mode waveguides such that the multi-mode interference corresponds to the linear optical controlled-NOT unitary. We measure the two-qubit transfer matrix with 0.938±0.0030.938\pm0.0030.938±0.003 fidelity, and we use the gate to generate entangled qubits with 0.945±0.0020.945\pm0.0020.945±0.002 fidelity by preparing the control photon in a superposition state. Our results highlight a new application for quantum walks that use a compact multi-mode interaction region to realize large multi-component quantum circuits.
Abstract The two-qubit controlled-NOT gate is one of the central entangling operations in quantum information technology. The controlled-NOT gate for single photon qubits is normally realized as a network of five individual beamsplitters on six optical modes. Quantum walks (QWs) are an alternative photonic architecture involving arrays of coupled waveguides, which have been successful for investigating condensed matter physics, however, have not yet been applied to quantum logical operations. Here, we engineer the tight-binding Hamiltonian of an array of lithium niobate-on-insulator waveguides to experimentally demonstrate the two-qubit controlled-NOT gate in a QW. We measure the two-qubit transfer matrix with 0.938 ± 0.003 fidelity, and we use the gate to generate entangled qubits with 0.945 ± 0.002 fidelity by preparing the control photon in a superposition state. Our results highlight a new application for QWs that use a compact multi-mode interaction region to realize large multi-component quantum circuits.
Abstract The realization of strong photon–photon interactions has presented an enduring challenge across photonics, particularly in quantum computing, where two-photon gates form essential components for scalable quantum information processing (QIP). While linear-optic schemes have enabled probabilistic entangling gates in spatio-polarization encoding, solutions for many other useful degrees of freedom remain missing. In particular, no two-photon gate for the important platform of frequency encoding has been experimentally demonstrated, due in large part to the additional challenges imparted by the mismatched wavelengths of the interacting photons. In this article, we design and implement an entangling gate for frequency-bin qubits, a coincidence-basis controlled-NOT (CNOT), using line-by-line pulse shaping and electro-optic modulation. We extract a quantum unitary fidelity of 0.91 ± 0.01 via a parameter inference approach based on Bayesian machine learning, which enables accurate gate reconstruction from measurements in the two-photon computational basis alone. Our CNOT imparts a single-photon frequency shift controlled by the frequency of another photon—an important capability in itself—and should enable new directions in fiber-compatible QIP.
We introduce our recent photonic quantum information processing experiments using the high-speed electro-optic modulator (EOM) based on a lithium niobate waveguides. First, we demonstrated the frequency shifter for single photons by using an optical single sideband (OSSB) modulator, which is based on the nested configuration of four phase modulators (PMs). By properly setting the RF modulation signal and the bias voltage to each PM, we can suppress unwanted sidebands to realize a frequency shifter that can tune the frequency of single photons with accuracy of an RF synthesizer. Using the OSSB modulator, we eliminated the frequency distinguishability between two single photons whose frequencies were different by 25 GHz, and as a result observed a Hong-Ou- Mandel interference with a visibility exceeding 90%. We also proposed and demonstrated a two-qubit controlled logic gate for time-bin qubits using a two-input, two-output optical switch. The switch enables us to individually perform different functions for two temporal bases as a time-dependent beam splitter, so that we can realize controlled-phase (C-Phase) gate for a time-bin qubit. We showed that the states of two separable single photons were entangled as a result of the C-Phase gate operation. We performed the quantum state tomography to obtain density matrices of the output states from the C-Phase gate for some specific input states, and confirmed that the averaged state fidelity to the pure states was 85%. These results indicate that the EOMs will be a useful tool for realizing advanced photonic quantum communication systems.