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Quantum Science and Technology

Quantum logical controlled-NOT gate in a lithium niobate-on-insulator photonic quantum walk

Robert J. Chapman, Samuel Häusler, Giovanni Finco, Fabian Kaufmann, Rachel Grange

Published Nov 7, 2023• 16 citations
Publisher

Abstract

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.

DOI
10.1088/2058-9565/ad0a48

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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.
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.
Photonic quantum walks (PQWs), realized in lattices of evanescently coupled waveguides, are a powerful platform for demonstrating quantum [1], topological [2] and localization phenomena [3]. The PQW dynamics are captured with a tight-binding Hamiltonian, whose parameters can be engineered with the geometry of the waveguide array. It has been proposed that the two-qubit controlled-NOT (CNOT) gate can be implemented by quantum interference of two-photons in a carefully engineered PQW [4]. Whereas photonic quantum logic gates typically rely on a network of beamsplitters [5], the PQW implements the quantum logic in a single step. While multi-photon experiments in PQWs have been demonstrated [1]–[3], where photon-photon bunching governs the dynamics, the controlled preparation of entangling logic gates is yet to be experimentally explored.
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.
Lithium niobate photonic circuits have the salutary property of permitting the generation, transmission, and processing of photons to be accommodated on a single chip. Compact photonic circuits such as these, with multiple components integrated on a single chip, are crucial for efficiently implementing quantum information processing schemes.We present a set of basic transformations that are useful for manipulating modal qubits in Ti:LiNbO(3) photonic quantum circuits. These include the mode analyzer, a device that separates the even and odd components of a state into two separate spatial paths; the mode rotator, which rotates the state by an angle in mode space; and modal Pauli spin operators that effect related operations. We also describe the design of a deterministic, two-qubit, single-photon, CNOT gate, a key element in certain sets of universal quantum logic gates. It is implemented as a Ti:LiNbO(3) photonic quantum circuit in which the polarization and mode number of a single photon serve as the control and target qubits, respectively. It is shown that the effects of dispersion in the CNOT circuit can be mitigated by augmenting it with an additional path. The performance of all of these components are confirmed by numerical simulations. The implementation of these transformations relies on selective and controllable power coupling among single- and two-mode waveguides, as well as the polarization sensitivity of the Pockels coefficients in LiNbO(3).
For quantum computation using photons, performing deterministic quantum gate operations is a challenge due to the probabilistic nature of the photon-photon interaction. Encoding qubits in multiple degrees-of-freedom of photons and controlling operations between them is one of the promising ways to navigate the probabilistic behavior. Using single-photon discrete-time quantum walk in combination with polarization and path degrees-of-freedom, we experimentally demonstrate the realization of a universal set of quantum gates with high fidelity at room temperature. The deterministic realization of quantum gates through photonic quantum walk are characterized via quantum state tomography. For a three-qubit system using a single photon, the first qubit is encoded using polarization information, and the other two qubits are encoded using path information, closely resembling a Galton-board setup. To generate a six-qubit Greenberger-Horne-Zeilinger state, entangled photon pairs are used to entangle the two three-qubit modules on which gate operations are performed. We also provide insights into the mapping of photonic quantum walk operations to quantum circuits and propose methods to resourcefully scale. This demonstration marks a significant progress towards using quantum walks for quantum computing and provides a framework for using fewer photons in combination with different degrees-of-freedom of photon to scale the number of qubits.
Abstract Quantum walks (QWs) are one of the fundamental concepts in quantum information science, being an essential component for various new applications. Implementing QWs using integrated photonic waveguide lattices allows for realizing long evolution times, for exploring novel lattice geometries, and even for controllable coupling to the environment. This tutorial gives an introduction to the field of on-chip QWs of single photons and photon pairs featuring non-classical two-photon correlations.