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.
Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of the scheme is demonstrated by using a set of walk operations on a closed lattice form to implement the universal set of quantum gates on multi-qubit system. We also present a set of experimentally realizable walk operations that can implement Grover's algorithm, quantum Fourier transformation and quantum phase estimation algorithms. An elementary implementation of error detection and correction is also presented. Analysis of space and time complexity of the scheme highlights the advantages of quantum walk based model for quantum computation on systems where implementation of quantum walk evolution operations is an inherent feature of the system.
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±0.003 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 quantum walks that use a compact multi-mode interaction region to realize large multi-component quantum circuits.