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IET Optoelectronics

Photonic scheme for implementing quantum square root controlled Z gate using phase and intensity encoding of light

Minakshi Mandal, Sourangshu Mukhopadhyay

Published Jan 11, 2021• 20 citations
Publisher

Abstract

Abstract Quantum logic gate operates on a number of qubits, where a controlled Z gate operates on two qubit data. Similarly, the square root of controlled Z (SRCZ) operates also on two qubit data. The SRCZ gate is very much advantageous in quantum computing. Different quantum gates are implemented by using the physical properties of light such as phase, polarization, intensity, and frequency. Here, the authors propose a photonic scheme for implementing quantum SRCZ logic gate using phase as well as intensity encoding. The non‐linear property of Pockels material with proper external biasing voltage is used to develop the scheme.

DOI
10.1049/ote2.12008

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Abstract Quantum logic gate operates on a number of qubits, where a controlled Z gate operates on two qubit data. Similarly, the square root of controlled Z (SRCZ) operates also on two qubit data. The SRCZ gate is very much advantageous in quantum computing. Different quantum gates are implemented by using the physical properties of light such as phase, polarization, intensity, and frequency. Here, the authors propose a photonic scheme for implementing quantum SRCZ logic gate using phase as well as intensity encoding. The non‐linear property of Pockels material with proper external biasing voltage is used to develop the scheme.
We propose an efficient scheme to implement a multiplex-controlled phase gate with multiple photonic qubits simultaneously controlling one target photonic qubit based on circuit quantum electrodynamics (QED). For convenience, we denote this multiqubit gate as MCP gate. The gate is realized by using a two-level coupler to couple multiple cavities. The coupler here is a superconducting qubit. This scheme is simple because the gate implementation requires only one step of operation. In addition, this scheme is quite general because the two logic states of each photonic qubit can be encoded with a vacuum state and an arbitrary non-vacuum state ∣ φ 〉 (e.g., a Fock state, a superposition of Fock states, a cat state, or a coherent state, etc.) which is orthogonal or quasi-orthogonal to the vacuum state. The scheme has some additional advantages: because only two levels of the coupler are used, i.e., no auxiliary levels are utilized, decoherence from higher energy levels of the coupler is avoided; the gate operation time does not depend on the number of qubits; and the gate is implemented deterministically because no measurement is applied. As an example, we numerically analyze the circuit-QED based experimental feasibility of implementing a three-qubit MCP gate with photonic qubits each encoded via a vacuum state and a cat state. The scheme can be applied to accomplish the same task in a wide range of physical system, which consists of multiple microwave or optical cavities coupled to a two-level coupler such as a natural or artificial atom.
To realize fault-tolerant quantum computing, it is necessary to store quantum information in logical qubits with error correction functions, realized by distributing a logical state among multiple physical qubits or by encoding it in the Hilbert space of a high-dimensional system. Quantum gate operations between these error-correctable logical qubits, which are essential for implementation of any practical quantum computational task, have not been experimentally demonstrated yet. Here we demonstrate a geometric method for realizing controlled-phase gates between two logical qubits encoded in photonic fields stored in cavities. The gates are realized by dispersively coupling an ancillary superconducting qubit to these cavities and driving it to make a cyclic evolution depending on the joint photonic state of the cavities, which produces a conditional geometric phase. We first realize phase gates for photonic qubits with the logical basis states encoded in two quasiorthogonal coherent states, which have important implications for continuous-variable-based quantum computation. Then we use this geometric method to implement a controlled-phase gate between two binomially encoded logical qubits, which have an error-correctable function.
We propose a scheme of quantum computation with nonlinear quantum optics. Polarization states of photons are used for qubits. Photons with different frequencies represent different qubits. Single qubit rotation operation is implemented through optical elements like the Faraday polarization rotator. Photons are separated into different optical paths, or merged into a single optical path using dichromatic mirrors. The controlled-NOT gate between two qubits is implemented by the proper combination of parametric up and down conversions. This scheme has the following features: (1) No auxiliary qubits are required in the controlled-NOT gate operation; (2) No measurement is required in the course of the computation; (3) It is resource efficient and conceptually simple.
We propose a linear optical scheme for direct realization of a nondestructive NNN-qubit controlled phase gate without resorting to a sequence of single- and two-qubit gates. The proposed setup involves linear optical elements, nonmaximally entangled pairs of photons, and multiphoton coincidence detection. To implement the scheme, physical qubits represented by the polarization states of single photons are probabilistically encoded into the two-photon states. Based on such encoding operation, a nondestructive NNN-qubit phase gate can be directly achieved by NNN-photon interference on an array of polarization beam splitters and NNN-photon coincidence detection.