[Paper Review] Phase gate of one qubit simultaneously controlling n qubits in a cavity or coupled to a resonator

Chui‐Ping Yang, Yu-xi Liu+1 more|arXiv (Cornell University)|Dec 21, 2009

Quantum Information and Cryptography3 citations

TL;DR

This paper proposes a three-step controlled-phase gate that enables one qubit to simultaneously control n qubits in a cavity or resonator system, with operation time independent of n. Using superconducting qubits or atoms, the gate operates regardless of the cavity's initial state and enables simultaneous multiqubit CNOT-like operations, offering a scalable, fast, and robust quantum gate architecture.

ABSTRACT

We propose how to realize a three-step controlled-phase gate of one qubit simultaneously controlling $n$ qubits in a cavity or coupled to a resonator. The $n$ two-qubit controlled-phase gates, forming this multiqubit phase gate, can be performed simultaneously. The operation time of this phase gate is independent of the number $n$ of qubits. This phase gate controlling at once $n$ qubits is insensitive to the initial state of the cavity mode and can be used to produce an analogous CNOT gate simultaneously acting on $n$ qubits. We present two alternative approaches to implement this gate. One approach is based on tuning the qubit frequency while the other method tunes the resonator frequency. Using superconducting qubits coupled to a resonator as an example, we show how to implement the proposed gate with one superconducting qubit simultaneously controlling $n$ qubits selected from $N$ qubits coupled to a resonator ($1<n<N$). We also give a discussion on realizing the proposed gate with atoms, by using one cavity initially in an arbitrary state.

Motivation & Objective

• To develop a scalable quantum gate that allows one control qubit to coherently entangle with n target qubits simultaneously in a cavity or resonator system.
• To address the challenge of scaling multiqubit gates by making operation time independent of the number of target qubits n.
• To design a gate insensitive to the initial state of the cavity mode, enhancing robustness in noisy environments.
• To enable the implementation of a CNOT-like gate acting on n qubits in parallel, facilitating efficient quantum circuit design.

Proposed method

• The gate is implemented through a three-step process involving controlled interactions between a control qubit and n target qubits via a common cavity or resonator mode.
• Two alternative implementation strategies are proposed: tuning the qubit frequency or tuning the resonator frequency to mediate the controlled-phase interaction.
• The method relies on resonant coupling between the control qubit and the cavity, with the target qubits coupled to the same cavity, enabling simultaneous entanglement via a common photonic mode.
• The gate operation is designed to be insensitive to the initial Fock state of the cavity, ensuring robustness against initial state preparation errors.
• The use of superconducting qubits coupled to a resonator is demonstrated as a physical realization platform, with explicit protocols for selecting n qubits from N coupled qubits.
• An alternative implementation using atoms in a cavity is discussed, where one atom acts as the control and the cavity mode is initially in an arbitrary state.

Experimental results

Research questions

• RQ1 Can a single control qubit simultaneously entangle with n target qubits in a cavity-based system with operation time independent of n?
• RQ2 How can the gate be made robust against the initial state of the cavity mode, especially when the cavity is not prepared in a known Fock state?
• RQ3 What are the viable physical implementations of such a gate using superconducting qubits or trapped atoms?
• RQ4 Can the proposed gate be used to generate a multiqubit CNOT operation in parallel, and what are the conditions for its successful implementation?
• RQ5 How do frequency tuning of the qubit or resonator enable the required controlled-phase operations without requiring sequential gate application?

Key findings

• The proposed phase gate achieves simultaneous control of n qubits with an operation time that is independent of n, enabling scalable multiqubit entanglement.
• The gate is robust against the initial state of the cavity mode, maintaining fidelity regardless of whether the cavity is in a vacuum, thermal, or Fock state.
• The gate can be implemented using either qubit frequency tuning or resonator frequency tuning, offering flexibility in experimental design.
• A CNOT-like gate acting on n qubits in parallel can be constructed using the proposed controlled-phase gate, enabling efficient quantum circuit compilation.
• The gate is realizable with superconducting qubits coupled to a resonator, where one control qubit can simultaneously entangle with n selected qubits from a larger set of N qubits.
• The protocol is extendable to atomic systems, where one atom controls n other atoms via a cavity mode initially in an arbitrary state, demonstrating broad physical applicability.