Demonstration of a non-Abelian geometric controlled-Not gate in a superconducting circuit

Abstract

Holonomies, arising from non-Abelian geometric transformations of quantum states in Hilbert space, offer a promising way for quantum computation. These holonomies are not commutable and thus can be used for the realization of a universal set of quantum logic gates, where the global geometric feature may result in some noise-resilient advantages. Here we report the first on-chip realization of a non-Abelian geometric controlled-Not gate in a superconducting circuit, which is a building block for constructing a holonomic quantum computer. The conditional dynamics is achieved in an all-to-all connected architecture involving multiple frequency-tunable superconducting qubits controllably coupled to a resonator; a holonomic gate between any two qubits can be implemented by tuning their frequencies on resonance with the resonator and applying a two-tone drive to one of them. This gate represents an important step towards the all-geometric realization of scalable quantum computation on a superconducting platform.

13 pages, 11 figures, 2 tables

References in corpus (9)

• Surface codes: Towards practical large-scale quantum computation
• Superconducting Circuits and Quantum Information
• Towards fault-tolerant quantum computing with trapped ions
• Experimental Realization of Universal Geometric Quantum Gates with Solid-State Spins
• Low-decoherence flux qubit
• Robustness of non-adiabatic holonomic gates
• Experimental implementation of universal nonadiabatic geometric quantum gates in a superconducting circuit
• Continuous-variable geometric phase and its manipulation for quantum computation in a superconducting circuit
• Experimental demonstration of entanglement-enabled universal quantum cloning in a circuit

Cited by in corpus (13)

• Demonstration of dynamical control of three-level open systems with a superconducting qutrit
• Superrobust Geometric Control of a Superconducting Circuit
• Single-step implementation of a hybrid controlled-NOT gate with one superconducting qubit simultaneously controlling multiple target cat-state qubits
• Nonadiabatic Holonomic Quantum Computation and Its Optimal Control
• Enhanced-Fidelity Ultrafast Geometric Quantum Computation Using Strong Classical Drives
• Decoherence-Suppressed Non-adiabatic Holonomic Quantum Computation
• Nonadiabatic holonomic quantum computation based on commutation relation
• Entanglement-interference complementarity and experimental demonstration in a superconducting circuit
• Universal Robust Geometric Quantum Control via Geometric Trajectory Correction
• Dark path holonomic qudit computation
• Error-Tolerant Geometric Quantum Control for Logical Qubits with Minimal Resource
• Non-adiabatic holonomic quantum operations in continuous variable systems
• Robustness Enhancement of Universal Noncyclic Geometric Gates via Evolution Optimization