Speed limits for quantum gates in multi-qubit systems

TL;DR

This paper determines the fundamental speed limits for various quantum gates and operations in multi-qubit systems, highlighting how system geometry and interaction types influence implementation times.

Contribution

It provides analytical and numerical bounds on the speed of multi-qubit gates and quantum-state transfer, revealing optimal implementation strategies and the impact of system configuration.

Findings

Two-qubit gates can be implemented at near-optimal speeds with simple methods.

The Toffoli gate duration depends heavily on interaction type and geometry.

Quantum-state transfer speed is limited by maximum spin-wave velocity.

Abstract

We use analytical and numerical calculations to obtain speed limits for various unitary quantum operations in multiqubit systems under typical experimental conditions. The operations that we consider include single-, two-, and three-qubit gates, as well as quantum-state transfer in a chain of qubits. We find in particular that simple methods for implementing two-qubit gates generally provide the fastest possible implementations of these gates. We also find that the three-qubit Toffoli gate time varies greatly depending on the type of interactions and the system's geometry, taking only slightly longer than a two-qubit controlled-NOT (CNOT) gate for a triangle geometry. The speed limit for quantum-state transfer across a qubit chain is set by the maximum spin-wave speed in the chain.