# Demonstration of measurement-free universal logical quantum computation

## TL;DR

This paper demonstrates a new approach to quantum computing that avoids mid-circuit measurements, enabling fault-tolerant operations and algorithms.

## Contribution

A measurement-free universal logical quantum computation toolbox is proposed and demonstrated experimentally on a trapped-ion processor.

## Key findings

- Modular logical state teleportation is achieved without mid-circuit measurements.
- A fault-tolerant universal gate set is realized using coherent operations only.
- Grover’s algorithm is implemented fault-tolerantly on three logical qubits encoded in eight physical qubits.

## Abstract

The ability to perform quantum error correction (QEC) and robust gate operations on encoded qubits opens the door to demonstrations of quantum algorithms. Contemporary QEC schemes typically require mid-circuit measurements with feed-forward control, which are challenging for qubit control, often slow, and susceptible to relatively high error rates. In this work, we propose and experimentally demonstrate a universal toolbox of fault-tolerant logical operations on error-detecting codes without mid-circuit measurements on a trapped-ion quantum processor. We present modular logical state teleportation between two four-qubit error-detecting codes without measurements during algorithm execution. Moreover, we realize a fault-tolerant universal gate set on an eight-qubit error-detecting code hosting three logical qubits, based on state injection, which can be executed by coherent gate operations only. We apply this toolbox to experimentally realize Grover’s quantum search algorithm fault-tolerantly on three logical qubits encoded in eight physical qubits, with the implementation displaying clear identification of the desired solution states. Our work demonstrates the practical feasibility and provides first steps into the largely unexplored direction of measurement-free quantum computation.

Measurement-free quantum error correction allows to avoid costly mid-circuit measurements and feed-forward controls. Here, the authors present a toolbox of logical operations needed for measurement-free fault-tolerant universal quantum computing and demonstrate a measurement-free logical fault-tolerant logical algorithm using an error-detecting code on an ion-trap quantum processor.