Quantum circuits for qubit fusion

TL;DR

This paper explores the use of four-dimensional qudits as pairs of qubits, establishing a hierarchy of Clifford operators, and introduces methods for converting between qubits and qudits using stabilizer circuits and resource states.

Contribution

It presents a novel framework for qubit-qudit conversion via fusion and fission, expanding the understanding of Clifford hierarchies in higher-dimensional systems.

Findings

Hierarchy of Clifford operators in qubit and qudit systems

Method for converting between logical qubits and qudits

Resource states enabling fault-tolerant qubit-qudit conversion

Abstract

We consider four-dimensional qudits as qubit pairs and their qudit Pauli operators as qubit Clifford operators. This introduces a nesting, $C_1^2 \subset C_2^4 \subset C_3^2$, where $C_n^m$ is the $n$th level of the $m$-dimensional qudit Clifford hierarchy. If we can convert between logical qubits and qudits, then qudit Clifford operators are qubit non-Clifford operators. Conversion is achieved by qubit fusion and qudit fission using stabilizer circuits that consume a resource state. This resource is a fused qubit stabilizer state with a fault-tolerant state preparation using stabilizer circuits.