Moving Quantum States without SWAP via Intermediate Higher Dimensional Qudits

TL;DR

This paper introduces a novel method for moving quantum states in quantum circuits using intermediate higher-dimensional qudits, significantly reducing quantum cost and circuit depth without relying on SWAP gates.

Contribution

It presents the first formalism for moving quantum states without SWAP gates by utilizing intermediate qudit states, applicable to any dimensional quantum system.

Findings

Achieves threefold reduction in gate count compared to SWAP-based methods.

Approximately twofold reduction in circuit depth.

Generalizes to any dimensional quantum system.

Abstract

Quantum algorithms can be realized in the form of a quantum circuit. To map quantum circuit for specific quantum algorithm to quantum hardware, qubit mapping is an imperative technique based on the qubit topology. Due to the neighbourhood constraint of qubit topology, the implementation of quantum algorithm rightly, is essential for moving information around in a quantum computer. Swapping of qubits using SWAP gate moves the quantum state between two qubits and solves the neighbourhood constraint of qubit topology. Though, one needs to decompose the SWAP gate into three CNOT gates to implement SWAP gate efficiently, but unwillingly quantum cost with respect to gate count and depth increases. In this paper, a new formalism of moving quantum states without using SWAP operation is introduced for the first time to the best of our knowledge. Moving quantum states through qubits have been attained with the adoption of temporary intermediate qudit states. This introduction of intermediate qudit states has exhibited a three times reduction in quantum cost with respect to gate count and approximately two times reduction in respect to circuit depth compared to the state-of-the-art approach of SWAP gate insertion. Further, the proposed approach is generalized to any dimensional quantum system.