# 1D Cluster State Generation On Superconducting Hardware

## TL;DR

This paper analytically and numerically investigates the generation of 4-qubit cluster states on superconducting charge-qubit arrays, highlighting the impact of decoherence and the importance of error mitigation for measurement-based quantum computation.

## Contribution

It provides analytical derivations and numerical validation of 4-qubit cluster state generation, comparing fidelities under ideal and noisy conditions, emphasizing the effects of decoherence.

## Key findings

- Energy relaxation ($T_1$) maintains >90% fidelity
- Pure dephasing ($T_2$) causes 70% decay at fourth harmonics
- Decoherence effects degrade cluster state fidelity significantly

## Abstract

Measurement-based Quantum Computation(MBQC) utilize entanglement as resource for performing quantum computation. Generating cluster state using entanglement as resource is a key bottleneck for the adoption of MBQC. To generate cluster state with charge-qubit arrrays, we provide analytical derivations and numerical validations for 4-qubit cluster state. We compare our fidelities under ideal (noise-free) Hamiltonian evolution and due to effect of decoherence. We show incorporating energy relaxation ($T_1$) yields $>$90\% fidelity while pure dephasing $T_2$ show $70\%$ decays at fourth harmonics. We further show under noise $T_2$ decays to 50\% within 15 time units, versus $>$70\% under relaxation time units ($T_1$)--only. This decay quantify degradation effect of $T_2$ on preparing cluster--state preparation is more than $T_1$. We highlight the critical need for targeted error-mitigation strategies in near-term MBQC implementations.