Improving Transmon Qudit Measurement on IBM Quantum Hardware

Abstract

The Hilbert space of a physical qubit typically features more than two energy levels. Using states outside the qubit subspace can provide advantages in quantum computation. To benefit from these advantages, individual states of the $d$-dimensional qudit Hilbert space have to be discriminated during readout. We propose and analyze two measurement strategies that improve the distinguishability of transmon qudit states. Based on a model describing the readout of a transmon qudit coupled to a resonator, we identify the regime in hardware parameter space where each strategy is optimal. We discuss these strategies in the context of a practical implementation of the default measurement of a ququart on IBM Quantum hardware whose states are prepared by employing higher-order $X$ gates that make use of two-photon transitions.

arXiv comment13 pages, 6 figures; corrected typos, references added, shortened section 2

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Cited by in corpus (5)

• Systematic study of High $E_J/E_C$ transmon qudits up to $d=12$
• Qudits for decomposing multiqubit gates and realizing quantum algorithms
• Multi-frequency control and measurement of a spin-7/2 system encoded in a transmon qudit
• Space-time correlations in monitored kinetically constrained discrete-time quantum dynamics
• Efficient fidelity estimation: Alternative derivation and related applications