Systematic study of High $E_J/E_C$ transmon qudits up to $d=12$

Abstract

Qudits provide a resource-efficient alternative to qubits for quantum information processing. The multilevel nature of the transmon, with its individually resolvable transition frequencies, makes it an attractive platform for superconducting circuit-based qudits. In this work, we systematically analyze the trade-offs associated with encoding high-dimensional quantum information in fixed-frequency transmons. Designing high $E_J/E_C$ ratios of up to 325, we observe up to 12 levels ($d=12$) on a single transmon. Despite the decreased anharmonicity, we demonstrate process infidelities $e_f<3\times 10^{-3}$ for qubit-like operations in each adjacent-level qubit subspace in the lowest 10 levels. Furthermore, we achieve a 10-state readout assignment fidelity of 93.8% with the assistance of deep neural network classification of a multi-tone dispersive measurement. We find that the Hahn echo time $T_{2E}$ for the higher levels is close to the limit of $T_1$ decay, primarily limited by bosonic enhancement. We verify the recently introduced Josephson harmonics model, finding that it yields better predictions for the transition frequencies and charge dispersion. Finally, we show strong $ZZ$-like coupling between the higher energy levels in a two-transmon system. Our high-fidelity control and readout methods, in combination with our comprehensive characterization of the transmon model, suggest that the high-$E_J/E_C$ transmon is a powerful tool for exploring excited states in circuit quantum electrodynamics.

18 pages, 9 figures

References in corpus (66)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Charge insensitive qubit design derived from the Cooper pair box
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Quantum Simulation
• Circuit Quantum Electrodynamics
• A Quantum Engineer's Guide to Superconducting Qubits
• Suppressing quantum errors by scaling a surface code logical qubit
• Resolving photon number states in a superconducting circuit
• Coherent Josephson qubit suitable for scalable quantum integrated circuits
• Robust randomized benchmarking of quantum processes
• Efficient quantum state tomography
• New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds
• Transmon qubit with relaxation time exceeding 0.5 milliseconds
• A universal qudit quantum processor with trapped ions
• Mitigating measurement errors in multi-qubit experiments
• Qudit Quantum State Tomography
• Surface participation and dielectric loss in superconducting qubits
• Quantum Simulation for High Energy Physics
• Maximum Likelihood, Minimum Effort
• Fast Reset and Suppressing Spontaneous Emission of a Superconducting Qubit
• Measuring and Suppressing Quantum State Leakage in a Superconducting Qubit
• Quantum Information Scrambling in a Superconducting Qutrit Processor
• Relaxation and frequency shifts induced by quasiparticles in superconducting qubits
• Hot non-equilibrium quasiparticles in transmon qubits
• Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography
• Coherence and Decay of Higher Energy Levels of a Superconducting Transmon Qubit
• Scalable error mitigation for noisy quantum circuits produces competitive expectation values
• Beating the break-even point with a discrete-variable-encoded logical qubit
• Leakage reduction in fast superconducting qubit gates via optimal control
• Control and Tomography of a Three Level Superconducting Artificial Atom
• Protocols for optimal readout of qubits using a continuous quantum nondemolition measurement
• Quantum State Tomography via Linear Regression Estimation
• Three Qubit Randomized Benchmarking
• Qutrit randomized benchmarking
• High-Fidelity Qutrit Entangling Gates for Superconducting Circuits
• Circuit QED with fluxonium qubits: theory of the dispersive regime
• Native qudit entanglement in a trapped ion quantum processor
• Superconducting circuit protected by two-Cooper-pair tunneling
• Dynamics of Transmon Ionization
• Overcoming leakage in scalable quantum error correction
• Transmon qubit readout fidelity at the threshold for quantum error correction without a quantum-limited amplifier
• Scqubits: a Python package for superconducting qubits
• Experimental single-setting quantum state tomography
• Measurement-Induced State Transitions in a Superconducting Qubit: Within the Rotating Wave Approximation
• Engineering superconducting qubits to reduce quasiparticles and charge noise
• Observation of Josephson Harmonics in Tunnel Junctions
• Universal qudit gate synthesis for transmons
• Measurement-Induced Transmon Ionization
• Experimental Realization of Two Qutrits Gate with Tunable Coupling in Superconducting Circuits
• Energy gap measurement of nanostructured thin aluminium films for use in single Cooper-pair devices
• High-fidelity software-defined quantum logic on a superconducting qudit
• Coexistence of nonequilibrium density and equilibrium energy distribution of quasiparticles in a superconducting qubit
• Demonstration of an All-Microwave Controlled-Phase Gate between Far Detuned Qubits
• Performing SU($d$) operations and rudimentary algorithms in a superconducting transmon qudit for $d=3$ and $d=4$
• Simultaneous gates in frequency-crowded multilevel systems using fast, robust, analytic control shapes
• Experimental investigation of quantum correlations in a two-qutrit spin system
• Blueprint of a Molecular Spin Quantum Processor
• Parity effect in superconducting aluminum single electron transistors with spatial gap profile controlled by film thickness
• Improving qubit coherence using closed-loop feedback
• Amplitude and frequency sensing of microwave fields with a superconducting transmon qudit
• Empowering high-dimensional quantum computing by traversing the dual bosonic ladder
• Emulating two qubits with a four-level transmon qudit for variational quantum algorithms
• On Clifford groups in quantum computing
• Exploring Ququart Computation on a Transmon using Optimal Control
• Randomized benchmarking for qudit Clifford gates
• Improving Transmon Qudit Measurement on IBM Quantum Hardware

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• Local fermion-to-qudit mappings: a practical recipe for four-level systems
• Quantum optimal control of the Dicke manifold in dipolar Rydberg atom arrays
• Exact amplitudes of parametric processes in driven Josephson circuits
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• Analog Circuit-QED Simulator of Quantum Spin Dynamics Through the Extended Bose-Hubbard Model
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