Emulating two qubits with a four-level transmon qudit for variational quantum algorithms

Abstract

Using quantum systems with more than two levels, or qudits, can scale the computation space of quantum processors more efficiently than using qubits, which may offer an easier physical implementation for larger Hilbert spaces. However, individual qudits may exhibit larger noise, and algorithms designed for qubits require to be recompiled to qudit algorithms for execution. In this work, we implemented a two-qubit emulator using a 4-level superconducting transmon qudit for variational quantum algorithm applications and analyzed its noise model. The major source of error for the variational algorithm was readout misclassification error and amplitude damping. To improve the accuracy of the results, we applied error-mitigation techniques to reduce the effects of the misclassification and qudit decay event. The final predicted energy value is within the range of chemical accuracy. Our work demonstrates that qudits are a practical alternative to qubits for variational algorithms.

References in corpus (59)

• Scikit-learn: Machine Learning in Python
• Charge insensitive qubit design derived from the Cooper pair box
• Variational Quantum Algorithms
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• A Quantum Engineer's Guide to Superconducting Qubits
• Trapped-Ion Quantum Computing: Progress and Challenges
• NMR Techniques for Quantum Control and Computation
• The Variational Quantum Eigensolver: a review of methods and best practices
• Quantum Entanglement of High Angular Momenta
• Multidimensional quantum entanglement with large-scale integrated optics
• Scalable Quantum Simulation of Molecular Energies
• Photonic quantum information processing: a concise review
• Efficient Z-Gates for Quantum Computing
• Qudits and high-dimensional quantum computing
• High-dimensional quantum communication: benefits, progress, and future challenges
• A universal qudit quantum processor with trapped ions
• Multi-photon entanglement in high dimensions
• Quantum Information Scrambling in a Superconducting Qutrit Processor
• Overcoming Noise in Entanglement Distribution
• Coherence and Decay of Higher Energy Levels of a Superconducting Transmon Qubit
• Gate Set Tomography
• Quantum Computing with NMR
• Tapering off qubits to simulate fermionic Hamiltonians
• Control and Tomography of a Three Level Superconducting Artificial Atom
• Qutrit randomized benchmarking
• High-Fidelity Qutrit Entangling Gates for Superconducting Circuits
• The QICK (Quantum Instrumentation Control Kit): Readout and control for qubits and detectors
• Topological Maxwell Metal Bands in a Superconducting Qutrit
• A general framework for randomized benchmarking
• Factoring with Qutrits: Shor's Algorithm on Ternary and Metaplectic Quantum Architectures
• Computational speed-up in a single qudit NMR quantum information processor
• Computational speed-up with a single qudit
• Circuit QED and engineering charge based superconducting qubits
• Multilevel superconducting circuits as two-qubit systems: Operations, state preparation, and entropic inequalities
• Scqubits: a Python package for superconducting qubits
• Single qubit gates in frequency-crowded transmon systems
• Experimental Observation of Tensor Monopoles with a Superconducting Qudit
• Introduction to Quantum Gate Set Tomography
• High-fidelity measurement of qubits encoded in multilevel superconducting circuits
• Dynamics of dispersive single qubit read-out in circuit quantum electrodynamics
• Double-sided coaxial circuit QED with out-of-plane wiring
• Probing quantum processor performance with pyGSTi
• Quantum Phase Estimation with Time-Frequency Qudits in a Single Photon
• High-fidelity software-defined quantum logic on a superconducting qudit
• Time-efficient implementation of quantum search with qudits
• Performing SU($d$) operations and rudimentary algorithms in a superconducting transmon qudit for $d=3$ and $d=4$
• Determining the parity of a permutation using an experimental NMR qutrit
• Simultaneous gates in frequency-crowded multilevel systems using fast, robust, analytic control shapes
• A programmable three-qubit superconducting processor with all-to-all connectivity
• Arithmetic Circuits for Multilevel Qudits Based on Quantum Fourier Transform
• High Coherence in a Tileable 3D Integrated Superconducting Circuit Architecture
• Quantum capacity analysis of multi-level amplitude damping channels
• The Decay of Multiqudit Entanglement
• Elementary gates for ternary quantum logic circuit
• Applications of Multi-Valued Quantum Algorithms
• Exploring Ququart Computation on a Transmon using Optimal Control
• Experimental demonstration of quantum contextuality on an NMR qutrit
• Realization of two-qutrit quantum algorithms on a programmable superconducting processor
• A Generalization of Bernstein-Vazirani Algorithm to Qudit Systems

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• Agents for self-driving laboratories applied to quantum computing
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• Demonstration of Discrete-Time Quantum Walks and Observation of Topological Edge States in a Superconducting Qutrit Chain
• Unitary Transformations using Robust Optimal Control on a Cold Atom Qudit
• Single-Qudit Quantum Neural Networks for Multiclass Classification
• Synthesis of Single Qutrit Circuits from Clifford+R
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• The Virtual Quantum Device (VQD): A tool for detailed emulation of quantum computers