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arXiv:2303.04796 · Quantum Science and Technology

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

Shuxiang Cao, Mustafa S. Bakr, Giulio Campanaro, Simone D Fasciati, James Wills, Deep Lall, Boris Shteynas, Vivek Chidambaram, Ivan Rungger, Peter Leek

Published Mar 26, 2024• 28 citations
arXivHTMLPDF

Abstract

Abstract Using quantum systems with more than two levels, or qudits, can scale the computational 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.

DOI
10.1088/2058-9565/ad37d4

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Abstract Using quantum systems with more than two levels, or qudits, can scale the computational 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.
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The influence of noise on quantum dynamics is one of the main factors preventing current quantum processors from performing accurate quantum computations. Sufficient noise characterization and modeling can provide key insights into the effect of noise on quantum algorithms and inform the design of targeted error protection protocols. However, constructing effective noise models that are sparse in model parameters, yet predictive can be challenging. In this work, we present an approach for effective noise modeling of multi-qubit operations on transmon-based devices. Through a comprehensive characterization of seven devices offered by the IBM Quantum Platform, we show that the model can capture and predict a wide range of single- and two-qubit behaviors, including non-Markovian effects resulting from spatiotemporally correlated noise sources. The model’s predictive power is further highlighted through multi-qubit dynamical decoupling demonstrations and an implementation of the variational quantum eigensolver. As a training proxy for the hardware, we show that the model can predict expectation values within a relative error of 0.5%; this is a sevenfold improvement over default hardware noise models. Through these demonstrations, we highlight key error sources in superconducting qubits and illustrate the utility of reduced noise models for predicting hardware dynamics.
Pre-fault tolerant quantum computers have already demonstrated the ability to estimate observable values accurately, at a scale beyond brute-force classical computation. This has been enabled by error mitigation techniques that often rely on a representative model of the device noise. However, learning and maintaining these models is complicated by fluctuations in the noise over unpredictable time scales, for instance, arising from resonant interactions between superconducting qubits and defect two-level systems (TLS). Such interactions affect the stability and uniformity of device performance as a whole, but also affect the noise model accuracy, leading to incorrect observable estimation. Here, we experimentally demonstrate that tuning of the qubit-TLS interactions helps reduce noise instabilities and consequently enables more reliable error-mitigation performance. These experiments provide a controlled platform for studying the performance of error mitigation in the presence of quasi-static noise. We anticipate that the capabilities introduced here will be crucial for the exploration of quantum applications on solid-state processors at non-trivial scales. Interactions between qubits and defect-related two-level systems in superconducting qubit devices are a major source of noise fluctuations that hinder error-mitigation performance. Here, the authors experimentally show that modulating this interaction can reduce noise fluctuation and improve error mitigation performance.
Multilevel quantum systems, or qudits, provide a powerful means to exploit larger Hilbert spaces. In this work, we investigate how flux-tunable superconducting transmons can be practical platforms for qudit-based operations. We examine the properties of a 2-transmon processor with a flux-tunable coupler and assess its suitability for state control and higher-dimensional gates. We also explore the application of Excited State Promoted (ESP) readout to this circuitry, which promises improved qudit readout fidelity. We also introduce a new approach to multilevel control, providing a step toward enhanced quantum algorithm execution.
Abstract Quantum computers have the potential to help solve a range of physics and chemistry problems, but noise in quantum hardware currently limits our ability to obtain accurate results from the execution of quantum-simulation algorithms. Various methods have been proposed to mitigate the impact of noise on variational algorithms, including several that model the noise as damping expectation values of observables. In this work, we benchmark various methods, including a new method proposed here. We compare their performance in estimating the ground-state energies of several instances of the 1D mixed-field Ising model using the variational-quantum-eigensolver algorithm with up to 20 qubits on two of IBM’s quantum computers. We find that several error-mitigation techniques allow us to recover energies to within 10% of the true values for circuits containing up to about 25 ansatz layers, where each layer consists of CNOT gates between all neighboring qubits and Y -rotations on all qubits.