Machine-Learning-Assisted Manipulation and Readout of Molecular Spin Qubits

Claudio Bonizzoni, Mirco Tincani, Fabio Santanni, and Marco Affronte

Phys. Rev. Applied 18, 064074 – Published 23 December 2022

Abstract

Machine learning finds application in the quantum control and readout of qubits. In this work we apply artificial neural networks to assist the manipulation and the readout of a prototypical molecular spin qubit-an oxovanadium(IV) moiety-in two experiments designed to test the amplitude and the phase recognition, respectively. We first successfully use an artificial network to analyze the output of a storage-retrieval protocol with four input pulses to recognize the echo positions and, with further post selection on the results, to infer the initial input pulse sequence. We then apply an artificial neural network to ascertain the phase of the experimentally measured Hahn echo, showing that it is possible to correctly detect its phase and to recognize additional single-pulse phase shifts added during manipulation.

Received 5 August 2022
Revised 11 November 2022
Accepted 14 November 2022

DOI:https://doi.org/10.1103/PhysRevApplied.18.064074

Physics Subject Headings (PhySH)

Artificial neural networks Magnetization dynamics Quantum information with hybrid systems Quantum protocols

Molecules

Electron spin resonance Machine learning Microwave techniques

Quantum Information, Science & TechnologyAtomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Claudio Bonizzoni ^1,2,*, Mirco Tincani ¹, Fabio Santanni ³, and Marco Affronte ^1,2

¹Dipartimento di Scienze Fisiche, Informatiche e Matematiche Università di Modena e Reggio Emilia, via G. Campi 213/A, 41125 Modena, Italy
²CNR Istituto Nanoscienze, Centro S3, via G. Campi 213/A, 41125 Modena, Italy
³Dipartimento di Chimica Ugo Schiff, via della Lastruccia 3, 50019 Sesto Fiorentino (FI), Italy

^*claudio.bonizzoni@unimore.it

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Vol. 18, Iss. 6 — December 2022

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Images

Figure 1
Summary of the experimental workflow. The flow chart at the top summarizes the main steps of our method, from data acquisition to signal processing and to the execution of the final task (classification or regression). The three bottom panels help in recognizing different steps (raw data acquisition, processing, prediction). We use off-line methods, in which acquisition and processing with ANN are done in two distinct steps. Details on training procedures are given in Supplemental Material [74].
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Figure 2
Machine-learning-assisted recognition of output echoes of a storage-retrieval protocol. Blue traces are the measured raw outputs from all the possible sequences of four classical bit input sequences (being $1 = pulse$ ON and $0 = pulse$ OFF, from “0000” or $j = 0$ at the top left down to “1111” or $j = 15$ at the bottom right; see labels), while red traces are the probability, $p_{e}$ , that the ANN gives in classifying the output as an echo. The probability scale $p_{e}$ is added on the right axis in red for better comparison and clarity.
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Figure 3
Fidelity of bit recognition after clusterization of the echo probability (red traces in Fig. 2) according to the definition of Eq. (1). (a) Fidelity of each bit (from 1 up to 4 in input order) as a function of the input bit sequence. (b) Average fidelity per bit resulting from the average of all fidelity values per bit in (a). Error bars are calculated as the standard deviation of each corresponding point.
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Figure 4
Machine-learning-assisted recognition of the phase of the output Hahn echo. (a) Inferred phase as a function of the input phase given to the $π / 2$ pulse for two different datasets (run 1 and run 2). The black trace shows the values expected from the analysis of the output quadratures. (b) Inferred phase as a function of the input phase sweep of the $π / 2$ pulse when an initial phase bias (up to $90^{\circ}$ , see legend) is added. Vertical blue arrows help in identifying the additional relative phase shift.
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Figure 5
Machine-learning-assisted recognition of the phase of the output Hahn echo when the phase given to the $π$ pulse is swept between $0^{\circ}$ and $360^{\circ}$ for $ϕ_{π / 2} = 0$ . Two different datasets taken under similar conditions (run 1 and run 2) are shown. The black trace shows the values expected from the analysis of the output quadratures, while the gray trace shows the result expected from a phase sweep of the $π / 2$ pulse at fixed $ϕ_{π} = 0$ for comparison.
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