We introduce and validate a machine learning-assisted protocol to classify time and space correlations of classical noise acting on a quantum system, using two interacting qubits as probe. We consider diferent classes of noise, according to their Markovianity and spatial correlations. Leveraging the sensitivity of a coherent population transfer protocol under three distinct driving conditions, the various noises are discriminated by only measuring the final transfer eficiencies. This approach reaches around 90% accuracy with a minimal experimental overhead.
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In this work, we propose a design of a quantum sensor for testing the presence of time- and spacecorrelated noise in solid-state quantum hardware, avoiding direct measurement of the noise crossspectra. The principal system consists of two ultrastrongly coupled qubits, their coupling strength being comparable to the individual Bohr energies ∼ . It may be a quantum sensor detecting material properties of a substrate or a subsystem of a larger quantum processing unit. We start with the Hamiltonian (ℏ = 1) sys = − 2 1 − 2 2 + 2 1 2, 2 }, where = 1 √︀ 2 + 2. The 2 system is subject to local longitudinal noise, which induces fluctuations of the individual qubit splittings, modeled by two classical stochastic processes [14] () noise() = − 1 1 − 2 2 2, 2 We consider three non-Markovian and two Markovian noise classes: uncorrelated local variables .
and anticorrelated local processes. • Non-Markovian: we consider the limit of quasistatic noise where are random variables picked from a Gaussian distribution. We identify three distinct classes: correlated, anticorrelated, and • Markovian noise: zero-mean, delta-correlated stochastic processes. We consider the correlated
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The system is operated to produce coherent population transfer through a STIRAP-like protocol [15, 16, 17]. Looking for a suitable design, we first consider the driven system in the absence of noise. Favorable conditions are found by operating in the ultra-strong coupling regime ∼ , and by driving symmetrically the two qubits.
() = () ( 1 + 2) , (3) This symmetry enforces a selection rule that excludes |3⟩ from the dynamics, which is then limited to a three-level system. Control is operated by a two-tone field, () = Ω20() cos(20)+Ω12() cos(12), where Ω () are slowly-varying pulse envelopes and match the energy splittings between eigenvalues − . In a doubly rotating frame and after using the rotating wave approximation (RWA) for we obtain the Hamiltonian ˜ = √1 {Ω()|0⟩⟨2| + Ω()|1⟩⟨2| + h.c.}. (4)
2 which implements a ladder configuration. Then coherent population transfer by STIRAP can be obtained using a suitable time dependence of pulse envelopes Ω/().
Asymmetries and imperfections, such as those caused by noise, modify this picture, since coherence is suppressed and selection rules are relaxed. The resulting 4-level dynamics, while deteriorating the eficiency of population transfer, has the key advantage of yielding an increased discrimination between diferent classes of noise correlations. To utilise the most accessible measurement protocol, we employ, as the figure of merit for the Neural Network, the average population of the state |⟩, that is = lim 1 ∑︁ () →∞ =1 (5) where () = ⟨| f()|⟩ and () is the density matrix of the system at the final time f for the f -th noise realization. Such quantity is computed accordingly for each of the noise classes, under 3 driving conditions, ()Ωmax = Ωmax, ()Ωmax = 2Ωmax, ()Ωmax = Ωmax/2. We use synthetic data generated by numerical simulations. For the correlated classes the correlation parameter is randomly drawn, while for the uncorrelated classes, the Gaussian width of the noise distributions is varied. For each class, we obtained 500 data points, each consisting of a 3-dimensional vector containing the average eficiency for the fixed noise parameters under the 3 driving conditions.
The dataset is used to classify noise afecting the qubits by Supervised Learning. The training [ 18] is performed by minimizing the sparse categorical cross-entropy, which measures the distance between the predicted label and the true label of the noise. The model reaches an accuracy of around 92% (Fig. 1a). The accuracy for the test datasets is summarised in Fig. 1b.
The model achieves an accuracy of 99.4% in distinguishing between non-Markovian and Markovian noise. Within the non-Markovian noise class, it correctly classifies correlations with an accuracy of 98.67%, whereas within the Markovian class, the classification accuracy is 82%. This contrasts with the three-level system case analyzed in [19], where the model was unable to discriminate between the two distinct Markovian noise types.
We finally observe that current experiments on time-[
DF and LG acknowledge support from the PNRR MUR project PE0000023-NQSTI "National Quantum Science and Technology Institute" - Spoke 1; SM acknowledge support from the "Centro Nazionale di Ricerca in High-Performance Computing, Big Data and Quantum Computing"-ICSC; GF acknowledges support from PRIN 2022 "SuperNISQ"; GF and EP acknowledge support from the University of Catania, Piano Incentivi Ricerca di Ateneo 2024-26, project QTCM; EP acknowledges the COST Action SUPERQUMAP (CA 21144); MP acknowledges support from the European Union’s Horizon Europe EIC-Pathfinder project QuCoM (101046973), the Department for the Economy of Northern Ireland under the US-Ireland R&D Partnership Programme, and the PNRR MUR project PE0000023-NQSTI - SPOKE 2 through project ASpEQCt.
The authors have not employed any Generative AI tools. Correlated Quantum Noise in Superconducting Qubits, PRX Quantum 1 (2020) 010305. URL: https://link.aps.org/doi/10.1103/PRXQuantum.1.010305. doi:10.1103/PRXQuantum.1.010305. [9] J. M. Boter, X. Xue, T. Krähenmann, T. F. Watson, V. N. Premakumar, D. R. Ward, D. E. Savage, M. G. Lagally, M. Friesen, S. N. Coppersmith, M. A. Eriksson, R. Joynt, L. M. K. Vandersypen, Spatial noise correlations in a Si/SiGe two-qubit device from Bell state coherences, Phys. Rev. B 101 (2020) 235133. URL: https://link.aps.org/doi/10.1103/PhysRevB.101.235133. doi:10.1103/ PhysRevB.101.235133. [10] J. Rojas-Arias, A. Noiri, P. Stano, T. Nakajima, J. Yoneda, K. Takeda, T. Kobayashi, A. Sammak, G. Scappucci, D. Loss, S. Tarucha, Spatial noise correlations beyond nearest neighbors in ${}^{28}\mathrm{Si}/$Si-Ge spin qubits, Phys. Rev. Appl. 20 (2023) 054024. URL: https://link.aps. org/doi/10.1103/PhysRevApplied.20.054024. doi:10.1103/PhysRevApplied.20.054024. [11] J. Yoneda, J. S. Rojas-Arias, P. Stano, K. Takeda, A. Noiri, T. Nakajima, D. Loss, S. Tarucha, Noisecorrelation spectrum for a pair of spin qubits in silicon, Nat. Phys. (2023) 1–6. doi:10.1038/ s41567-023-02238-6. [12] A. D’Arrigo, G. Piccitto, G. Falci, E. Paladino, Open-loop quantum control of small-size networks for high-order cumulants and cross-correlations sensing, Sci Rep 14 (2024) 16681. URL: https:// www.nature.com/articles/s41598-024-67503-x. doi:10.1038/s41598-024-67503-x, publisher: Nature Publishing Group. [13] C.-K. Li, Y. Li, D. C. Pelejo, S. Stanish, Quantum error correction scheme for fully-correlated noise, Quantum Inf Process 22 (2023) 310. URL: https://doi.org/10.1007/s11128-023-04009-x. doi:10.1007/s11128-023-04009-x. [14] L. Mandel, E. Wolf, Optical Coherence and Quantum Optics, Cambridge ; New York, 1995. [15] N. V. Vitanov, A. A. Rangelov, B. W. Shore, K. Bergmann, Stimulated Raman adiabatic passage in physics, chemistry, and beyond, Rev. Mod. Phys. 89 (2017) 015006. doi:10.1103/RevModPhys. 89.015006. [16] G. Falci, A. La Cognata, M. Berritta, A. D’Arrigo, E. Paladino, B. Spagnolo, Design of a Lambda system for population transfer in superconducting nanocircuits, Phys. Rev. B 87 (2013) 214515. URL: https://link.aps.org/doi/10.1103/PhysRevB.87.214515. doi:10.1103/PhysRevB.87.214515. [17] L. Giannelli, S. Sgroi, J. Brown, G. S. Paraoanu, M. Paternostro, E. Paladino, G. Falci, A tutorial on optimal control and reinforcement learning methods for quantum technologies, Physics Letters A 434 (2022) 128054. URL: https://www.sciencedirect.com/science/article/pii/S0375960122001360. doi:10.1016/j.physleta.2022.128054. [18] F. Marquardt, Machine learning and quantum devices, SciPost Physics Lecture Notes (2021) 029.
doi:10.21468/SciPostPhysLectNotes.29. [19] S. Mukherjee, D. Penna, F. Cirinnà, M. Paternostro, E. Paladino, G. Falci, L. Giannelli, Noise classification in three-level quantum networks by Machine Learning, Mach. Learn.: Sci. Technol. 5 (2024) 045049. doi:10.1088/2632-2153/ad9193.