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arXiv:2607.15909

Reconstruction of the noise correlation spectral density from the cavity emission in a two-qubit system

Nadine Lenke, Guido Burkard

quant-phcond-mat.mes-hallSubmitted Jul 17, 2026• Announced Jul 20, 2026• 0 citations
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Abstract

A significant challenge in the field of large-scale fault-tolerant quantum computation is the influence of noise. In addition to the influence of noise on individual qubits, the smaller additional effect of noise correlations is also of high significance because correlated errors pose a challenge for quantum error correction. We describe the dynamics of two cavity-coupled qubits that are subject to correlated noise, assuming that the qubits are affected by longitudinal noise and not coupled directly. We find that the cavity emission enables the characterization of the noise correlations and describe the cases of white noise, quasi-static noise, and Ornstein-Uhlenbeck noise. For a known frequency spectrum, the reconstruction of the noise correlation spectral density from the cavity emission is possible by averaging over many different noise realizations. We demonstrate that, in the case of white noise, the noise correlation effects scale with the fifth order of the cavity-qubit coupling constant and are thus strongly suppressed compared with the case of quasi-static noise, where they scale with the third order. Furthermore, we present a method for extracting the noise correlation spectral density from the cavity emission in the case where the underlying noise type remains unidentified. This can be achieved by applying the convolution theorem.

Comments
13+5 pages, 4 figures

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A significant challenge in the field of large-scale fault-tolerant quantum computation is the influence of noise. In addition to the influence of noise on individual qubits, the smaller additional effect of noise correlations is also of high significance because correlated errors pose a challenge for quantum error correction. We describe the dynamics of two cavity-coupled qubits that are subject to correlated noise, assuming that the qubits are affected by longitudinal noise and not coupled directly. We find that the cavity emission enables the characterization of the noise correlations and describe the cases of white noise, quasi-static noise, and Ornstein-Uhlenbeck noise. For a known frequency spectrum, the reconstruction of the noise correlation spectral density from the cavity emission is possible by averaging over many different noise realizations. We demonstrate that, in the case of white noise, the noise correlation effects scale with the fifth order of the cavity-qubit coupling constant and are thus strongly suppressed compared with the case of quasi-static noise, where they scale with the third order. Furthermore, we present a method for extracting the noise correlation spectral density from the cavity emission in the case where the underlying noise type remains unidentified. This can be achieved by applying the convolution theorem.
Noise-induced decoherence is one of the main threats to large-scale quantum computation. In an attempt to assess the noise affecting a qubit, we go beyond the standard steady-state solution of the transmission through a qubit-coupled cavity in input-output theory by including dynamical noise in the description of the system. We solve the quantum Langevin equations exactly for a noise-free system and treat the noise as a perturbation. In the long-time limit the corrections may be written as a sum of convolutions of the noise power spectral density with an integration kernel that depends on external control parameters. Using the convolution theorem, we invert the corrections and obtain relations for the noise spectral density as an integral over measurable quantities. Additionally, we treat the noise exactly in the dispersive regime and again find that noise characteristics are imprinted in the long-time transmission in convolutions containing the power spectral density.
Noise affects the coherence of qubits and thereby places a bound on the performance of quantum computers. We theoretically study a generic two-level system with fluctuating control parameters in a photonic cavity and find that basic features of the noise spectral density are imprinted in the transient transmission through the cavity. We obtain analytical expressions for generic noise and proceed to study the cases of quasistatic, white and 1/f^{α} noise in more detail. Additionally, we propose a way of extracting the noise power spectral density in a frequency band only bounded by the range of the qubit-cavity detuning and with an exponentially decaying error due to finite measurement times. Our results suggest that measurements of the time-dependent transmission probability represent a novel way of extracting noise characteristics.
We analytically investigate the fidelity dynamics of a Jaynes--Cummings qubit coupled to a single-mode cavity in the presence of stochastic fluctuations of the qubit--cavity coupling. Such fluctuations naturally arise in cavity- and circuit-QED platforms due to fabrication imperfections, control-field noise, mechanical vibrations, and environmental disturbances. Since the qubit--cavity coupling governs the rate of coherent energy and information exchange, understanding the effects of its fluctuations is essential for assessing the performance of quantum communication, quantum sensing, and quantum information-processing protocols. We consider both Gaussian white noise and Ornstein--Uhlenbeck noise with finite correlation time as models for the coupling fluctuations. Exploiting the closed dynamics within each excitation manifold, we derive exact analytical expressions for the noise-averaged density matrix and the fidelity relative to the ideal noiseless evolution. We show that the fidelity is determined by a single decoherence factor governed by the integrated noise correlation function, establishing a direct connection between microscopic coupling fluctuations and macroscopic coherence loss. In the white-noise limit, the fidelity decays exponentially, whereas finite noise correlation times produce nonexponential decay and slower coherence loss. We further show that the crossover between Markovian-like and non-Markovian regimes is controlled by the ratio of the noise correlation rate to the coherent coupling strength, and that decoherence increases with photon number because of the enhanced effective qubit--cavity coupling. These results provide a unified analytical framework for quantifying decoherence induced by stochastic coupling fluctuations and for evaluating the robustness of cavity-QED protocols under correlated noise.
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The unavoidable interaction of a quantum system with its environment usually degrades its coherence and quantumness. The environment and the decoherence process may be described as the interaction with a classical or quantized bath. As a matter of fact, the classical description becomes progressively more reliable as far as the environment has many degrees of freedom, i.e. it becomes complex, or when the interaction between a quantum system and a classical fluctuating field is taken into account. In this thesis, I consider a qubit system coupled to a stochastic classical field and address�the decoherence and non-Markovianity induced by the external noise as well as the spectral characterization of the classical field by quantum-limited measurement on the qubit. I thus analyze the dynamics of quantum correlations between two non-interacting, initially entangled qubits subject to a classical noise generated by a stochastic process. Two relevant classes of noise are taken into account: Gaussian noise, such as the Ornstein-Uhlenbeck process, and non-Gaussian noise, such as the random telgraph noise and the colored noise with 1/f spectrum. I also discuss the evaluation of non-Markovianity of the induced dynamical map and link the presence of revivals of quantum correlations with the information backflow to the system. The precise characterization of the stochastic process generating the classical noise, possibly using minimal resources, is a crucial ingredient for the design of high-precision measurements and reliable communication protocols. To this purpose, I also address the characterization of the spectral parameters of classical noise by quantum probes, e.g. a qubit coupled to the stochastic process generating the noise. By using the tools of quantum estimation theory, I explore the performances of quantum measurements on the qubit and show that it is possible to effectively extract information about the noise.
I present a theory of environmental noise spectroscopy via dynamical decoupling of a qubit at an optimal working point. Considering a sequence of nnn pulses and pure dephasing due to quadratic coupling to Gaussian distributed noise $\ensuremath{\xi}(t)$, I use the linked-cluster (cumulant) expansion to calculate the coherence decay. Solutions allowing for reconstruction of spectral density of noise are given. For noise with correlation time shorter than the time scale on which coherence decays, the noise filtered by the dynamical decoupling procedure can be treated as effectively Gaussian at large nnn, and well-established methods of noise spectroscopy can be used to reconstruct the spectrum of ${\ensuremath{\xi}}^{2}(t)$ noise. On the other hand, for noise of dominant low-frequency character $(1/{f}^{\ensuremath{\beta}}$ noise with $\ensuremath{\beta}>1)$, an infinite-order resummation of the cumulant expansion is necessary, and it leads to an analytical formula for coherence decay having a power-law tail at long times. In this case, the coherence at time ttt depends both on spectral density of $\ensuremath{\xi}(t)$ noise at $\ensuremath{\omega}=n\ensuremath{\pi}/t$, and on the effective low-frequency cutoff of the noise spectrum, which is typically given by the inverse of the data acquisition time. Simulations of decoherence due to purely transverse noise show that the analytical formulas derived in this paper apply in this often encountered case of an optimal working point, provided that the number of pulses is not very large, and that the longitudinal qubit splitting is much larger than the transverse noise amplitude.