Abstract We introduce Lindblad-like quantum tomography (LℓQT) as a quantum characterization technique of time-correlated noise in quantum information processors. This approach enables the estimation of time-local master equations, including their possible negative decay rates, by maximizing a likelihood function subject to dynamical constraints. We discuss LℓQT for the dephasing dynamics of single qubits in detail, which allows for a neat understanding of the importance of including multiple snapshots of the quantum evolution in the likelihood function, and how these need to be distributed in time depending on the noise characteristics. By a detailed comparative study employing both frequentist and Bayesian approaches, we assess the accuracy and precision of LℓQT of a dephasing quantum dynamical map that goes beyond the Lindblad limit, focusing on two different microscopic noise models that can be realised in either trapped-ion or superconducting-circuit architectures. We explore the optimization of the distribution of measurement times to minimize the estimation errors, assessing the superiority of each learning scheme conditioned on the degree of non-Markovinity of the noise, and setting the stage for future experimental designs of non-Markovian quantum tomography.
Abstract We introduce Lindblad-like quantum tomography (LℓQT) as a quantum characterization technique of time-correlated noise in quantum information processors. This approach enables the estimation of time-local master equations, including their possible negative decay rates, by maximizing a likelihood function subject to dynamical constraints. We discuss LℓQT for the dephasing dynamics of single qubits in detail, which allows for a neat understanding of the importance of including multiple snapshots of the quantum evolution in the likelihood function, and how these need to be distributed in time depending on the noise characteristics. By a detailed comparative study employing both frequentist and Bayesian approaches, we assess the accuracy and precision of LℓQT of a dephasing quantum dynamical map that goes beyond the Lindblad limit, focusing on two different microscopic noise models that can be realised in either trapped-ion or superconducting-circuit architectures. We explore the optimization of the distribution of measurement times to minimize the estimation errors, assessing the superiority of each learning scheme conditioned on the degree of non-Markovinity of the noise, and setting the stage for future experimental designs of non-Markovian quantum tomography.
As progress is made towards the first generation of error-corrected quantum computers, robust characterization and validation protocols are required to assess the noise environments of physical quantum processors. While standard coherence metrics and characterization protocols such as T1 and T2, process tomography, and randomized benchmarking are now ubiquitous, these techniques provide only partial information about the dynamic multiqubit loss channels responsible for processor errors, which can be described more fully by a Lindblad operator in the master equation formalism. Here, we introduce and experimentally demonstrate Lindblad tomography, a hardware-agnostic characterization protocol for tomographically reconstructing the Hamiltonian and Lindblad operators of a quantum noise environment from an ensemble of time-domain measurements. Performing Lindblad tomography on a small superconducting quantum processor, we show that this technique naturally builds on standard process tomography and T1/T2 measurement protocols, characterizes and accounts for state-preparation and measurement errors, and allows one to place bounds on the fit to a Markovian model. Comparing the results of single- and two-qubit measurements on a superconducting quantum processor, we demonstrate that Lindblad tomography can also be used to identify and quantify sources of crosstalk on quantum processors, such as the presence of always-on qubit-qubit interactions.
Abstract Characterizing the dynamics of quantum systems is a central task for the development of quantum information processors (QIPs). It serves to benchmark different devices, learn about their specific noise, and plan the next hardware upgrades. However, this task is also very challenging, for it requires a large number of measurements and time-consuming classical processing. Moreover, when interested in the time dependence of the noise, there is an additional overhead since the characterization must be performed repeatedly within the time interval of interest. To overcome this limitation while, at the same time, ordering the learned sources of noise by their relevance, we focus on the inference of the dynamical generators of the noisy dynamics using Lindbladian quantum tomography (LQT). We propose two different improvements of LQT that alleviate previous shortcomings. In the weak-noise regime of current QIPs, we manage to linearize the maximum likelihood estimation of LQT, turning the constrained optimization into a convex problem to reduce the classical computation cost and to improve its robustness. Moreover, by introducing compressed sensing techniques, we reduce the number of required measurements without sacrificing accuracy. To illustrate these improvements, we apply our LQT tools to trapped-ion experiments of single- and two-qubit gates, advancing in this way the previous state of the art.
Characterizing the dynamics of quantum systems is a central task for the development of quantum information processors (QIPs). It serves to benchmark different devices, learn about their specific noise, and plan the next hardware upgrades. However, this task is also very challenging, for it requires a large number of measurements and time-consuming classical processing. Moreover, when interested in the time dependence of the noise, there is an additional overhead since the characterization must be performed repeatedly within the time interval of interest. To overcome this limitation while, at the same time, ordering the learned sources of noise by their relevance, we focus on the inference of the dynamical generators of the noisy dynamics using Lindbladian quantum tomography (LQT). We propose two different improvements of LQT that alleviate previous shortcomings. In the weak-noise regime of current QIPs, we manage to linearize the maximum likelihood estimation of LQT, turning the constrained optimization into a convex problem to reduce the classical computation cost and to improve its robustness. Moreover, by introducing compressed sensing techniques, we reduce the number of required measurements without sacrificing accuracy. To illustrate these improvements, we apply our LQT tools to trapped-ion experiments of single- and two-qubit gates, advancing in this way the previous state of the art.
Fault-tolerant quantum computing requires extremely precise knowledge and control of qubit dynamics during the application of a gate. We develop a data-driven learning protocol for characterizing quantum gates that builds off previous work on learning the Nakajima-Mori-Zwanzig (NMZ) formulation of open system dynamics from time series data, which allows detailed reconstruction of quantum evolution, including non-Markovian dynamics. We demonstrate this learning technique on three different systems: a simulation of a qubit whose dynamics are purely Markovian, a simulation of a driven qubit coupled to stochastic noise produced by an Ornstein-Uhlenbeck process, and trapped-ion experimental data of a driven qubit whose noise environment is not characterized ahead of time. Our technique is able to learn the generators of time evolution, or the NMZ operators, in all three cases and can learn the timescale in which the qubit dynamics can no longer be accurately described by a purely Markovian model. Our technique complements existing quantum gate characterization methods such as gate set tomography by explicitly capturing non-Markovianity in the gate generator, thus allowing for more thorough diagnosis of noise sources.
Accurate noise characterization is essential for scaling quantum processors toward fault-tolerant operation. Although reduced qubit dynamics are often modeled with Markovian master equations, present-day devices can exhibit memory effects generated by residual qubit-qubit couplings, structured environments, and finite bath correlation times. Here we develop a channel-resolved, Post-Markovian Master Equation model for non-Markovian noise and test it in superconducting qubits. Using idle-evolution tomography on IBM Quantum processors, we identify complementary operational signatures of non-Markovianity, including violations of CP-divisibility and revivals of distinguishability-based information-backflow measures. We further derive a closed-form spectator-ZZ model with local dissipation and show that it captures the observed transverse Bloch-vector revivals while leaving the longitudinal relaxation mode Markovian within the model. The fitted closed-form dynamics enable an analytical reconstruction of the transverse memory kernel, whose damped oscillatory structure captures the non-Markovian correction beyond the fitted Markovian baseline. Two-qubit tomography shows buildup and revivals of quantum mutual information on comparable timescales, supporting spectator-induced crosstalk as an important contributor to the observed memory effects. Our results connect operational non-Markovianity diagnostics, microscopic crosstalk modeling, and reduced memory-kernel reconstruction in a single experimental framework for superconducting quantum hardware.
Noise is both ubiquitous and generally deleterious in settings where precision is required. This is especially true in the quantum technology sector where system utility typically decays rapidly under its influence. Understanding the noise in quantum devices is thus a prerequisite for efficient strategies to mitigate or even eliminate its harmful effects. However, this requires resources that are often prohibitive, such that the typically used noise models rely on simplifications that sometimes depart from experimental reality. Here we derive a compact microscopic error model for single-qubit gates that only requires a single experimental input—the noise power spectral density. Our model goes beyond standard depolarizing or Pauli-twirled noise models, explicitly including non-Clifford and non-Markovian contributions to the dynamical error map. We gauge our predictions for experimentally relevant metrics against established characterization techniques run on a trapped-ion quantum computer. In particular, we find that experimental estimates of average gate errors measured through randomized benchmarking and reconstructed via quantum process tomography are tightly lower-bounded by our analytical estimates, while the depolarizing model overestimates the gate error. Our noise modeling including non-Markovian contributions can be readily applied to established frameworks such as dynamical decoupling and dynamically corrected gates, or to provide more realistic thresholds for quantum error correction.