Lindblad Tomography of a Superconducting Quantum Processor

Abstract

As progress is made towards the first generation of error-corrected quantum computers, careful characterization of a processor's noise environment will be crucial to designing tailored, low-overhead error correction protocols. 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 multi-qubit 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 hardwareagnostic characterization protocol for tomographically reconstructing the Hamiltonian and Lindblad operators of a quantum channel from an ensemble of time-domain measurements. Performing Lindblad Tomography on a small superconducting quantum processor, we show that this technique characterizes and accounts for state-preparation and measurement (SPAM) errors and allows one to place strong bounds on the degree of non-Markovianity in the channels of interest. 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.

Neural Network Based Qubit Environment Characterization

“…To further analyze the predictive power of strongly and weakly coupled fluctuators, panels (d-f) displays the relative error of the data with respect to the coupling strength parameter η i , defined in Eq. (25). A clear downward trend is observed in the relative error of the predictions of all three parameters, showing that most of the error in our reconstruction stems from the weakly coupled impurities with less of an influence on the qubit behaviour.…”

“…the characterization or "learning" of the noise in superconducting qubits either via classical [24][25][26] or, increasingly popular, machine learning techniques [27][28][29][30][31][32]. The latter have been applied to study the behaviour of a qubit by completely circumventing the issue of the exact nature of the environment [31,32].…”

“…However, even if the theoretical model is clear, choosing the best fitting parameters can often be a daunting task due to the often large or even unknown number of variables. Recently, more effort has been dedicated to finding the best fitting environment descriptions in terms of Lindblad operators [25,26], however the long coherence times associated with 1/f noise imply that a Markovian approximation might not be justified, and characterizing a non-Markovian environment has become an increasingly important focus of current research [28][29][30]. Furthermore, in order to connect the theoretical approach to the underlying physical picture even better, we believe a description in terms of two-level systems is necessary [27].…”

How to engineer a quantum wavefunction

“…3 With the advent of versatile and universal quantum simulators and computers, ways have been developed of both characterising directly and verifying the features of the object of interest in an experimental scenario -the quantum state, Hamiltonian, or process (Eisert et al, 2020). But also for analogue systems, methods for direct validation of the experimentally implemented object of interest have been developed, including in particular the identification of the Hamiltonian or Liouvillian parameters (Hangleiter et al, 2021;Samach et al, 2021), benchmarking of Hamiltonian time-evolution across the parameter range accessible in the experiment (Helsen et al, 2020;Derbyshire et al, 2020;Shaffer et al, 2021), and fidelity estimation of a quantum state (Elben et al, 2020). In another vein, it has also been argued that analogue simulations might often be insensitive to certain details of the experiment, for example due to slack in the model space (Sarovar et al, 2017), or because certain noise processes affect both the simulator and the target in the same way (Cubitt et al, 2018).…”

Precise Hamiltonian identification of a superconducting quantum processor

“…Sev-eral theoretical methods have been proposed that allow learning a partially unknown Hamiltonian from data for qubits [9][10][11][12][13][14] and bosonic systems [15,16]. Very recently, learning of two-qubit dissipative Lindblad dynamics has been demonstrated [17,18]. The challenge remains to develop scalable methods that live up to the demands of a robust recovery of Hamiltonians arising in the experimental context that involves both incoherent noise and systematic errors in the state preparation and the measurement.…”