Fitting quantum noise models to tomography data

Abstract

The presence of noise is currently one of the main obstacles to achieving large-scale quantum computation. Strategies to characterise and understand noise processes in quantum hardware are a critical part of mitigating it, especially as the overhead of full error correction and fault-tolerance is beyond the reach of current hardware. Non-Markovian effects are a particularly unfavorable type of noise, being both harder to analyse using standard techniques and more difficult to control using error correction. In this work we develop a set of efficient algorithms, based on the rigorous mathematical theory of Markovian master equations, to analyse and evaluate unknown noise processes.In the case of time-independent Markovian (or nearly Markovian) dynamics, our algorithm outputs the best-fit Lindbladian, i.e. the Lindblad master equation which best approximates the tomographic data to within the given precision. In the case of non-Markovian dynamics, our algorithm returns a quantitative and operationally meaningful measure of non-Markovianity in terms of isotropic noise addition.We provide a Python implementation of all our algorithms, and benchmark these on a range of 1-and 2-qubit examples of synthesised noisy tomography data, generated using the Cirq platform. The numerical results show that our algorithms succeed both in extracting a full description of the best-fit Lindbladian to the measured dynamics, and in computing accurate measures of non-Markovianity that match analytical calculations.

Quantum and classical dynamical semigroups of superchannels and semicausal channels

“…A further natural question would be a quantum superchannel analogue of the Markovianity problem: When can a quantum superchannel Ŝ be written as e L for some L that generates a semigroup of superchannels? Several works have investigated the Markovianity problem for quantum channels [21,[36][37][38] and a divisibility variant of this question, both for quantum channels and for stochastic matrices [39][40][41]. It would be interesting to see how these results translate to quantum or classical superchannels.…”

Neural Network Based Qubit Environment Characterization

“…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].…”

Classical Shadows for Quantum Process Tomography on Near-term Quantum Computers

“…Earlier attempts at QPT used the linear inversion method [7,8]. Later various statistical methods were developed including maximum likelihood methods [9][10][11][12][13], Bayesian methods [14][15][16], compressed sensing methods [17], tensor network methods [18] and other optimization techniques [19][20][21][22][23][24][25]. Theoretically, quantum process tomography can be related to quantum state tomography through the Jamio lkowski process-state isomorphism [26,27].…”