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Quantum Science and Technology

Modelling non-Markovian noise in driven superconducting qubits

Abhishek Agarwal, Lachlan P. Lindoy, Deep Lall, François Jamet, Ivan Rungger

Published Apr 11, 2024• 23 citations
Publisher

Abstract

Abstract Non-Markovian noise can be a significant source of errors in superconducting qubits. We develop gate sequences utilising mirrored pseudoidentities that allow us to characterise and model the effects of non-Markovian noise on both idle and driven qubits. We compare three approaches to modelling the observed noise: (i) a Markovian noise model, (ii) a model including interactions with a two-level system (TLS), (iii) a model utilising the post Markovian master equation, which we show to be equivalent to the qubit-TLS model in certain regimes. When running our noise characterisation circuits on a superconducting qubit device we find that purely Markovian noise models cannot reproduce the experimental data. Our model based on a qubit-TLS interaction, on the other hand, is able to closely capture the observed experimental behaviour for both idle and driven qubits. We investigate the stability of the noise properties of the hardware over time, and find that the parameter governing the qubit-TLS interaction strength fluctuates significantly even over short time-scales of a few minutes. Finally, we evaluate the changes in the noise parameters when increasing the qubit drive pulse amplitude. We find that although the hardware noise parameters fluctuate significantly over different days, their drive pulse induced relative variation is rather well defined within computed uncertainties: both the phase error and the qubit-TLS interaction strength change significantly with the pulse strength, with the phase error changing quadratically with the amplitude of the applied pulse. Since our noise model can closely describe the behaviour of idle and driven qubits, it is ideally suited to be used in the development of quantum error mitigation and correction methods.

DOI
10.1088/2058-9565/ad3d7e

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Modelling non-Markovian noise in driven superconducting qubits

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Non-Markovian noise can be a significant source of errors in superconducting qubits. We develop gate sequences utilising mirrored pseudoidentities that allow us to characterise and model the effects of non-Markovian noise on both idle and driven qubits. We compare three approaches to modelling the observed noise: (i) a Markovian noise model, (ii) a model including interactions with a two-level system (TLS), (iii) a model utilising the post Markovian master equation (PMME), which we show to be equivalent to the qubit-TLS model in certain regimes. When running our noise characterisation circuits on a superconducting qubit device we find that purely Markovian noise models cannot reproduce the experimental data. Our model based on a qubit-TLS interaction, on the other hand, is able to closely capture the observed experimental behaviour for both idle and driven qubits. We investigate the stability of the noise properties of the hardware over time, and find that the parameter governing the qubit-TLS interaction strength fluctuates significantly even over short time-scales of a few minutes. Finally, we evaluate the changes in the noise parameters when increasing the qubit drive pulse amplitude. We find that although the hardware noise parameters fluctuate significantly over different days, their drive pulse induced relative variation is rather well defined within computed uncertainties: both the phase error and the qubit-TLS interaction strength change significantly with the pulse strength, with the phase error changing quadratically with the amplitude of the applied pulse. Since our noise model can closely describe the behaviour of idle and driven qubits, it is ideally suited to be used in the development of quantum error mitigation and correction methods.

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Non-Markovian noise model for superconducting qubits

Tuomisto, Lauri

Quantum computers are capable of carrying out calculations that are challenging or even impossible for classical computers. Quantum computers consist of quantum bits (qubits) which can exhibit a phenomenon called superposition where the qubit is in multiple states at the same time. Qubits can also be entangled with other qubits, which means that the states of the qubits are dependant on each other in a way that the state of a single qubit can not be expressed independently of the other qubits. These properties of qubits that enable quantum computing, are very sensitive to perturbations a ecting the system of qubits from the outside. A common choice for the physical architecture of a qubit is a superconducting qubit, which has its quantum properties implemented with a superconducting circuit. Realising a su ciently large qubit system has remained a challenge, since increasing the size of the system leads to more unwanted noise that interacts with the qubits. We have only just achieved systems that can outperform classical computers in speci c tasks. These devices do not o er signi cant advantages and the goal remains to grow the qubit systems, and overcoming the challenges caused by noise is of high importance. The e ect of noise can be reduced by designing hardware that has minimal sources of noise, or by creating qubits with error correction, meaning a way of undoing the e ect of noise on a qubit. Both of these approaches demand a way of recognising the noise mechanisms and their signi cance. Noise characterisation can be done with combining a theoretical model for the dynamics of a qubit with measurement data obtained from the qubit system in question. A su cient t of a theoretical model to noisy measurement data provides parametrisation of the noise, and a well designed model can link the noise to real physical phenomena. In this work, we introduce a noise model based on the Non-Markovian Quantum State Di usion equation. We present the physical processes the model describes and showcase its performance with noisy measurement data obtained with a real quantum processor consisting of superconducting qubits.

•Dec 4, 2025•0 citations
Abstract Non-Markovian noise can be a significant source of errors in superconducting qubits. We develop gate sequences utilising mirrored pseudoidentities that allow us to characterise and model the effects of non-Markovian noise on both idle and driven qubits. We compare three approaches to modelling the observed noise: (i) a Markovian noise model, (ii) a model including interactions with a two-level system (TLS), (iii) a model utilising the post Markovian master equation, which we show to be equivalent to the qubit-TLS model in certain regimes. When running our noise characterisation circuits on a superconducting qubit device we find that purely Markovian noise models cannot reproduce the experimental data. Our model based on a qubit-TLS interaction, on the other hand, is able to closely capture the observed experimental behaviour for both idle and driven qubits. We investigate the stability of the noise properties of the hardware over time, and find that the parameter governing the qubit-TLS interaction strength fluctuates significantly even over short time-scales of a few minutes. Finally, we evaluate the changes in the noise parameters when increasing the qubit drive pulse amplitude. We find that although the hardware noise parameters fluctuate significantly over different days, their drive pulse induced relative variation is rather well defined within computed uncertainties: both the phase error and the qubit-TLS interaction strength change significantly with the pulse strength, with the phase error changing quadratically with the amplitude of the applied pulse. Since our noise model can closely describe the behaviour of idle and driven qubits, it is ideally suited to be used in the development of quantum error mitigation and correction methods.
Non-Markovian noise can be a significant source of errors in superconducting qubits. We develop gate sequences utilising mirrored pseudoidentities that allow us to characterise and model the effects of non-Markovian noise on both idle and driven qubits. We compare three approaches to modelling the observed noise: (i) a Markovian noise model, (ii) a model including interactions with a two-level system (TLS), (iii) a model utilising the post Markovian master equation (PMME), which we show to be equivalent to the qubit-TLS model in certain regimes. When running our noise characterisation circuits on a superconducting qubit device we find that purely Markovian noise models cannot reproduce the experimental data. Our model based on a qubit-TLS interaction, on the other hand, is able to closely capture the observed experimental behaviour for both idle and driven qubits. We investigate the stability of the noise properties of the hardware over time, and find that the parameter governing the qubit-TLS interaction strength fluctuates significantly even over short time-scales of a few minutes. Finally, we evaluate the changes in the noise parameters when increasing the qubit drive pulse amplitude. We find that although the hardware noise parameters fluctuate significantly over different days, their drive pulse induced relative variation is rather well defined within computed uncertainties: both the phase error and the qubit-TLS interaction strength change significantly with the pulse strength, with the phase error changing quadratically with the amplitude of the applied pulse. Since our noise model can closely describe the behaviour of idle and driven qubits, it is ideally suited to be used in the development of quantum error mitigation and correction methods.
Simulation of one and two qubit superconducting quantum gates under the non-Markovian 1/f1/f1/f noise
Non-Markovian 1/f1/f1/f noise consists a dominant source of decoherence in superconducting qubits, yet its slow nature poses a significant challenge for accurate simulation. Here we develop a hierarchical equations of motion (HEOM) framework that enables efficient and reliable modeling of qubit dynamics and gate operations under 1/f1/f1/f noise. By using the approach, it is first shown that perturbative quantum master equations may fail to reproduce the correct dephasing dynamics of a qubit coupled to slow baths. We then analyze dynamical decoupling sequences by including effects of finite pulse duration. It is found that different pulse sequences results in different behavior in error accumulation: all X-CPMG sequences exhibit linear scaling with parity effects, Y-CPMG follows quadratic growth, and alternating XY-type sequences can suppress the error accumulation significantly. Finally, we extend the framework to two-qubit cross-resonance (CR) gates, reconstructing the full Choi matrix and Pauli Transfer Matrix (PTM) to identify the incoherent error induced by 1/f1/f1/f noise. Together, these results establish HEOM as a robust methodology for simulating the environmental noise in superconducting circuits and provide new insights into error mechanisms in both single- and two-qubit gates.
Superconducting qubits have seen rapid increases in their coherence in the last few decades. However, instability in qubit parameters and their noise environment remains as a major challenge that limits the device performance. Qubit metrology to collectively measure and characterise different sources of noise and fluctuations is essential for accurately benchmarking devices but can be challenging, and typically different noise sources are characterised independently. In order to characterise the combined noise, we develop a tool that uses few-measurement data to detect and diagnose noise fluctuations, as well as a time series segmentation tool to further disambiguate different sources of fluctuations. We demonstrate the tool by computing time resolved properties of individual superconducting qubits. We find large changes of the dominating noise contributions, such as qubit frequency fluctuations, over both long time-scales of hours and days, and also over very short milli-seconds time-scales. We show that this information can be used alongside accurate noise models to learn physical properties of the coupled noise sources as well as benchmark device stability.
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-ZZZZZZ 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.
Abstract In the scale-up of quantum computers, the framework underpinning fault-tolerance generally relies on the strong assumption that environmental noise affecting qubit logic is uncorrelated (Markovian). However, as physical devices progress well into the complex multi-qubit regime, attention is turning to understanding the appearance and mitigation of correlated — or non-Markovian — noise, which poses a serious challenge to the progression of quantum technology. This error type has previously remained elusive to characterisation techniques. Here, we develop a framework for characterising non-Markovian dynamics in quantum systems and experimentally test it on multi-qubit superconducting quantum devices. Where noisy processes cannot be accounted for using standard Markovian techniques, our reconstruction predicts the behaviour of the devices with an infidelity of 10 −3 . Our results show this characterisation technique leads to superior quantum control and extension of coherence time by effective decoupling from the non-Markovian environment. This framework, validated by our results, is applicable to any controlled quantum device and offers a significant step towards optimal device operation and noise reduction.
Quantum computers are capable of carrying out calculations that are challenging or even impossible for classical computers. Quantum computers consist of quantum bits (qubits) which can exhibit a phenomenon called superposition where the qubit is in multiple states at the same time. Qubits can also be entangled with other qubits, which means that the states of the qubits are dependant on each other in a way that the state of a single qubit can not be expressed independently of the other qubits. These properties of qubits that enable quantum computing, are very sensitive to perturbations a ecting the system of qubits from the outside. A common choice for the physical architecture of a qubit is a superconducting qubit, which has its quantum properties implemented with a superconducting circuit. Realising a su ciently large qubit system has remained a challenge, since increasing the size of the system leads to more unwanted noise that interacts with the qubits. We have only just achieved systems that can outperform classical computers in speci c tasks. These devices do not o er signi cant advantages and the goal remains to grow the qubit systems, and overcoming the challenges caused by noise is of high importance. The e ect of noise can be reduced by designing hardware that has minimal sources of noise, or by creating qubits with error correction, meaning a way of undoing the e ect of noise on a qubit. Both of these approaches demand a way of recognising the noise mechanisms and their signi cance. Noise characterisation can be done with combining a theoretical model for the dynamics of a qubit with measurement data obtained from the qubit system in question. A su cient t of a theoretical model to noisy measurement data provides parametrisation of the noise, and a well designed model can link the noise to real physical phenomena. In this work, we introduce a noise model based on the Non-Markovian Quantum State Di usion equation. We present the physical processes the model describes and showcase its performance with noisy measurement data obtained with a real quantum processor consisting of superconducting qubits.