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.
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.
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.
In the early 1980’s, it was suggested that a computer obeying the laws of quantum mechanics would be able to solve problems beyond the capabilities of a classical computer. The novel ways in which such a quantum computer works relies on the quantum properties of the quantum bits (qubits) used to store the information. Any candidate for a quantum computer must thus be able to sustain these properties and offer means to manipulate and read-out the information. One such candidate are quantum mechanical, superconducting circuits, where the logical bit is encoded in the energy eigenstates of the system. In circuit quantum electrodynamics, such a qubit is coupled to a microwave cavity allowing the qubit to be coherently controlled and read-out by probing the cavity. In this thesis, we theoretically investigate the destructive effects of noise which couple to the system as one tries to measure and control the qubits. We study the so called quantum capacitance read-out scheme, where the state of the qubit is mapped onto an equivalent capacitance of the circuit. It is shown that this is quantum limited, in the sense that the state of the qubit can be determined while simultaneously adding a minimum amount of noise to the system. Apart from the added noise, a measurement on a qubit will perturb it, causing the state to collapse to one of the measurement eigenstates. Such a state collapse can be utilized to generate entanglement between qubits by measuring on the cavity. We show that high-fidelity entangled states can be produced in this way and discuss the potential of the measurement to violate a bound given by local hidden variable theories. The possibility to prolong the life-time of the quantum state by active error correction is also investigated and we discuss limits on gate operation times to benefit from such a code, given realistic values for the error probabilities. This work was supported by the European Commission through IST-015708 EuroSQIP integrated pro ject, and by the Swedish Research Council.
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.
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.
Superconducting qubits are a leading platform for quantum computation, yet decoherence and scalability challenges continue to limit progress toward fault-tolerant systems. This review synthesizes research on architectures, noise sources, and error correction to clarify performance trade-offs and guide development. The transition from Transmon to Fluxonium has dramatically improved qubit performance, achieving millisecond-scale coherence times. However, this success reveals a fundamental limit of coherence now being primarily restricted by the physical properties of the materials, specifically dielectric losses occurring at the Josephson junction leads and within the surrounding materials. As overcoming these material limits becomes increasingly difficult, system-level engineering determines whether high-coherence qubits can scale.Scaling quantum systems is difficult because current cooling and control systems create too much heat and this forces a shift to integrated digital superconducting circuits and cryogenic light-based links. While these hardware challenges restrict scaling, experiments in error correction show that logical qubits can already outperform physical ones. For example, a distance-7 surface code improved logical qubit lifetime by 2.4×. Achieving practical fault tolerance, however, requires moving beyond simple error models. Future systems must combine techniques like Dynamical Decoupling and Machine Learning-based Optimal Control with dynamic classical control capable of handling complex, correlated faults such as Multi-Bit Burst Errors. Progress in materials, cryogenic system integration for control, and adaptive error management must advance together to realize scalable, high-fidelity quantum hardware.
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.