Wavelet correlation noise analysis for qubit operation variable time series
Amanda E. Seedhouse, Nard Dumoulin Stuyck, Santiago Serrano, Will Gilbert, Jonathan Y. Huang, Fay E. Hudson, Kohei M. Itoh, Arne Laucht, Wee Han Lim, Chih Hwan Yang, Tuomo Tanttu, Andrew S. Dzurak, André Saraiva
In quantum computing, characterizing the full noise profile of qubits can aid in increasing coherence times and fidelities by developing error-mitigating techniques specific to the noise present. This characterization also supports efforts in advancing device fabrication to remove sources of noise. Qubit properties can be subject to non-trivial correlations in space and time, for example, spin qubits in MOS quantum dots are exposed to noise originating from the complex glassy behavior of two-level fluctuator ensembles. Engineering progress in spin qubit experiments generates large amounts of data, necessitating analysis techniques from fields experienced in managing large data sets. Fields such as astrophysics, finance, and climate science use wavelet-based methods to enhance their data analysis. Here, we propose and demonstrate wavelet-based analysis techniques to decompose signals into frequency and time components, enhancing our understanding of noise sources in qubit systems by identifying features at specific times. We apply the analysis to a state-of-the-art two-qubit experiment in a pair of SiMOS quantum dots with feedback applied to relevant operation variables. The observed correlations serve to identify common microscopic causes of noise, such as two-level fluctuators and hyperfine coupled nuclei, as well as to elucidate pathways for multi-qubit operation with more scalable feedback systems.
In quantum computing, characterizing the full noise profile of qubits can aid in increasing coherence times and fidelities by developing error-mitigating techniques specific to the noise present. This characterization also supports efforts in advancing device fabrication to remove sources of noise. Qubit properties can be subject to non-trivial correlations in space and time, for example, spin qubits in MOS quantum dots are exposed to noise originating from the complex glassy behavior of two-level fluctuator ensembles. Engineering progress in spin qubit experiments generates large amounts of data, necessitating analysis techniques from fields experienced in managing large data sets. Fields such as astrophysics, finance, and climate science use wavelet-based methods to enhance their data analysis. Here, we propose and demonstrate wavelet-based analysis techniques to decompose signals into frequency and time components, enhancing our understanding of noise sources in qubit systems by identifying features at specific times. We apply the analysis to a state-of-the-art two-qubit experiment in a pair of SiMOS quantum dots with feedback applied to relevant operation variables. The observed correlations serve to identify common microscopic causes of noise, such as two-level fluctuators and hyperfine coupled nuclei, as well as to elucidate pathways for multi-qubit operation with more scalable feedback systems.
Recently, several groups have demonstrated two-qubit gate fidelities in semiconductor spin qubit systems above 99%. Achieving this regime of fault-tolerant compatible high fidelities is nontrivial and requires exquisite stability and precise control over the different qubit parameters over an extended period of time. This motivates the search for the efficient calibration of qubit control parameters against different sources of micro- and macroscopic noise and methods for noise analysis. Here, we present several single- and two-qubit parameter feedback protocols, optimized for and implemented in the state-of-the-art fast field-programmable gate array hardware. Furthermore, we present a wavelet-based analysis on feedback data collected over a ∼9 h time frame to gain insight into the different sources of noise in the system. Scalable feedback is an outstanding challenge and the presented implementation and analysis gives insight into the benefits and drawbacks of qubit parameter feedback, as feedback related overhead increases. This work demonstrates a pathway toward robust qubit parameter feedback and systematic noise analysis, crucial for mitigation strategies toward systematic high-fidelity qubit operation compatible with quantum error correction protocols.
As quantum devices make steady progress towards intermediate scale and fault-tolerant quantum computing, it is essential to develop rigorous and efficient measurement protocols that account for known sources of noise. Most existing quantum characterization protocols such as gate-set tomography and randomized benchmarking assume the noise acting on the qubits is Markovian. However, this assumption is often not valid, as for the case of 1/f charge noise or hyperfine nuclear spin noise. Here, we present a general framework for quantum process tomography (QPT) in the presence of time-correlated noise. We further introduce fidelity benchmarks that quantify the relative strength of different sources of Markovian and non-Markovian noise. As an application of our method, we perform a comparative theoretical and experimental analysis of silicon spin qubits. We first develop a detailed noise model that accounts for the dominant sources of noise and validate the model against experimental data. Applying our framework for time-correlated QPT, we find that the number of independent parameters needed to characterize one- and two-qubit gates can be compressed by 10× and 100× , respectively, when compared to the fully generic case. These compressions reduce the amount of tomographic measurements needed in experiment, while also significantly speeding up numerical simulations of noisy quantum circuit dynamics compared to time-dependent Hamiltonian simulation. Using this compressed noise model, we find good agreement between our theoretically predicted process fidelities and two-qubit interleaved randomized benchmarking fidelities of 99.8% measured in recent experiments on silicon spin qubits. More broadly, our formalism can be directly extended to develop efficient and scalable tuning protocols for high-fidelity control of large arrays of quantum devices with non-Markovian noise. Published by the American Physical Society 2024
Characterizing and understanding the environment affecting quantum systems is critical to elucidate its physical properties and engineer better quantum devices. We develop an approach to reduce the quantum environment causing single-qubit dephasing to a simple yet predictive noise model. Our approach, inspired by quantum noise spectroscopy, is to define a ``self-consistent'' classical noise spectrum, that is, compatible with all observed decoherence under various qubit dynamics. We demonstrate the power and limits of our approach by characterizing, with nanoscale spatial resolution, the noise experienced by two electronic spins in diamond that, despite their proximity, surprisingly reveal the presence of a complex quantum spin environment, both classically reducible and not. Our results overcome the limitations of existing noise spectroscopy methods and highlight the importance of finding predictive models to accurately characterize the underlying environment. Extending our work to multiqubit systems would enable spatially resolved quantum sensing of complex environments and quantum device characterization, notably to identify correlated noise between qubits, which is crucial for practical realization of quantum error correction.
The efficiency of the future devices for quantum information processing will be limited mostly by the finite decoherence rates of the qubits. Recently, substantial progress was achieved in enhancing the time within which a solid-state qubit demonstrates coherent dynamics. This progress is based mostly on a successful isolation of the qubits from external decoherence sources. Under these conditions, the material-inherent sources of noise start to play a crucial role. In most cases, the noise that the quantum device demonstrates has a 1/ f spectrum. This suggests that the environment that destroys the phase coherence of the qubit can be thought of as a system of two-state fluctuators, which experience random hops between their states. In this short review, the current state of the theory of the decoherence due to the qubit interaction with the fluctuators is discussed. The effect of such an environment on two different protocols of the qubit manipulations, free induction and echo signal, is described. It turns out that in many important cases the noise produced by the fluctuators is non-Gaussian. Consequently, the results of the interaction of the qubit with the fluctuators are not determined by the pair correlation function alone. We describe the effect of the fluctuators using the so-called spin-fluctuator model. Being quite realistic, this model allows one to exactly evaluate the qubit dynamics in the presence of one fluctuator. This solution is found, and its features, including non-Gaussian effects, are analyzed in detail. We extend this consideration to systems of large numbers of fluctuators, which interact with the qubit and lead to the 1/ f noise. We discuss existing experiments on the Josephson qubit manipulation and try to identify non-Gaussian behavior.
We present novel techniques for modelling and mitigating the effects of time-dependent noise created by interactions between a quantum system and its environment, and by errors in applied controls. Our scope encompasses quantum storage and nontrivial QIP tasks in both single- and multi-qubit systems, with a particular focus on control operations applied to trapped-ion qubits. The work begins with the introduction of a computationally efficient approach to characterizing the impact of time-dependent noise in single-qubit systems, in terms of the spectral characteristics of the noise and a set of generalized control filter functions. In conjunction with brute-force numerical simulation, we show that this novel analytical technique can used to model the evolution of a noisy single-qubit system subject to an arbitrary piecewise-constant control sequence, and to accurately predict the effects of experimentally engineered noise in single-qubit trapped ion systems. We also obtain a number of new and important results that extend the range of utility of state-preserving dynamical decoupling control sequences. These device-independent results provide a means to create a practically useful high-fidelity, long-time quantum memory in both single- and multi-qubit systems. We go on to explain how, given the freedom to arbitrarily and quasi-instantaneously change the phase of the interaction between a system of qubits and a finite collection of oscillators, frequency-specific phase modulation protocols can be implemented that decouple the qubits from targeted oscillator modes at pre-determined times. This technique can be used to generate fast, high-fidelity multi-qubit entangling operations in, for example, ion trap QIP devices.
Accurate modeling of noise in realistic quantum processors is critical for constructing fault-tolerant quantum computers. While a full simulation of actual noisy quantum circuits provides information about correlated noise among all qubits and is therefore accurate, it is, however, computationally expensive as it requires resources that grow exponentially with the number of qubits. We propose an efficient systematic construction of approximate noise channels, where their accuracy can be enhanced by incorporating noise components with higher qubit-qubit correlation degree. To formulate such approximate channels, we first present a method, dubbed the cluster expansion approach, to decompose the Lindbladian generator of an actual noise channel into components based on interqubit correlation degree. We generate a k -th order approximate noise channel by truncating the cluster expansion and incorporating noise components with correlations up to the k -th degree. We require that the approximate noise channels must be accurate and also “honest", i.e., the actual errors are not underestimated in our physical models. As an example application, we apply our method to model noise in a three-qubit quantum processor that stabilizes a [[2,0,2]] codeword, which is one of the four Bell states. We find that, for realistic noise strength typical for fixed-frequency superconducting qubits coupled via always-on static interactions, correlated noise beyond two-qubit correlation can significantly affect the code simulation accuracy. Since our approach provides a systematic characterization of multi-qubit noise correlations, it enables the potential for accurate, honest and scalable approximations to simulate large numbers of qubits from full modeling or experimental characterizations of small enough quantum subsystems, which are efficient yet still retain essential noise features of the entire device.