Monitoring Fast Superconducting Qubit Dynamics Using a Neural Network
Gerwin Koolstra, Noah Stevenson, Shiva Lotfallahzadeh Barzili, Lucas Burns, Karthik Siva, Sacha Greenfield, William P. Livingston, Akel Hashim, Ravi Naik, John Mark Kreikebaum, Kevin P. O’Brien, David Santiago, Justin Dressel, Irfan A. Siddiqi
Weak measurements of a superconducting qubit produce noisy voltage signals that are weakly correlated with the qubit state.To recover individual quantum trajectories from these noisy signals, traditional methods require slow qubit dynamics and substantial prior information in the form of calibration experiments.Monitoring rapid qubit dynamics, e.g., during quantum gates, requires more complicated methods with increased demand for prior information.Here, we experimentally demonstrate an alternative method for accurately tracking rapidly driven superconducting qubit trajectories that uses a long short-term memory (LSTM) artificial neural network with minimal prior information.Despite few training assumptions, the LSTM produces trajectories that include qubit-readout resonator correlations due to a finite detection bandwidth.In addition to revealing rotated measurement eigenstates and a reduced measurement rate in agreement with theory for a fixed drive, the trained LSTM also correctly reconstructs evolution for an unknown drive with rapid modulation.Our work enables new applications of weak measurements with faster or initially unknown qubit dynamics, such as the diagnosis of coherent errors in quantum gates.
Weak measurements of a superconducting qubit produce noisy voltage signals that are weakly correlated with the qubit state.To recover individual quantum trajectories from these noisy signals, traditional methods require slow qubit dynamics and substantial prior information in the form of calibration experiments.Monitoring rapid qubit dynamics, e.g., during quantum gates, requires more complicated methods with increased demand for prior information.Here, we experimentally demonstrate an alternative method for accurately tracking rapidly driven superconducting qubit trajectories that uses a long short-term memory (LSTM) artificial neural network with minimal prior information.Despite few training assumptions, the LSTM produces trajectories that include qubit-readout resonator correlations due to a finite detection bandwidth.In addition to revealing rotated measurement eigenstates and a reduced measurement rate in agreement with theory for a fixed drive, the trained LSTM also correctly reconstructs evolution for an unknown drive with rapid modulation.Our work enables new applications of weak measurements with faster or initially unknown qubit dynamics, such as the diagnosis of coherent errors in quantum gates.
At its core, quantum mechanics is a theory developed to describe fundamental observations in the spectroscopy of solids and gases.Despite these practical roots, however, quantum theory is infamous for being highly counterintuitive, largely due to its intrinsically probabilistic nature.Neural networks have recently emerged as a powerful tool that can extract nontrivial correlations in vast datasets.These networks routinely outperform state-of-the-art techniques in language translation, medical diagnosis, and image recognition.It remains to be seen if neural networks can be trained to predict stochastic quantum evolution without a priori specifying the rules of quantum theory.Here, we demonstrate that a recurrent neural network can be trained in real time to infer the individual quantum trajectories associated with the evolution of a superconducting qubit under unitary evolution, decoherence, and continuous measurement from physical observations only.The network extracts the system Hamiltonian, measurement operators, and physical parameters.It is also able to perform tomography of an unknown initial state without any prior calibration.This method has the potential to greatly simplify and enhance tasks in quantum systems such as noise characterization, parameter estimation, feedback, and optimization of quantum control.
Accurate quantum state readout is crucial for error correction and algorithms, but measurement errors are detrimental. Readout fidelity is typically limited by a poor signal-to-noise ratio (SNR) and energy relaxation (T1 decay), a significant problem for superconducting qubits. While most approaches classify results using clustering algorithms on integrated readout signals, these methods cannot distinguish a qubit that was initially in the ground state from one that decayed to it during measurement. We instead propose using machine learning (ML) on the raw, non-integrated analog signal. We apply time-series classification models, such as a long short-term memory (LSTM) network, to the full data trajectory. We find that our LSTM model, combined with filtering and feature engineering, consistently outperforms clustering. The largest improvements come from reclassifying points in the boundary regions between clusters. These points correspond to atypical measurement records, likely due to transient or noisy features lost during data integration. By retaining temporal information, sequence-aware models like LSTMs can better discriminate these trajectories, whereas clustering methods based on integrated values are more prone to misclassification.
Quantum technology has been rapidly growing; in particular, the experiments that have been performed with superconducting qubits and circuit QED have allowed us to explore the light-matter interaction at its most fundamental level. The study of coherent dynamics between two-level systems and resonator modes can provide insight into fundamental aspects of quantum physics, such as how the state of a system evolves while being continuously observed. To study such an evolving quantum system, experimenters need to verify the accuracy of state preparation and control since quantum systems are very fragile and sensitive to environmental disturbance. In this thesis, I look at these continuous monitoring and state estimation problems from a modern point of view. With the help of machine learning techniques, it has become possible to explore regimes that are not accessible with traditional methods: for example, tracking the state of a superconducting transmon qubit continuously with dynamics fast compared with the detector bandwidth. These results open up a new area of quantum state tracking, enabling us to potentially diagnose errors that occur during quantum gates. In addition, I investigate the use of supervised machine learning, in the form of a modified denoising autoencoder, to simultaneously remove experimental noise while encoding one and two-qubit quantum state estimates into a minimum number of nodes within the latent layer of a neural network. I automate the decoding of these latent representations into positive density matrices and compare them to similar estimates obtained via linear inversion and maximum likelihood estimation. Using a superconducting multiqubit chip, I experimentally verify that the neural network estimates the quantum state with greater fidelity than either traditional method. Furthermore, the network can be trained using only product states and still achieve high fidelity for entangled states. This simplification of the training overhead permits the network to aid experimental calibration, such as the diagnosis of multi-qubit crosstalk. As quantum processors increase in size and complexity, I expect automated methods such as those presented in this thesis to become increasingly attractive.
Fast and accurate qubit-state assignment is essential for feedback, calibration, and error correction in quantum processors. In superconducting platforms, frequency-multiplexed readout makes this task intrinsically multivariate as measured traces can encode crosstalk, qubit-state relaxation events, and other transient nonidealities that are not fully captured by conventional matched filtering. Here, we introduce spiking neural network (SNN) discriminators for superconducting qubit readout. By processing the measurement window in successive time chunks, the networks exploit temporal structure and update classification scores as data arrive, rather than waiting until the end of the readout window. The spiking networks outperform matched-filter discrimination and approach the accuracy of a full-trace artificial neural network. Beyond reaching the performance of artificial neural networks, the key advantage of SNNs is that they provide a streaming, time-resolved estimate of the qubit state that evolves as the readout signal is acquired. Using quantisation-aware training and hls4ml synthesis, we further demonstrate that each FPGA inference update can be completed before the next readout chunk arrives. These results establish spiking neural networks as a promising route to low-latency, real-time qubit readout on FPGA hardware, with broader implications for time-critical quantum-control and scientific-inference applications.
Abstract Measurement errors in quantum computers are very detrimental to quantum computations. The ability to efficiently and accurately readout quantum states is crucial for quantum error correction schemes and quantum algorithms. Readout fidelity is typically limited by a poor signal-to-noise (SNR) ratio between the quantum states we intend to classify, as well as energy relaxation (e.g., T1 decay) from an excited state to a lower state during readout. Superconducting quantum bits (qubit), one of the leading candidates for scalable quantum computing hardware, are particularly limited by energy relaxation due to their relatively short coherence times. While most approaches for classifying the results of readout on superconducting qubits typically utilize clustering algorithms (e.g., a Gaussian mixture model) on integrated readout signals, these cannot distinguish between a quantum bit that was in the ground state prior to measurement from a qubit that decays to the ground state during measurement. For this reason, we instead propose using machine learning (ML) on the raw (non-integrated) analog signal and classification models on the full time series data (i.e., the \emph{trajectory}). We observe that time series classification methods, such as our chosen long short-term memory (LSTM) model, in combination with filtering and feature engineering techniques, consistently outperform clustering models. In particular, we find that the largest improvements come from reclassifying points in the boundary regions between neighboring clusters. These boundary points correspond to measurement records that deviate from the typical cluster, likely due to transient or noisy features in the signal that are not captured when the data is integrated. By retaining temporal information, sequence-aware models such as LSTMs can better discriminate these trajectories, whereas clustering methods based on integrated values are more prone to misclassifications.
Machine learning (ML) architectures such as convolutional neural networks (CNNs) have garnered considerable recent attention in the study of quantum many-body systems. However, advanced ML approaches such as gated recurrent neural networks (RNNs) have seldom been applied to such contexts. Here we demonstrate that a special class of RNNs known as long short-term memory (LSTM) networks is capable of learning and accurately predicting the time evolution of one-dimensional (1D) Ising model with simultaneous transverse and parallel magnetic fields, as quantitatively corroborated by relative entropy measurements and magnetization between the predicted and exact state distributions. In this unsupervised learning task, the many-body state evolution was predicted in an autoregressive way from an initial state, without any guidance or knowledge of any Hamiltonian. Our work paves the way for future applications of advanced ML methods in quantum many-body dynamics without relying on the explicit form of the Hamiltonian.