New Technique Cuts Quantum Simulation Time by Exploiting Data Patterns
Summarize this article with:
Scientists are tackling a significant challenge in quantum simulation and device characterisation: efficiently estimating numerous local expectation values over time. Joseph Barreto and Daniel Lidar, both from the Department of Physics and Astronomy and the Center for Quantum Information Science & Technology at the University of Southern California, alongside colleagues from the Department of Electrical and Computer Engineering, the Department of Chemistry at USC, and Quantum Elements, Inc., present a novel approach called Compressed Shadow Tomography (CSST).
This research introduces a protocol combining local classical shadows and compressed sensing to minimise the number of device measurements needed to reconstruct the Pauli-signal matrix for low-weight Pauli observables across multiple timesteps. By strategically sampling time and leveraging spectral sparsity, CSST offers potential shot savings scaling up to polylogarithmic factors compared to conventional methods, representing a substantial advancement for resource-efficient quantum information processing. Estimating numerous local expectation values, quantifying the average outcome of measurements on a quantum system, is computationally expensive and demands substantial resources. This work addresses the problem of reconstructing the Pauli-signal matrix, representing the time-dependent behaviour of low-weight Pauli observables, while minimising the total number of measurements required from a quantum device. Operationally, the protocol intelligently samples timesteps, collects shadows only at these selected times, and then reconstructs the complete time series using standard recovery techniques in the transformed domain. The research provides rigorous mathematical guarantees for the accuracy of CSST, explicitly combining the inherent errors in shadow estimation with the bounds achievable through compressed sensing. For signals that are exactly sparse in a unitary transform basis, the study demonstrates that a number of randomly selected timesteps, scaling favourably with the signal’s sparsity, is sufficient to achieve accurate reconstruction with high probability, leading to substantial savings in the total number of measurements needed, potentially scaling up to polylogarithmic factors better than traditional methods. Furthermore, for signals that are approximately sparse, the reconstruction error depends on both the signal’s compressibility and the level of noise present in the system. Numerical experiments on complex, many-qubit dynamics corroborate the strong Fourier compressibility of Pauli traces and demonstrate the protocol’s ability to achieve significant shot reductions while maintaining accurate reconstruction. These experiments demonstrate that the technique accurately reconstructs signals even in the presence of noise, validating its practical applicability. Signals reconstructed via CSST demonstrate substantial shot reductions when estimating Pauli expectation values over time. Specifically, for exactly sparse signals in a unitary transform basis, the research establishes that random sampling of timesteps is sufficient, achieving total-shot savings that scale up to polylogarithmic factors relative to collecting shadows at all timesteps. This means that, for a given level of accuracy, the number of measurements needed can be significantly reduced by strategically selecting which moments in time to sample. The study focuses on reconstructing the Pauli-signal matrix for low-weight Pauli observables across N timesteps, minimising the total number of device shots required. The reconstruction error for approximately sparse signals decomposes into a compressibility term, reflecting the signal’s inherent structure, and a noise term, allowing for precise control over accuracy. This decomposition is crucial for understanding the limitations and potential of the method in realistic scenarios. The work provides end-to-end guarantees combining shadow estimation error with compressed recovery bounds, quantifying the relationship between sampled timesteps, snapshot count, Pauli weight, and target failure probability. These guarantees establish that the number of required sampled timesteps, m, can be significantly less than N, the total number of timesteps, provided the signals exhibit sufficient sparsity or compressibility in a unitary transform domain. A 72-qubit superconducting processor is not central to this work; instead, the research focuses on CSST, a novel data acquisition protocol designed to efficiently estimate time-dependent expectation values of Pauli observables. CSST combines local classical shadows and compressed sensing to minimise the total number of device shots required. Local classical shadows are employed at each sampled timestep to reduce the dimensionality of the observable space, allowing for the estimation of multiple Pauli expectation values from a single set of randomized measurements, scaling logarithmically with the number of target observables and exponentially with their maximum weight. Crucially, the study does not collect shadows at every timestep but instead samples times uniformly at random, forming the basis of the compressed sensing component. The core innovation lies in exploiting the spectral properties of the time series data, recognising that many expectation-value traces exhibit sparsity or compressibility when transformed into a unitary basis, such as a Fourier or discrete cosine transform, and reconstructing each signal within this transformed domain. By leveraging this compressibility, CSST can accurately recover the full time series from a significantly reduced number of measurements, applying standard recovery techniques and providing end-to-end guarantees that combine shadow estimation error with compressed recovery bounds. This approach yields substantial shot savings, scaling up to polylogarithmic factors relative to traditional methods that collect shadows at all timesteps.
Scientists have long struggled with the escalating demands of simulating quantum systems and verifying the performance of quantum devices. A core challenge lies in efficiently measuring numerous expectation values as these systems evolve over time. Traditional methods require an exhaustive number of measurements, quickly becoming impractical as the complexity of the system increases. Now, CSST offers a significant step towards alleviating this bottleneck, representing a smarter approach to information gathering by combining techniques of local classical shadows and compressed sensing to reconstruct a comprehensive picture of the system’s behaviour from a fraction of the data previously needed. This is akin to reconstructing a detailed image from a handful of carefully selected pixels, rather than requiring every single pixel to be measured. The method leverages the fact that many quantum signals exhibit inherent patterns, a form of ‘compressibility’, allowing for accurate reconstruction even with incomplete data. However, the effectiveness of this approach hinges on the degree to which these signals are indeed compressible, and the level of noise present in the system. While the experiments demonstrate promising results on several qubit dynamics, extending this to significantly larger and more complex systems remains an open question. Furthermore, the computational cost of the reconstruction process itself could become a limiting factor. Looking ahead, this work opens avenues for more efficient quantum simulations, potentially accelerating the development of new materials and drugs. Beyond simulation, it could also streamline the validation of quantum hardware, paving the way for more reliable and scalable quantum computers. 👉 More information 🗞 Compressed Sensing Shadow Tomography 🧠 ArXiv: https://arxiv.org/abs/2602.12518 Tags: