Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session Y70: Quantum System Learning |
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Sponsoring Units: DQI Chair: Shouvanik Chakrabarti, JPMorgan Chase Room: Room 409 |
Friday, March 10, 2023 8:00AM - 8:12AM |
Y70.00001: Entanglement features of random neural network quantum states Xiao-Qi Sun, Tamra Nebabu, Xizhi Han, Michael Flynn, Xiao-Liang Qi Neural networks offer a novel approach to represent wave functions for solving quantum many-body problems. But what kinds of quantum states are efficiently represented by neural networks? In this talk, we will discuss entanglement properties of an ensemble of neural network states represented by random restricted Boltzmann machines. Phases with distinct entanglement features are identified and characterized. For certain parameters, we will show that these neural network states can look typical in their entanglement profile while still being distinguishable from a typical state by their fractal dimensions. The obtained phase diagrams may help inform the initialization of neural network ansatzes for future computational tasks. |
Friday, March 10, 2023 8:12AM - 8:24AM |
Y70.00002: Training a decoder to retrieve information from a t-doped Clifford black hole Stefano Piemontese, Lorenzo Leone, Salvatore Francesco Emanuele Oliviero, Sarah True, Alioscia Hamma In a seminal paper[1], Hayden and Preskill showed that information can be retrieved from a black hole that is sufficiently scrambling provided that the retriever has total control over the emitted Hawking radiation and perfect knowledge of the internal dynamics of the black hole. In our work, we introduce a new quantum machine learning protocol that eliminates the latter requirement. We show that for t−doped Clifford unitaries - that is, black holes modeled by random Clifford circuits doped with an amount t of non-Clifford resources - an information retrieval decoder can be learned with fidelity decreasing exponentially in t using only out-of-time-order correlation functions. We show that the crossover between learnability and non-learnability is driven by the amount of non-Cliffordness in the black hole, demonstrating the link between non-stabilizerness and the onset of quantum chaos. |
Friday, March 10, 2023 8:24AM - 8:36AM |
Y70.00003: Implicit differentiation of variational quantum algorithms Shahnawaz Ahmed, Nathan Killoran, Juan Carrasquilla We show how to leverage implicit differentiation for gradient computation through variational quantum algorithms. A function defined implicitly as the solution of a quantum algorithm, e.g., a variationally obtained ground- or steady-state, can be differentiated using implicit differentiation while being agnostic to how the solution is computed. Since unrolling all the steps in the quantum algorithm is not required, implicit differentiation can be memory efficient compared to backpropagation. Physical quantities of interest in condensed-matter systems such as generalized susceptibility or nuclear gradients can be computed easily using implicit differentiation as we discuss in this work. We also develop two novel applications of implicit differentiation --- hyperparamter optimization in a quantum machine learning algorithm, and creating entangled quantum states variationally with gradient-based optimization of a geometric measure of entanglement. |
Friday, March 10, 2023 8:36AM - 8:48AM |
Y70.00004: Out-of-distribution generalization for learning quantum dynamics Matthias C Caro, Hsin-Yuan Huang, Nic Ezzell, Joe Gibbs, Andrew T Sornborger, Lukasz Cincio, Patrick J Coles, Zoe Holmes Generalization bounds are a critical tool to assess the training data requirements of Quantum Machine Learning (QML). Recent work has established guarantees for in-distribution generalization of quantum neural networks (QNNs), where training and testing data are drawn from the same data distribution. However, there are currently no results on out-of-distribution generalization in QML, where we require a trained model to perform well even on data drawn from a different distribution to the training distribution. Here, we prove out-of-distribution generalization for the task of learning an unknown unitary. In particular, we show that one can learn the action of a unitary on entangled states having trained only product states. Since product states can be prepared using only single-qubit gates, this advances the prospects of learning quantum dynamics on near term quantum hardware, and further opens up new methods for both the classical and quantum compilation of quantum circuits. |
Friday, March 10, 2023 8:48AM - 9:00AM |
Y70.00005: Overparameterization of Realistic Quantum Systems Matthew Duschenes, Juan Carrasquilla, Raymond Laflamme In order for quantum computing devices to accomplish preparation of quantum states, or compilation of operators, exceptional control of experimental parameters is required. The optimal parameters, such as time dependent magnetic fields for nuclear magnetic resonance, are found via classical simulation and optimization. Such idealized parameterized quantum systems have been shown to exhibit different regimes of training during optimization, such as overparameterization and lazy training, where global optima may potentially be reached exponentially quickly, while parameters negligibly change (Larocca et al., arXiv:2109.11676, 2021). Here, we study the effects of imposing constraints on the controls, such as bounding or sharing parameters across operators, and relevant noise channels are added after each time step. The constrained system is able to reach the overparameterized regime for certain noise models, however an order of magnitude more time steps are required. Compromises arise between numerical feasibility of exponential convergence, and experimental feasibility depending on the resolution of controls. This realistic approach offers insight into quantum control, as well as quantum learning, and will be tested in physical hardware. |
Friday, March 10, 2023 9:00AM - 9:12AM |
Y70.00006: Differential Optimization of Quantum Circuits Dominated by Clifford Gates Andi Gu, Hong-Ye Hu, Di Luo, Yi Tan, Taylor L Patti, Nicholas C Rubin, Ryan Babbush, Susanne F Yelin Finding a good initialization for variational quantum algorithms is believed to be crucial for successful training for near-term applications. However, the methodology for finding quality initializations is yet unclear. In this work, we propose to use the classical differential architecture search method to optimize quantum circuits dominated by Clifford gates, which we call the Clifford+kT ansatz. The optimal solution found within this ansatz can be viewed as a promising initialization for universal variational quantum circuits. In the regime of a small number of T-gates k, we numerically demonstrate that such optimization with differential architecture search is scalable. We illustrate the effectiveness of our methods for variational quantum eigensolver (VQE) using a molecular Hamiltonian of many qubits. We also compare differential architecture search with simulated annealing and numerically show the effect of adding T-gates to the ansatz. Last but not the least, we establish that our initialization strategy indeed helps with the training of variational algorithms on near-term quantum devices. |
Friday, March 10, 2023 9:12AM - 9:24AM |
Y70.00007: Extraction of Hamiltonian parameters from quantum ground states using variational quantum convolutional neural network Jian Feng Kong, Jun Yong Khoo Quantum convolutional neural network has been shown to be capable of efficiently and accurately classifying quantum states into topologically trivial and non-trivial phases. At the same time, recent work on hybrid quantum-classical neural networks has shown that such architectures can be used to perform classification tasks. Motivated by these developments, we construct and train a hybrid variational quantum convolutional neural network under the supervised regression mode. In particular, we demonstrate that given an input quantum circuit representing the ground state of a 1-dimensional Ising Hamiltonian, the hybrid network is capable of extracting the interaction parameters of the Hamiltonian. These input quantum circuits can be generated either by amplitude encoding or variational optimization. We further show that a network trained on a particular ansatz architecture can successfully process input circuits of a different architecture. This work thus illustrates the potential of hybrid quantum-classical neural networks in regression tasks, as well as in extracting information from quantum states prepared by near-term variational algorithms. |
Friday, March 10, 2023 9:24AM - 9:36AM |
Y70.00008: Learning Energy-Based Representations of Many-Body Quantum States Andrey Y Lokhov, Abhijith Jayakumar, Marc Vuffray We propose a new generative classical representation of many-body quantum states. This energy-based representation is derived from Gibbs distributions used for modeling thermal states of classical spin systems. This approach has the advantage of focusing on the structure of the energy function instead of attempting to directly model the probability density function. Based on the prior information on a family of quantum states, the energy function can be parametrized by an explicit low-degree polynomial or by a generic parametric family such as neural nets, and can naturally include the known symmetries of the system. In this work, we show how to efficiently learn the energy function representations for different families of quantum states from the available measurement data. Through a variety of examples, we show that the learned models can be used as generative models for predicting expectation values of physical observables. |
Friday, March 10, 2023 9:36AM - 9:48AM |
Y70.00009: Symmetry exploitation in quantum circuits Maximilian B Mansky We observe the high permutative symmetry in quantum machine learning and use it as a tool to restrict the Hilbert space necessary for finding the solution.
Quantum Machine Learning (QML) as an intermix of machine learning and quantum computing uses tunable quantum circuits to train models. These models exhibit a number of unique problems, in particular a heightened presence of barren plateaus[1], high noise and expensive training, both in time and financial cost. Our approach relies on the high permutation symmetry in machine learning. Permuting the input vectors and matrices inside the weights of each layer returns the same model prediction. In the context of QML this can be exploited to order the states within the model by the value of their corresponding weights. Simple counting arguments can be used to restrict the solution space to ½^n of the total Hilbert space, n the number of available states. This follows from the realization that the weights have either negative or positive values. With a permutation of the values we can ensure that they are always located in their respective halves of the Hilbert space. Our work is a necessary stepping stone to increasing the applicability of QML and countering some of the problems that are experienced in practice. Our solution is a simple yet powerful restriction in the search space without losing any of the generality that makes machine learning so broadly applicable. [1] McClean, J. R. et al. Barren plateaus in quantum neural network training landscapes. Nat. Comm. 9, 1 |
Friday, March 10, 2023 9:48AM - 10:00AM |
Y70.00010: Learning quantum systems via out-of-time-order correlators Masoud Mohseni, Thomas Schuster, Jordan Cotler, Murphy Yuezhen Niu, Thomas E O'Brien, Jarrod McClean Learning the properties of dynamical quantum systems underlies applications ranging from nuclear magnetic resonance spectroscopy to quantum device characterization. A central challenge in this pursuit is the learning of strongly-interacting systems, where conventional observables decay quickly in time and space, limiting the information that can be learned from their measurement. In this work, we introduce a new class of observables into the context of quantum learning---the out-of-time-order correlator---which we show can substantially improve the learnability of strongly-interacting systems by virtue of displaying informative physics at large times and distances. We identify two general scenarios in which out-of-time-order correlators provide a significant advantage for learning tasks in locally-interacting systems: (i) when experimental access to the system is spatially-restricted, for example via a single ``probe'' degree of freedom, and (ii) when one desires to characterize weak interactions whose strength is much less than the typical interaction strength. We numerically characterize these advantages across a variety of learning problems, and find that they are robust to both read-out error and decoherence. Finally, we introduce a binary classification task that can be accomplished in constant time with out-of-time-order measurements; however, we prove that this task is exponentially hard with any adaptive learning protocol that only involves time-ordered operations. |
Friday, March 10, 2023 10:00AM - 10:12AM |
Y70.00011: Decoding imperfect stabilizer codes with quantum neural networks Weishun Zhong, Oles Shtanko, Ramis Movassagh Error correction remains a key challenge for realizing fault-tolerant quantum computation in the noisy intermediate-scale quantum era. Stabilizer codes are among the leading candidates for the realization of fault-tolerant quantum computation. Stabilizer codes can be realized as ground states of physical systems. Although there has been much work on decoding ideal codes, the utility of imperfect codes is less understood. Motivated by practical realization of quantum codes on near-term devices, we develop a theoretical framework for decoding imperfect codes. Using Brillouin-Wigner perturbation theory, we prove that the scaling of the decoding error in standard procedure is independent of the underlying code distance. We corroborate the theory by numerical simulations of codes with various distances. We numerically find that the distant-independent scaling of the decoding error can be superseded by Quantum Neural Networks (QNNs). We provide theoretical guarantees by proving a QNN performance lower-bound on decoding imperfect codes from corrupted data, and show that QNNs are capable of achieving errors exponentially small in code distance, suggesting an scaling advantage over standard decoding procedures. We then numerically demonstrate that QNNs outperform standard procedures in decoding imperfect stabilizer codes. Our theoretical framework and numerical protocol provide a first step toward the understanding and practical decoding of imperfect stabilizer codes. |
Friday, March 10, 2023 10:12AM - 10:24AM |
Y70.00012: Decoding surface codes with deep reinforcement learning and probabilistic policy reuse Elisha Siddiqui Matekole, Esther Ye, Ramya Iyer, Samuel Yen-Chi Chen, Tzu-Chieh Wei Quantum computing (QC) promises significant advantages on certain hard computational tasks over classical computers. However, existing quantum hardware, the so-called noisy intermediate-scale quantum computers (NISQ), are still unable to carry out computations faithfully mainly because of the lack of quantum error correction (QEC) capability. |
Friday, March 10, 2023 10:24AM - 10:36AM |
Y70.00013: A Convergence Theory for Over-parameterized Variational Quantum Eigensolvers Xuchen You, Shouvanik Chakrabarti, Xiaodi Wu The Variational Quantum Eigensolver (VQE) is a promising candidate for applications on Noisy Intermediate-Scale Quantum computers. Despite empirical studies and theoretical progress in understanding the VQE optimization landscape, the convergence for optimizing VQE is less understood. We provide an analysis of the convergence of VQEs in the over-parameterization regime. By connecting the training dynamics with the Riemannian Gradient Flow on the unit-sphere, we establish a threshold on the number of parameters for efficient convergence, which depends polynomially on the system dimension and the spectral ratio, a property of the problem Hamiltonian. We further illustrate that this over-parameterization threshold could be vastly reduced for specific VQE instances by establishing an ansatz-dependent threshold, which serves as a proxy of the trainability of different VQE ansatzes and leads to a principled way of evaluating ansatz design. We showcase with quantum neural networks that our analysis may be extended to characterize variational quantum algorithms in general. |
Friday, March 10, 2023 10:36AM - 10:48AM |
Y70.00014: Error-tolerant quantum convolutional neural networks for the recognition of symmetry-protected topological phases Petr Zapletal, Nathan A McMahon, Michael J Hartmann The development and application of quantum computers require tools to evaluate noisy quantum data produced by near-term quantum hardware. Quantum neural networks based on parametrized quantum circuits, measurements and feedforward can process large quantum data, to detect non-local quantum correlations with reduced measurement and computational efforts compared to standard characterization techniques. Here we construct quantum convolutional neural networks (QCNNs) based on the multiscale entanglement renormalization ansatz that can recognize different symmetry-protected topological phases of generalized cluster-Ising Hamiltonians in the presence of incoherent errors, simulating the effects of decoherence under NISQ conditions. Using matrix product state simulations, we show that the QCNN output is robust against symmetry-preserving errors if the error channel is invertible. Moreover, the QCNNs tolerate symmetry-breaking errors below a threshold error probability in contrast to previous QCNN designs and string order parameters (SOPs), which are significantly suppressed for any non-vanishing error probability. Even though the error tolerance is limited close to phase boundaries due to a diverging correlation length, the QCNNs can precisely determine critical values of Hamiltonian parameters. To facilitate the implementation of QCNNs on near-term quantum computers, we show how to shorten a general class of QCNN circuits from logarithmic to constant depth in system size by performing a large part of computation in classical post-processing after the measurement of all qubits. The QCNN with a constant-depth quantum circuit reduces sample complexity exponentially with system size in comparison to the direct sampling of the QCNN output using local Pauli measurements with only logarithmic classical computational costs. |
Friday, March 10, 2023 10:48AM - 11:00AM Author not Attending |
Y70.00015: Online adaptive estimation of decoherence timescales for a single qubit Muhammad Junaid Arshad, Christiaan Bekker, Ben Haylock, Krzysztof Skrzypczak, Daniel White, Benjamin Griffiths, Joe Gore, Gavin Morley, Patrick Salter, Jason Smith, Inbar Zohar, Amit Finkler, Yoann Altmann, Erik Gauger, Cristian Bonato The rate of decoherence is a critical parameter in the performance of quantum bits, memories and sensors. Fast estimation of these timescales is necessary for the efficient characterisation of large arrays of quantum devices and to achieve peak sensitivities during sensor operation. The usual method for determining a quantum system’s decoherence rate involves a suite of experiments probing the entire expected range of the parameter and extracting the resulting estimation in post-processing. Here we present an adaptive Bayesian approach, based on a simple analytical update rule, to estimate the key decoherence timescales (T1, T∗2 and T2) in a quantum system in real-time, using information gained |
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