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 M64: Algorithms for Quantum Machine Learning and Its ApplicationsFocus
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Sponsoring Units: DQI Chair: Olivia Di Matteo, The University of British Columbia Room: Room 415 |
Wednesday, March 8, 2023 8:00AM - 8:12AM |
M64.00001: Quantum Scientific Machine Learning for Multiphysics simulations. Panagiotis Barkoutsos, Oleksandr Kyriienko, Vincent E Elfving The natural and socioeconomic world is fundamentally governed by conservation laws and rates of change; these systems are mostly modelled by differential equations (DEs). Solving intricate DEs can be computationally challenging due to their scale and complexity. As such, recently novel methodological approaches and computational paradigms have been explored to target them efficiently and accurately. In our work, we combine the efforts made by the classical machine learning community towards Scientific Machine Learning (SciML), i.e. using machine learning to solve and optimize systems governed by DEs, and the recent developments in the field of Quantum Machine Learning (QML), to form Quantum Scientific Machine Learning (QSciML). In the talk we will focus specifically on the advancements of variational quantum algorithms in this direction, including the Differentiable Quantum Circuits paradigm, and present results of their applications in various types of physics and engineering problems towards industrial-scale relevant applications. |
Wednesday, March 8, 2023 8:12AM - 8:24AM |
M64.00002: Expressivity of Variational Quantum Machine Learning on the Boolean Cube Dylan Herman Categorical data plays an important part in machine learning research and appears in a variety of applications. Models that can express large classes of real-valued functions on the Boolean cube are useful for problems involving discrete-valued data types, including those which are not Boolean. To this date, the commonly used schemes for embedding classical data into variational quantum machine learning models encode continuous values. Here we investigate quantum embeddings for encoding Boolean-valued data into parameterized quantum circuits used for machine learning tasks. We narrow down representability conditions for functions on the $n$-dimensional Boolean cube with respect to previously known results, using two quantum embeddings: a phase embedding and an embedding based on quantum random access codes. We show that for any real-valued function on the $n$-dimensional Boolean cube, there exists a variational linear quantum model based on a phase embedding using $n$ qubits that can represent it and an ensemble of such models using $d |
Wednesday, March 8, 2023 8:24AM - 8:36AM |
M64.00003: Machine Learning for Image Classification on a Trapped Ion Quantum Computer Jason Iaconis, Sonika Johri, Sang Hyun Kim, Sooncheol Park, Sangtae Kim, Hanlae Jo Machine learning has recently emerged as one of the most promising areas for applications of near-term quantum computers. The ability of quantum computers to apply nonclassical feature maps to classical data opens new possibilities for enhancing part or all of existing ML models. In supervised learning, image classification has stood out as one of the benchmark problems, and has been one of the most popular areas for testing QML algorithms. To date, most of the work in this direction has focused on classification of a subset of the relatively simple MNIST images. Furthermore, there has been a relative scarcity of implementations of these algorithms on quantum hardware. In this work, we report results of applying a hybrid quantum convolutional neural network model for classification of a complex real world dataset of road sign images. We will discuss our methods of classical processing and quantum encoding of the data, as well as the quantum circuit design and optimization methods. We will present results of training a full end-to-end classification model on up to 8 qubits on a trapped ion quantum computer as well as performing inference on the QPU backend with 16 qubits to classify up to 10 categories of images. We will also discuss projections of future performance of this model. |
Wednesday, March 8, 2023 8:36AM - 9:12AM |
M64.00004: New Approaches to Hamiltonian Simulation Invited Speaker: Nathan Wiebe In recent years quantum simulation has made giant leaps but there still remain a number of open issues that arise. In this work I will review recent results by my collaborators and I that have changed the way that we think about simulation. We will show how extrapolation ideas can allow Trotter simulations to be performed with super-polynomially better error scaling than previously believed. I will also show how Qubitization can be adapted to work for time-dependent Hamiltonians, which is a problem that has long vexed the community. Further, I will show how methods such as Trotter formulas, qubitization and randomized product formulas can be combined into a single framework that allows simulations to be performed faster than existing methods. I will then discuss open problems and the prospect of using simulation as a computational primitive for finding exponential speedups for broad classes of problems. |
Wednesday, March 8, 2023 9:12AM - 9:24AM |
M64.00005: Quantifying Quantum Advantage in Topological Data Analysis Ryan Babbush Lloyd et al. were first to demonstrate the promise of quantum algorithms for computing Betti numbers, a way to characterize topological features of data sets. Here, we propose, analyze, and optimize an improved quantum algorithm for topological data analysis (TDA) with reduced scaling, including a method for preparing Dicke states based on inequality testing, a more efficient amplitude estimation algorithm using Kaiser windows, and an optimal implementation of eigenvalue projectors based on Chebyshev polynomials. We compile our approach to a fault-tolerant gate set and estimate constant factors in the Toffoli complexity. Our analysis reveals that super-quadratic quantum speedups are only possible for this problem when targeting a multiplicative error approximation and the Betti number grows asymptotically. Further, we propose a dequantization of the quantum TDA algorithm that shows that having exponentially large dimension and Betti number are necessary, but insufficient conditions, for super-polynomial advantage. We then introduce and analyze specific problem examples for which super-polynomial advantages may be achieved, and argue that quantum circuits with tens of billions of Toffoli gates can solve some seemingly classically intractable instances. |
Wednesday, March 8, 2023 9:24AM - 9:36AM |
M64.00006: Quantum algorithms for approximate function loading Javier Gonzalez-Conde, Gabriel Marin-Sanchez, Mikel Sanz Loading classical data into quantum computers represents an essential stage in many relevant quantum algorithms, especially in the field of quantum machine learning. Therefore, the inefficiency of this loading process means a major bottleneck for the application of these algorithms. Here, we introduce two approximate quantum-state preparation methods inspired by the Grover-Rudolph algorithm without making use of ancillary qubits, which partially solve the problem of loading real functions. Indeed, by allowing for an infidelity ε and under certain smoothness conditions, we prove that the complexity of Grover-Rudolph algorithm without making use of ancillary qubits can be reduced from O(2n) to O(2k0(ε)), with n the number of qubits and k0(ε) asymptotically independent of n. This leads to a dramatic reduction in the number of required two-qubit gates. Aroused by this result, we also propose a variational algorithm capable of loading functions beyond the aforementioned smoothness conditions. Our variational ansatz is explicitly tailored to the landscape of the function, leading to a quasi-optimized number of hyperparameters. This allows us to achieve high fidelity in the loaded state with high speed convergence for the studied examples. Additionally, this technique can be easily extended for loading complex valued functions. |
Wednesday, March 8, 2023 9:36AM - 9:48AM |
M64.00007: Encoding quantum circuits in optimal tensor network structures with gradient descent methods Sergi Masot Llima Tensor networks are a well-known structure for the simulation of quantum systems and a useful alternative to current quantum devices, also being flexible enough to have applications in other computing fields such as machine learning. The expressibility available to a specific tensor network depends on how big the bond dimensions between tensors are and how much they are connected, at the cost of computational difficulty. Structures that are adapted to a specific problem offer a way to achieve higher faithfulness while keeping the computational cost down but are in general hard to find. Here we propose an algorithm to find optimal structures for an arbitrary problem and showcase some examples where a tree structure offers an advantage over a chain while not being much more costly. To achieve so, we use different flavours of gradient descent to iterate over the connections between tensors. The tools used in this algorithm have been developed specifically with high-performance computing in mind so that these structures can be used in large simulations to explore quantum systems that are not yet within reach of quantum computing. In addition, it allows us to identify correlation patterns in complex condensed matter systems, for example, so that multipartite entanglement can be better understood and characterized. |
Wednesday, March 8, 2023 9:48AM - 10:00AM |
M64.00008: Feedback-based quantum algorithms Alicia B Magann, Kenneth Rudinger, Matthew D Grace, James B Larsen, Christian Arenz, Andrew D Baczewski, Mohan Sarovar This talk will present feedback-based quantum algorithms (FQAs) as an optimization-free paradigm that is applicable to solving a broad range of problems on quantum computers. Within this paradigm, feedback from qubit measurements is used to build up quantum circuits in a layer-wise manner, such that the quality of the solution to a problem under consideration improves monotonically with each added layer. I will begin this talk by overviewing the theoretical foundations of FQAs, which are rooted in quantum Lyapunov control theory. I will then outline the general steps for formulating and implementing FQAs, highlight the tradeoffs associated with different FQA design choices, and discuss new developments in FQAs from the last year. Throughout this talk, context will be provided using examples of FQAs for quantum simulation, optimization, and machine learning applications. Sandia National Labs is managed and operated by NTESS under DOE NNSA contract DENA0003525. SAND2022-14644 A. |
Wednesday, March 8, 2023 10:00AM - 10:12AM |
M64.00009: On nonlinear transformations in quantum computation Yigit Subasi, Zoe Holmes, Nolan Coble, Andrew T Sornborger While quantum computers are naturally well-suited to implementing linear operations, it is less clear how to implement nonlinear operations on quantum computers. However, nonlinear subroutines may prove key to a range of applications of quantum computing from solving nonlinear equations to data processing and quantum machine learning. Here we develop algorithms for implementing nonlinear transformations of input quantum states. Our algorithms are framed around the concept of a weighted state, a mathematical entity describing the output of an operational procedure involving both quantum circuits and classical post-processing. |
Wednesday, March 8, 2023 10:12AM - 10:24AM |
M64.00010: Noise-induced barren plateaus in variational quantum algorithms due to non-unital and Hamiltonian control noise Phattharaporn Singkanipa Variational Quantum Algorithms (VQAs) are leading practical applications of Noisy Intermediate-Scale Quantum (NISQ) devices. Despite their promise, VQAs suffer from the problem of vanishing gradients, also known as the barren plateau (BP) phenomenon. BP can arise from fundamentally different mechanisms, e.g., parameter initialization, the structure of the problem Hamiltonian, and noise. Noise-induced barren plateaus (NIBPs) have been shown to exist subject to unital CPTP maps. We generalize this result to non-unital CPTP noise via parameter shift rules and derive the validity of the rules in the presence of noise. We demonstrate the effects of noise on VQA training via simulations. |
Wednesday, March 8, 2023 10:24AM - 10:36AM |
M64.00011: Experimental Loading of Normal Probability Distributions to Quantum States Sonika Johri, Jason Iaconis, Elton Zhu State preparation is a necessary component of many quantum algorithms, and in particular is fundamental in quantum sampling algorithms such as quantum Monte Carlo integration. In this work, we combine a method for efficiently representing smooth differentiable probability distributions using matrix product states with newly discovered techniques for initializing quantum states to approximate matrix product states. Using this, we generate quantum states encoding a class of normal probability distributions in a trapped ion quantum computer for up to 20 qubits. We provide an in depth analysis of the different sources of error which contribute to the overall fidelity of this state preparation procedure. Our work provides the first study in quantum hardware for scalable distribution loading, which is the basis of a wide variety of algorithms that provide quantum advantage. |
Wednesday, March 8, 2023 10:36AM - 10:48AM |
M64.00012: The efficient preparation of normal distributions in quantum registers Pierre Minssen, Marco Pistoia, Yue Sun, Arthur Rattew The efficient preparation of input distributions is an important problem in obtaining quantum advantage in a wide range of domains. We propose a novel quantum algorithm for the efficient preparation of arbitrary normal distributions in quantum registers. To the best of our knowledge, our work is the first to leverage the power of Mid-Circuit Measurement and Reuse (MCMR), in a way that is broadly applicable to a range of state-preparation problems. Specifically, our algorithm employs a repeat-until-success scheme, and only requires a constant-bounded number of repetitions in expectation. In the experiments presented, the use of MCMR enables up to a 862.6 x reduction in required qubits. Furthermore, the algorithm is provably resistant to both phase-flip and bit-flip errors, leading to a first-of-its-kind empirical demonstration on real quantum hardware, the MCMR-enabled Honeywell System Models H0 and H1-2. |
Wednesday, March 8, 2023 10:48AM - 11:00AM |
M64.00013: Quantum Metropolis Solver: QMS Roberto Campos Ortiz, Pablo Antonio M Casares, Miguel Angel Martin-Delgado The efficient resolution of optimization problems is one of the key issues in today's industry. This task relies mainly on classical algorithms that present scalability problems and processing limitations. Quantum computing has emerged to challenge these types of problems. In this paper, we focus on the Metropolis-Hastings quantum algorithm that is based on quantum walks. We use this algorithm to build a quantum software tool called Quantum Metropolis Solver (QMS). We validate QMS with the N-Queen problem to show a potential quantum advantage in an example that can be easily extrapolated to an Artificial Intelligence domain. We carry out different simulations to validate the performance of QMS and its configuration. |
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