Quantum classifiers are trainable quantum circuits used as machine learning models. The first part of the circuit implements a quantum feature map that encodes classical inputs into quantum states, embedding the data in a high-dimensional Hilbert space; the second part of the circuit executes a quantum measurement interpreted as the output of the model. Usually, the measurement is trained to distinguish quantum-embedded data. We propose to instead train the first part of the circuit -- the embedding -- with the objective of maximally separating data classes in Hilbert space, a strategy we call quantum metric learning. As a result, the measurement minimizing a linear classification loss is already known and depends on the metric used: for embeddings separating data using the l1 or trace distance, this is the Helstrom measurement, while for the l2 or Hilbert-Schmidt distance, it is a simple overlap measurement. This approach provides a powerful analytic framework for quantum machine learning and eliminates a major component in current models, freeing up more precious resources to best leverage the capabilities of near-term quantum information processors.
Machine learning is seen as a promising application of quantum computation. For near-term noisy intermediate-scale quantum (NISQ) devices, parametrized quantum circuits (PQCs) have been proposed as machine learning models due to their robustness and ease of implementation. However, the cost function is normally calculated classically from repeated measurement outcomes, such that it is no longer encoded in a quantum state. This prevents the value from being directly manipulated by a quantum computer. To solve this problem, we give a routine to embed the cost function for machine learning into a…
We present a new scheme to efficiently establish entanglement between optical modes in a time-multiplexed coherent Ising machine (CIM) by means of nonlocal measurement and feedback. We numerically simulate and evaluate the generation of steady-state entanglement in a system with nearest-neighbor interactions on a 1D ring, and we compare the results to those of a conventional CIM with all-optical interactions mediated by delay lines. We show that the delay-line architecture has a fundamental limit on accessible entanglement that our measurement-based scheme can substantially surpass. These resu…
Quantum embedding learning is an important step in the application of quantum machine learning to classical data. In this paper we propose a quantum few-shot embedding learning paradigm, which learns embeddings useful for training downstream quantum machine learning tasks. Crucially, we identify the circuit bypass problem in hybrid neural networks, where learned classical parameters do not utilize the Hilbert space efficiently. We observe that the few-shot learned embeddings generalize to unseen classes and suffer less from the circuit bypass problem compared with other approaches.
This paper introduces a novel quantum embedding search algorithm (QES, pronounced as "quest"), enabling search for optimal quantum embedding design for a specific dataset of interest. First, we establish the connection between the structures of quantum embedding and the representations of directed multi-graphs, enabling a well-defined search space. Second, we instigate the entanglement level to reduce the cardinality of the search space to a feasible size for practical implementations. Finally, we mitigate the cost of evaluating the true loss function by using surrogate models via sequential m…
Introducing creation and annihilation operators for negative frequency components extends the algebra of smeared local observables of quantum optics to include an associated classical random field optics.
Quantum annealing promises to be an effective heuristic for complex NP-hard problems. However, clear demonstrations of quantum advantage are wanting, primarily constrained by the difficulty of embedding the problem into the quantum hardware. Community detection methods such as the Girvin--Newman algorithm can provide a divide-and-conquer approach to large problems. Here, we propose a problem-focused division for embedding, deliberately worsening typical measures of embedding quality to improve the partial solutions we obtain. We apply this approach first to the highly irregular graph of an int…
Sequential learning on a Tensor Network Born machine with Trainable Token Embedding
Department of Physics, University of California, San Diego, CA 92093, USA（加州大学圣地亚哥分校物理系）；School of Physics, Zhejiang University, Hangzhou 310027, China（浙江大学物理学院）；Department of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA（佐治亚理工学院物理系）
The role of data-induced randomness in quantum machine learning classification tasks
Barcelona Supercomputing Center（巴塞罗那超级计算中心）；Universitat de Barcelona（巴塞罗那大学）；Universiteit Leiden（莱顿大学）；Lorentz Instituut（洛伦兹研究所）；Honda Research Institute Europe GmbH（本田欧洲研究院）
Embedding-Aware Quantum-Classical SVMs for Scalable Quantum Machine Learning
National Irish Centre for AI (CeADAR), University College Dublin (UCD), Dublin, Ireland（爱尔兰人工智能国家中心（CeADAR）、都柏林大学（UCD））；SISTEMIC Research Group, University of Antioquia, Medellín, Colombia（SISTEMIC研究组、安蒂奎亚大学）；Department of Computer Science, University of Torino, Torino, Italy（计算机科学系、托里诺大学）；Corporation for Aerospace Initiatives (CASIRI), University of Cauca, Popayán, Colombia（航空航天倡议公司（CASIRI）、考卡大学）
The classification of big data usually requires a mapping onto new data clusters which can then be processed by machine learning algorithms by means of more efficient and feasible linear separators. Recently, Lloyd et al. have advanced the proposal to embed classical data into quantum ones: these live in the more complex Hilbert space where they can get split into linearly separable clusters. Here, we implement these ideas by engineering two different experimental platforms, based on quantum optics and ultra-cold atoms respectively, where we adapt and numerically optimize the quantum embedding…
Quantum kernel methods, i.e., kernel methods with quantum kernels, offer distinct advantages as a hybrid quantum-classical approach to quantum machine learning (QML), including applicability to Noisy Intermediate-Scale Quantum (NISQ) devices and usage for solving all types of machine learning problems. Kernel methods rely on the notion of similarity between points in a higher (possibly infinite) dimensional feature space. For machine learning, the notion of similarity assumes that points close in the feature space should be close in the machine learning task space. In this paper, we discuss th…
In order to treat all-to-all connected quadratic binary optimization problems (QUBO) with hardware quantum annealers, an embedding of the original problem is required due to the sparsity of the hardware's topology. Embedding fully-connected graphs - typically found in industrial applications - incurs a quadratic space overhead and thus a significant overhead in the time to solution. Here we investigate this embedding penalty of established planar embedding schemes such as minor embedding on a square lattice, minor embedding on a Chimera graph, and the Lechner-Hauke-Zoller scheme using simulate…
We consider quantum XOR games, defined in [11], from the perspective of unitary correlations defined in [7]. We show that Connes' embedding problem has a positive answer if and only if every quantum XOR game has entanglement bias equal to the commuting bias. In particular, the embedding problem is equivalent to determining whether every quantum XOR game $G$ with a winning strategy in the commuting model also has a winning strategy in the approximate finite-dimensional model.
Freie Universität Berlin（柏林自由大学）；University of Cologne（科隆大学）
Kernel methods are a cornerstone of classical machine learning. The idea of using quantum computers to compute kernels has recently attracted attention. Quantum embedding kernels (QEKs) constructed by embedding data into the Hilbert space of a quantum computer are a particular quantum kernel technique that allows to gather insights into learning problems and that are particularly suitable for noisy intermediate-scale quantum devices. In this work, we first provide an accessible introduction to quantum embedding kernels and then analyze the practical issues arising when realizing them on a nois…
We obtain sufficient conditions on kernels of quantum states under which Wigner functions, optical quantum tomograms and linking their formulas are correctly defined. Our approach is based upon the Sobolev embedding theorem. The transition probability formula and the fractional Fourier transform are discussed in this framework.
We introduce the concept of embedding quantum simulators, a paradigm allowing the efficient quantum computation of a class of bipartite and multipartite entanglement monotones. It consists in the suitable encoding of a simulated quantum dynamics in the enlarged Hilbert space of an embedding quantum simulator. In this manner, entanglement monotones are conveniently mapped onto physical observables, overcoming the necessity of full tomography and reducing drastically the experimental requirements. Furthermore, this method is directly applicable to pure states and, assisted by classical algorithm…
