Non-Unitary Quantum Machine Learning

• URL: http://arxiv.org/abs/2405.17388v1
• Date: Mon, 27 May 2024 17:42:02 GMT
• Title: Non-Unitary Quantum Machine Learning
• Authors: Jamie Heredge, Maxwell West, Lloyd Hollenberg, Martin Sevior,
• Abstract summary: We introduce several novel probabilistic quantum algorithms that overcome the normal unitary restrictions in quantum machine learning. Among our contributions are quantum native implementations of Residual Networks (ResNet); demonstrating a path to avoiding barren plateaus. We also show how this framework can be used to parameterise and control the amount of symmetry in an encoding.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce several novel probabilistic quantum algorithms that overcome the normal unitary restrictions in quantum machine learning by leveraging the Linear Combination of Unitaries (LCU) method. Among our contributions are quantum native implementations of Residual Networks (ResNet); demonstrating a path to avoiding barren plateaus while maintaining the complexity of models that are hard to simulate classically. Furthermore, by generalising to allow control of the strength of residual connections, we show that the lower bound of the LCU success probability can be set to any arbitrary desired value. We also implement a quantum analogue of average pooling layers from convolutional networks. Our empirical analysis demonstrates that the LCU success probability remains stable for the MNIST database, unlocking a potential quadratic advantage in terms of image size compared to classical techniques. Finally, we propose a general framework for irreducible subspace projections for quantum encoded data. Using this, we demonstrate a novel rotationally invariant encoding for point cloud data via Schur-Weyl duality. We also show how this framework can be used to parameterise and control the amount of symmetry in an encoding; demonstrating improved classification performance for partially permutation invariant encoded point cloud data when compared to non-invariant or fully permutation invariant encodings. These new general algorithmic frameworks are all constructed under the same LCU method, suggesting that even more novel algorithms could be achieved by utilising the LCU technique.

Related papers

• Quantum-Efficient Convolution through Sparse Matrix Encoding and Low-Depth Inner Product Circuits [0.0]
  We present a resource-efficient quantum algorithm that reformulates the convolution product as a structured matrix multiplication.<n>We construct a quantum framework wherein sparse input patches are prepared using optimized key-value QRAM state encoding.<n>Our architecture supports batched convolution across multiple filters using a generalized SWAP circuit.
  arXiv  Detail & Related papers  (2025-07-25T20:08:12Z)
• Efficient Quantum Access Model for Sparse Structured Matrices using Linear Combination of Things [0.6138671548064355]
  We present a novel framework for Linear Combination of Unitaries (LCU)-style decomposition tailored to structured sparse matrices.<n>LCU is a foundational primitive in both variational and fault-tolerant quantum algorithms.<n>We introduce the Sigma basis, a compact set of simple, non-unitary operators that can better capture sparsity and structure.
  arXiv  Detail & Related papers  (2025-07-04T17:05:07Z)
• Tensor Cross Interpolation of Purities in Quantum Many-Body Systems [0.0]
  In quantum many-body systems the exponential scaling of the Hilbert space with the number of degrees of freedom renders a complete state characterization. Recently, a compact way of storing subregions' purities by encoding them as amplitudes of a fictitious quantum wave function, known as entanglement feature, was proposed. In this work, we demonstrate that the entanglement feature can be efficiently defining using only a amount of samples in the number of degrees of freedom.
  arXiv  Detail & Related papers  (2025-03-21T15:33:00Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Near-Term Distributed Quantum Computation using Mean-Field Corrections and Auxiliary Qubits [77.04894470683776]
  We propose near-term distributed quantum computing that involve limited information transfer and conservative entanglement production. We build upon these concepts to produce an approximate circuit-cutting technique for the fragmented pre-training of variational quantum algorithms.
  arXiv  Detail & Related papers  (2023-09-11T18:00:00Z)
• Explainable quantum regression algorithm with encoded data structure [0.0]
  In this paper, we construct the first interpretable quantum regression algorithm.<n>The encoded data structure reduces the time complexity of computing the regression map.<n>We envision potential quantum utilities with multi-qubit gates implemented in neutral cold atoms and ions.
  arXiv  Detail & Related papers  (2023-07-07T00:30:16Z)
• Robust Dequantization of the Quantum Singular value Transformation and Quantum Machine Learning Algorithms [0.0]
  We show how many techniques from randomized linear algebra can be adapted to work under this weaker assumption. We also apply these results to obtain a robust dequantization of many quantum machine learning algorithms.
  arXiv  Detail & Related papers  (2023-04-11T02:09:13Z)
• Implementing any Linear Combination of Unitaries on Intermediate-term Quantum Computers [0.0]
  We develop three new methods to implement any Linear Combination of Unitaries (LCU) The first method estimates expectation values of observables with respect to any quantum state prepared by an LCU procedure. The second approach is a simple, physically motivated, continuous-time analogue of LCU, tailored to hybrid qubit-qumode systems. The third method (Ancilla-free LCU) requires no ancilla qubit at all and is useful when we are interested in the projection of a quantum state.
  arXiv  Detail & Related papers  (2023-02-27T07:15:14Z)
• Quantum Worst-Case to Average-Case Reductions for All Linear Problems [66.65497337069792]
  We study the problem of designing worst-case to average-case reductions for quantum algorithms. We provide an explicit and efficient transformation of quantum algorithms that are only correct on a small fraction of their inputs into ones that are correct on all inputs.
  arXiv  Detail & Related papers  (2022-12-06T22:01:49Z)
• Decomposition of Matrix Product States into Shallow Quantum Circuits [62.5210028594015]
  tensor network (TN) algorithms can be mapped to parametrized quantum circuits (PQCs) We propose a new protocol for approximating TN states using realistic quantum circuits. Our results reveal one particular protocol, involving sequential growth and optimization of the quantum circuit, to outperform all other methods.
  arXiv  Detail & Related papers  (2022-09-01T17:08:41Z)
• Variational Quantum and Quantum-Inspired Clustering [0.0]
  We present a quantum algorithm for clustering data based on a variational quantum circuit. The algorithm allows to classify data into many clusters, and can easily be implemented in few-qubit Noisy Intermediate-Scale Quantum (NISQ) devices.
  arXiv  Detail & Related papers  (2022-06-20T17:02:19Z)
• Quantum State Preparation and Non-Unitary Evolution with Diagonal Operators [0.0]
  We present a dilation based algorithm to simulate non-unitary operations on unitary quantum devices. We use this algorithm to prepare random sub-normalized two-level states on a quantum device with high fidelity. We also present the accurate non-unitary dynamics of two-level open quantum systems in a dephasing channel and an amplitude damping channel computed on a quantum device.
  arXiv  Detail & Related papers  (2022-05-05T17:56:41Z)
• A Hybrid Quantum-Classical Algorithm for Robust Fitting [47.42391857319388]
  We propose a hybrid quantum-classical algorithm for robust fitting. Our core contribution is a novel robust fitting formulation that solves a sequence of integer programs. We present results obtained using an actual quantum computer.
  arXiv  Detail & Related papers  (2022-01-25T05:59:24Z)
• Quantum Error Mitigation Relying on Permutation Filtering [84.66087478797475]
  We propose a general framework termed as permutation filters, which includes the existing permutation-based methods as special cases. We show that the proposed filter design algorithm always converges to the global optimum, and that the optimal filters can provide substantial improvements over the existing permutation-based methods.
  arXiv  Detail & Related papers  (2021-07-03T16:07:30Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.