Non-Unitary Quantum Machine Learning

• URL: http://arxiv.org/abs/2405.17388v2
• Date: Wed, 20 Nov 2024 06:34:06 GMT
• Title: Non-Unitary Quantum Machine Learning
• Authors: Jamie Heredge, Maxwell West, Lloyd Hollenberg, Martin Sevior,
• Abstract summary: We introduce several probabilistic quantum algorithms that overcome the normal unitary restrictions in quantum machine learning. We show that residual connections between layers of a variational ansatz can prevent barren plateaus in models which would otherwise contain them. We also demonstrate a novel rotationally invariant encoding for point cloud data via Schur-Weyl duality.
• Score: 0.0
• License:
• Abstract: We introduce several probabilistic quantum algorithms that overcome the normal unitary restrictions in quantum machine learning by leveraging the Linear Combination of Unitaries (LCU) method. Among our investigations are quantum native implementations of Residual Networks (ResNet), where we show that residual connections between layers of a variational ansatz can prevent barren plateaus in models which would otherwise contain them. Secondly, we implement a quantum analogue of average pooling layers from convolutional networks using single qubit controlled basic arithmetic operators and show that the LCU success probability remains stable for the MNIST database. This method can be further generalised to convolutional filters, while using exponentially fewer controlled unitaries than previous approaches. Finally, we propose a general framework for applying a linear combination of irreducible subspace projections on quantum encoded data. This enables a quantum state to remain within an exponentially large space, while selectively amplifying specific subspaces relative to others, alleviating simulability concerns that arise when fully projecting to a polynomially sized subspace. We demonstrate improved classification performance for partially amplified permutation invariant encoded point cloud data when compared to non-invariant or fully permutation invariant encodings. We also demonstrate a novel rotationally invariant encoding for point cloud data via Schur-Weyl duality. These quantum computing frameworks are all constructed using the LCU method, suggesting that further novel quantum machine learning algorithms could be created by utilising the LCU technique.

Related papers

• 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)
• 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.