Trainability and Expressivity of Hamming-Weight Preserving Quantum Circuits for Machine Learning

• URL: http://arxiv.org/abs/2309.15547v2
• Date: Thu, 26 Sep 2024 21:14:42 GMT
• Title: Trainability and Expressivity of Hamming-Weight Preserving Quantum Circuits for Machine Learning
• Authors: Léo Monbroussou, Eliott Z. Mamon, Jonas Landman, Alex B. Grilo, Romain Kukla, Elham Kashefi,
• Abstract summary: We analyze the trainability and controllability of variational quantum circuits (VQCs) We first design and prove the feasibility of new data loaders, performing quantum amplitude encoding of $binomnk$-dimensional vectors. Lastly, we analyze the trainability of Hamming weight preserving circuits, and show that the variance of the $binomnk$ of the subspace is bounded according to the $binomnk$ of the subspace.
• Score: 2.2301710048942103
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum machine learning (QML) has become a promising area for real world applications of quantum computers, but near-term methods and their scalability are still important research topics. In this context, we analyze the trainability and controllability of specific Hamming weight preserving variational quantum circuits (VQCs). These circuits use qubit gates that preserve subspaces of the Hilbert space, spanned by basis states with fixed Hamming weight $k$. In this work, we first design and prove the feasibility of new heuristic data loaders, performing quantum amplitude encoding of $\binom{n}{k}$-dimensional vectors by training an $n$-qubit quantum circuit. These data loaders are obtained using dimensionality reduction techniques, by checking the Quantum Fisher Information Matrix (QFIM)'s rank. Second, we provide a theoretical justification for the fact that the rank of the QFIM of any VQC state is almost-everywhere constant, which is of separate interest. Lastly, we analyze the trainability of Hamming weight preserving circuits, and show that the variance of the $l_2$ cost function gradient is bounded according to the dimension $\binom{n}{k}$ of the subspace. This proves conditions of existence/lack of Barren Plateaus for these circuits, and highlights a setting where a recent conjecture on the link between controllability and trainability of variational quantum circuits does not apply.

Related papers

• Quantum Homogenization as a Quantum Steady State Protocol on NISQ Hardware [42.52549987351643]
  Quantum homogenization is a reservoir-based quantum state approximation protocol. We extend the standard quantum homogenization protocol to the dynamically-equivalent ($mathttSWAP$)$alpha$ formulation. We show that our proposed protocol yields a completely positive, trace preserving (CPTP) map under which the code subspace is correctable.
  arXiv  Detail & Related papers  (2024-12-19T05:50:54Z)
• Quantum Wasserstein Compilation: Unitary Compilation using the Quantum Earth Mover's Distance [2.502222151305252]
  We present a quantum Wasserstein compilation (QWC) cost function based on the quantum Wasserstein distance of order 1. An estimation method based on measurements of local Pauli-observable is utilized in a generative adversarial network to learn a given quantum circuit.
  arXiv  Detail & Related papers  (2024-09-09T17:46:40Z)
• Solving an Industrially Relevant Quantum Chemistry Problem on Quantum Hardware [31.15746974078601]
  We calculate the lowest energy eigenvalue of active space Hamiltonians of industrially relevant and strongly correlated metal chelates on trapped ion quantum hardware. We are able to achieve chemical accuracy by training a variational quantum algorithm on quantum hardware, followed by a classical diagonalization in the subspace of states measured as outputs of the quantum circuit.
  arXiv  Detail & Related papers  (2024-08-20T12:50:15Z)
• Parallel Quantum Computing Simulations via Quantum Accelerator Platform Virtualization [44.99833362998488]
  We present a model for parallelizing simulation of quantum circuit executions. The model can take advantage of its backend-agnostic features, enabling parallel quantum circuit execution over any target backend.
  arXiv  Detail & Related papers  (2024-06-05T17:16:07Z)
• Quantum encoder for fixed Hamming-weight subspaces [0.0]
  We present an exact $n$-qubit computational-basis amplitude encoder of real- or complex data vectors of $d=binomnk$valued into a subspace of fixed Hamming weight $k$. We show how our encoder can improve the performance of variational quantum algorithms for problems that include particle-string symmetries. Our results constitute a versatile framework for quantum data compression with various potential applications in fields such as quantum chemistry, quantum machine learning, and constrained $k$ optimizations.
  arXiv  Detail & Related papers  (2024-05-30T18:26:41Z)
• Hybrid Quantum-Classical Scheduling for Accelerating Neural Network Training with Newton's Gradient Descent [37.59299233291882]
  We propose Q-Newton, a hybrid quantum-classical scheduler for accelerating neural network training with Newton's GD. Q-Newton utilizes a streamlined scheduling module that coordinates between quantum and classical linear solvers. Our evaluation showcases the potential for Q-Newton to significantly reduce the total training time compared to commonly used quantum machines.
  arXiv  Detail & Related papers  (2024-04-30T23:55:03Z)
• The Power of Unentangled Quantum Proofs with Non-negative Amplitudes [55.90795112399611]
  We study the power of unentangled quantum proofs with non-negative amplitudes, a class which we denote $textQMA+(2)$. In particular, we design global protocols for small set expansion, unique games, and PCP verification. We show that QMA(2) is equal to $textQMA+(2)$ provided the gap of the latter is a sufficiently large constant.
  arXiv  Detail & Related papers  (2024-02-29T01:35:46Z)
• QuantumSEA: In-Time Sparse Exploration for Noise Adaptive Quantum Circuits [82.50620782471485]
  QuantumSEA is an in-time sparse exploration for noise-adaptive quantum circuits. It aims to achieve two key objectives: (1) implicit circuits capacity during training and (2) noise robustness. Our method establishes state-of-the-art results with only half the number of quantum gates and 2x time saving of circuit executions.
  arXiv  Detail & Related papers  (2024-01-10T22:33:00Z)
• Variational-quantum-eigensolver-inspired optimization for spin-chain work extraction [39.58317527488534]
  Energy extraction from quantum sources is a key task to develop new quantum devices such as quantum batteries. One of the main issues to fully extract energy from the quantum source is the assumption that any unitary operation can be done on the system. We propose an approach to optimize the extractable energy inspired by the variational quantum eigensolver (VQE) algorithm.
  arXiv  Detail & Related papers  (2023-10-11T15:59:54Z)
• Classical variational optimization of PREPARE circuit for quantum phase estimation of quantum chemistry Hamiltonians [0.8009842832476994]
  We propose a method for constructing $textttPREPARE$ circuits for quantum phase estimation of a molecular Hamiltonian in quantum chemistry. The $textttPREPARE$ circuit generates a quantum state which encodes the coefficients of the terms in the Hamiltonian as probability amplitudes.
  arXiv  Detail & Related papers  (2023-08-26T05:32:38Z)
• Training Quantum Boltzmann Machines with the $β$-Variational Quantum Eigensolver [0.3670008893193884]
  The quantum Boltzmann machine (QBM) is a generative machine learning model for both classical data and quantum states. We show that low-rank representations obtained by $beta$-VQE provide an efficient way to learn low-rank target states. We implement a trained model on a physical quantum device.
  arXiv  Detail & Related papers  (2023-04-17T21:56:52Z)
• An Introduction to Quantum Machine Learning for Engineers [36.18344598412261]
  Quantum machine learning is emerging as a dominant paradigm to program gate-based quantum computers. This book provides a self-contained introduction to quantum machine learning for an audience of engineers with a background in probability and linear algebra.
  arXiv  Detail & Related papers  (2022-05-11T12:10:52Z)
• Configurable sublinear circuits for quantum state preparation [1.9279780052245203]
  We show a configuration that encodes an $N$-dimensional state by a quantum circuit with $O(sqrtN)$ width and depth and entangled information in ancillary qubits. We show a proof-of-principle on five quantum computers and compare the results.
  arXiv  Detail & Related papers  (2021-08-23T13:52:43Z)
• Trainable Discrete Feature Embeddings for Variational Quantum Classifier [4.40450723619303]
  We show how to map discrete features with fewer quantum bits using Quantum Random Access Coding (QRAC) We propose a new method to embed discrete features with trainable quantum circuits by combining QRAC and a recently proposed strategy for training quantum feature map called quantum metric learning.
  arXiv  Detail & Related papers  (2021-06-17T12:02:01Z)
• QUANTIFY: A framework for resource analysis and design verification of quantum circuits [69.43216268165402]
  QUANTIFY is an open-source framework for the quantitative analysis of quantum circuits. It is based on Google Cirq and is developed with Clifford+T circuits in mind. For benchmarking purposes QUANTIFY includes quantum memory and quantum arithmetic circuits.
  arXiv  Detail & Related papers  (2020-07-21T15:36:25Z)
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms [87.04438831673063]
  We present an efficient read-out protocol that yields the classical vector form of the generated state. Our protocol suits the case that the output state lies in the row space of the input matrix. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
  arXiv  Detail & Related papers  (2020-04-14T11:05:26Z)
• Quantum embeddings for machine learning [5.16230883032882]
  Quantum classifiers are trainable quantum circuits used as machine learning models. We propose to train the first part of the circuit -- the embedding -- with the objective of maximally separating data classes in Hilbert space. This approach provides a powerful analytic framework for quantum machine learning.
  arXiv  Detail & Related papers  (2020-01-10T19:00:01Z)

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.