Limitations of measure-first protocols in quantum machine learning

• URL: http://arxiv.org/abs/2311.12618v1
• Date: Tue, 21 Nov 2023 14:03:29 GMT
• Title: Limitations of measure-first protocols in quantum machine learning
• Authors: Casper Gyurik, Riccardo Molteni, Vedran Dunjko
• Abstract summary: We study a natural supervised learning setting where quantum states constitute data points, and the labels stem from an unknown measurement. We show that there exist problems that can be efficiently learned by fully-quantum protocols but which require exponential resources for measure-first protocols. Our result underscores the role of quantum data processing in machine learning and highlights scenarios where quantum advantages appear.
• Score: 2.209921757303168
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In recent works, much progress has been made with regards to so-called randomized measurement strategies, which include the famous methods of classical shadows and shadow tomography. In such strategies, unknown quantum states are first measured (or ``learned''), to obtain classical data that can be used to later infer (or ``predict'') some desired properties of the quantum states. Even if the used measurement procedure is fixed, surprisingly, estimations of an exponential number of vastly different quantities can be obtained from a polynomial amount of measurement data. This raises the question of just how powerful ``measure-first'' strategies are, and in particular, if all quantum machine learning problems can be solved with a measure-first, analyze-later scheme. This paper explores the potential and limitations of these measure-first protocols in learning from quantum data. We study a natural supervised learning setting where quantum states constitute data points, and the labels stem from an unknown measurement. We examine two types of machine learning protocols: ``measure-first'' protocols, where all the quantum data is first measured using a fixed measurement strategy, and ``fully-quantum'' protocols where the measurements are adapted during the training process. Our main result is a proof of separation. We prove that there exist learning problems that can be efficiently learned by fully-quantum protocols but which require exponential resources for measure-first protocols. Moreover, we show that this separation persists even for quantum data that can be prepared by a polynomial-time quantum process, such as a polynomially-sized quantum circuit. Our proofs combine methods from one-way communication complexity and pseudorandom quantum states. Our result underscores the role of quantum data processing in machine learning and highlights scenarios where quantum advantages appear.

Related papers

• Entanglement measurement based on convex hull properties [0.0]
  We will propose a scheme for measuring quantum entanglement, which starts with treating the set of quantum separable states as a convex hull of quantum separable pure states. Although a large amount of data is required in the measurement process, this method is not only applicable to 2-qubit quantum states, but also a entanglement measurement method that can be applied to any dimension and any fragment.
  arXiv  Detail & Related papers  (2024-11-08T08:03:35Z)
• The curse of random quantum data [62.24825255497622]
  We quantify the performances of quantum machine learning in the landscape of quantum data. We find that the training efficiency and generalization capabilities in quantum machine learning will be exponentially suppressed with the increase in qubits. Our findings apply to both the quantum kernel method and the large-width limit of quantum neural networks.
  arXiv  Detail & Related papers  (2024-08-19T12:18:07Z)
• Separable Power of Classical and Quantum Learning Protocols Through the Lens of No-Free-Lunch Theorem [70.42372213666553]
  The No-Free-Lunch (NFL) theorem quantifies problem- and data-independent generalization errors regardless of the optimization process. We categorize a diverse array of quantum learning algorithms into three learning protocols designed for learning quantum dynamics under a specified observable. Our derived NFL theorems demonstrate quadratic reductions in sample complexity across CLC-LPs, ReQu-LPs, and Qu-LPs. We attribute this performance discrepancy to the unique capacity of quantum-related learning protocols to indirectly utilize information concerning the global phases of non-orthogonal quantum states.
  arXiv  Detail & Related papers  (2024-05-12T09:05:13Z)
• Measurement-induced entanglement and teleportation on a noisy quantum processor [105.44548669906976]
  We investigate measurement-induced quantum information phases on up to 70 superconducting qubits. We use a duality mapping, to avoid mid-circuit measurement and access different manifestations of the underlying phases. Our work demonstrates an approach to realize measurement-induced physics at scales that are at the limits of current NISQ processors.
  arXiv  Detail & Related papers  (2023-03-08T18:41:53Z)
• Simple Tests of Quantumness Also Certify Qubits [69.96668065491183]
  A test of quantumness is a protocol that allows a classical verifier to certify (only) that a prover is not classical. We show that tests of quantumness that follow a certain template, which captures recent proposals such as (Kalai et al., 2022) can in fact do much more. Namely, the same protocols can be used for certifying a qubit, a building-block that stands at the heart of applications such as certifiable randomness and classical delegation of quantum computation.
  arXiv  Detail & Related papers  (2023-03-02T14:18:17Z)
• Anticipative measurements in hybrid quantum-classical computation [68.8204255655161]
  We present an approach where the quantum computation is supplemented by a classical result. Taking advantage of its anticipation also leads to a new type of quantum measurements, which we call anticipative. In an anticipative quantum measurement the combination of the results from classical and quantum computations happens only in the end.
  arXiv  Detail & Related papers  (2022-09-12T15:47:44Z)
• Certification of quantum states with hidden structure of their bitstrings [0.0]
  We propose a numerically cheap procedure to describe and distinguish quantum states. We show that it is enough to characterize quantum states with different structure of entanglement. Our approach can be employed to detect phase transitions of different nature in many-body quantum magnetic systems.
  arXiv  Detail & Related papers  (2021-07-21T06:22:35Z)
• On exploring the potential of quantum auto-encoder for learning quantum systems [60.909817434753315]
  We devise three effective QAE-based learning protocols to address three classically computational hard learning problems. Our work sheds new light on developing advanced quantum learning algorithms to accomplish hard quantum physics and quantum information processing tasks.
  arXiv  Detail & Related papers  (2021-06-29T14:01:40Z)
• Pure State Tomography with Fourier Transformation [3.469001874498102]
  Two adaptive protocols are proposed, with their respective quantum circuits. Experiments on the IBM 5-qubit quantum computer, as well as numerical investigations, demonstrate the feasibility of the proposed protocols.
  arXiv  Detail & Related papers  (2020-08-20T17:13:09Z)
• Experimental characterisation of unsharp qubit observables and sequential measurement incompatibility via quantum random access codes [0.0]
  We report an experimental implementation of unsharp qubit measurements in a sequential communication protocol. The protocol involves three parties; the first party prepares a qubit system, the second party performs operations which return a classical and quantum outcome, and the latter is measured by the third party.
  arXiv  Detail & Related papers  (2020-01-14T13:37:04Z)
• 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.