Test of Quantumness with Small-Depth Quantum Circuits

• URL: http://arxiv.org/abs/2105.05500v2
• Date: Tue, 10 Aug 2021 00:11:46 GMT
• Title: Test of Quantumness with Small-Depth Quantum Circuits
• Authors: Shuichi Hirahara and Fran\c{c}ois Le Gall
• Abstract summary: Recently, we have shown how to construct a test of quantumness based on the learning with errors (LWE) assumption. This test has lead to several cryptographic applications. In this paper, we show that this test of quantumness, and essentially all the above applications, can actually be implemented by a very weak class of quantum circuits.
• Score: 1.90365714903665
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recently Brakerski, Christiano, Mahadev, Vazirani and Vidick (FOCS 2018) have shown how to construct a test of quantumness based on the learning with errors (LWE) assumption: a test that can be solved efficiently by a quantum computer but cannot be solved by a classical polynomial-time computer under the LWE assumption. This test has lead to several cryptographic applications. In particular, it has been applied to producing certifiable randomness from a single untrusted quantum device, self-testing a single quantum device and device-independent quantum key distribution. In this paper, we show that this test of quantumness, and essentially all the above applications, can actually be implemented by a very weak class of quantum circuits: constant-depth quantum circuits combined with logarithmic-depth classical computation. This reveals novel complexity-theoretic properties of this fundamental test of quantumness and gives new concrete evidence of the superiority of small-depth quantum circuits over classical computation.

Related papers

• Efficient Quantum Pseudorandomness from Hamiltonian Phase States [41.94295877935867]
  We introduce a quantum hardness assumption called the Hamiltonian Phase State (HPS) problem. We show that our assumption is plausibly fully quantum; meaning, it cannot be used to construct one-way functions. We show that our assumption and its variants allow us to efficiently construct many pseudorandom quantum primitives.
  arXiv  Detail & Related papers  (2024-10-10T16:10:10Z)
• Rapidly Achieving Chemical Accuracy with Quantum Computing Enforced Language Model [22.163742052849432]
  QiankunNet-VQE is a transformer based language models enforced with quantum computing to learn and generate quantum states. It has been implemented using up to 12 qubits and attaining an accuracy level competitive with state-of-the-art classical methods.
  arXiv  Detail & Related papers  (2024-05-15T07:50:57Z)
• Long-lived Particles Anomaly Detection with Parametrized Quantum Circuits [0.0]
  We propose an anomaly detection algorithm based on a parametrized quantum circuit. This algorithm has been trained on a classical computer and tested with simulations as well as on real quantum hardware.
  arXiv  Detail & Related papers  (2023-12-07T11:50:42Z)
• Quantum data learning for quantum simulations in high-energy physics [55.41644538483948]
  We explore the applicability of quantum-data learning to practical problems in high-energy physics. We make use of ansatz based on quantum convolutional neural networks and numerically show that it is capable of recognizing quantum phases of ground states. The observation of non-trivial learning properties demonstrated in these benchmarks will motivate further exploration of the quantum-data learning architecture in high-energy physics.
  arXiv  Detail & Related papers  (2023-06-29T18:00:01Z)
• 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)
• Quantum Machine Learning: from physics to software engineering [58.720142291102135]
  We show how classical machine learning approach can help improve the facilities of quantum computers. We discuss how quantum algorithms and quantum computers may be useful for solving classical machine learning tasks.
  arXiv  Detail & Related papers  (2023-01-04T23:37:45Z)
• Experimental Implementation of an Efficient Test of Quantumness [49.588006756321704]
  A test of quantumness is a protocol where a classical user issues challenges to a quantum device to determine if it exhibits non-classical behavior. Recent attempts to implement such tests on current quantum computers rely on either interactive challenges with efficient verification, or non-interactive challenges with inefficient (exponential time) verification.
  arXiv  Detail & Related papers  (2022-09-28T18:00:04Z)
• Depth-efficient proofs of quantumness [77.34726150561087]
  A proof of quantumness is a type of challenge-response protocol in which a classical verifier can efficiently certify quantum advantage of an untrusted prover. In this paper, we give two proof of quantumness constructions in which the prover need only perform constant-depth quantum circuits.
  arXiv  Detail & Related papers  (2021-07-05T17:45:41Z)
• Towards understanding the power of quantum kernels in the NISQ era [79.8341515283403]
  We show that the advantage of quantum kernels is vanished for large size datasets, few number of measurements, and large system noise. Our work provides theoretical guidance of exploring advanced quantum kernels to attain quantum advantages on NISQ devices.
  arXiv  Detail & Related papers  (2021-03-31T02:41:36Z)
• Quantum supremacy in driven quantum many-body systems [0.0]
  We show that quantum supremacy can be obtained in generic periodically-driven quantum many-body systems. Our proposal opens the way for a large class of quantum platforms to demonstrate and benchmark quantum supremacy.
  arXiv  Detail & Related papers  (2020-02-27T07:20:15Z)
• Forging quantum data: classically defeating an IQP-based quantum test [0.0]
  We describe a classical algorithm that can convince the verifier that the (classical) prover is quantum. We show that the key extraction algorithm is efficient in practice for problem sizes of hundreds of qubits.
  arXiv  Detail & Related papers  (2019-12-11T19:00:00Z)

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.