A Cryptographic Perspective on the Verifiability of Quantum Advantage

• URL: http://arxiv.org/abs/2310.14464v1
• Date: Mon, 23 Oct 2023 00:31:51 GMT
• Title: A Cryptographic Perspective on the Verifiability of Quantum Advantage
• Authors: Nai-Hui Chia, Honghao Fu, Fang Song and Penghui Yao
• Abstract summary: This paper investigates the verification of quantum advantage from a cryptographic perspective. We establish a strong connection between the verifiability of quantum advantage and cryptographic and complexity primitives. Our work shows that the quest for verifiable quantum advantages may lead to applications of quantum cryptography.
• Score: 5.857929080874288
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In recent years, achieving verifiable quantum advantage on a NISQ device has emerged as an important open problem in quantum information. The sampling-based quantum advantages are not known to have efficient verification methods. This paper investigates the verification of quantum advantage from a cryptographic perspective. We establish a strong connection between the verifiability of quantum advantage and cryptographic and complexity primitives, including efficiently samplable, statistically far but computationally indistinguishable pairs of (mixed) quantum states ($\mathsf{EFI}$), pseudorandom states ($\mathsf{PRS}$), and variants of minimum circuit size problems ($\mathsf{MCSP}$). Specifically, we prove that a) a sampling-based quantum advantage is either verifiable or can be used to build $\mathsf{EFI}$ and even $\mathsf{PRS}$ and b) polynomial-time algorithms for a variant of $\mathsf{MCSP}$ would imply efficient verification of quantum advantages. Our work shows that the quest for verifiable quantum advantages may lead to applications of quantum cryptography, and the construction of quantum primitives can provide new insights into the verifiability of quantum advantages.

Related papers

• Quantum Indistinguishable Obfuscation via Quantum Circuit Equivalence [6.769315201275599]
  Quantum computing solutions are increasingly deployed in commercial environments through delegated computing. One of the most critical issues is to guarantee the confidentiality and proprietary of quantum implementations. Since the proposal of general-purpose indistinguishability obfuscation (iO) and functional encryption schemes, iO has emerged as a seemingly versatile cryptography primitive.
  arXiv  Detail & Related papers  (2024-11-19T07:37:24Z)
• 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)
• 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)
• QuanGCN: Noise-Adaptive Training for Robust Quantum Graph Convolutional Networks [124.7972093110732]
  We propose quantum graph convolutional networks (QuanGCN), which learns the local message passing among nodes with the sequence of crossing-gate quantum operations. To mitigate the inherent noises from modern quantum devices, we apply sparse constraint to sparsify the nodes' connections. Our QuanGCN is functionally comparable or even superior than the classical algorithms on several benchmark graph datasets.
  arXiv  Detail & Related papers  (2022-11-09T21:43:16Z)
• Unclonability and Quantum Cryptanalysis: From Foundations to Applications [0.0]
  Unclonability is a fundamental concept in quantum theory and one of the main non-classical properties of quantum information. We introduce new notions of unclonability in the quantum world, namely quantum physical unclonability. We discuss several applications of this new type of unclonability as a cryptographic resource for designing provably secure quantum protocols.
  arXiv  Detail & Related papers  (2022-10-31T17:57:09Z)
• Optimal Stochastic Resource Allocation for Distributed Quantum Computing [50.809738453571015]
  We propose a resource allocation scheme for distributed quantum computing (DQC) based on programming to minimize the total deployment cost for quantum resources. The evaluation demonstrates the effectiveness and ability of the proposed scheme to balance the utilization of quantum computers and on-demand quantum computers.
  arXiv  Detail & Related papers  (2022-09-16T02:37:32Z)
• Is quantum computing green? An estimate for an energy-efficiency quantum advantage [0.0]
  We show that the green quantum advantage threshold depends on (i) the quality of the experimental quantum gates and (ii) the entanglement generated in the QPU. We compute the green quantum advantage threshold for a few paradigmatic examples in terms of algorithms and hardware platforms.
  arXiv  Detail & Related papers  (2022-05-24T14:14:00Z)
• Revisiting dequantization and quantum advantage in learning tasks [3.265773263570237]
  We show that classical algorithms with sample and query (SQ) access can accomplish some learning tasks exponentially faster than quantum algorithms with quantum state inputs. Our findings suggest that the absence of exponential quantum advantage in some learning tasks may be due to SQ access being too powerful relative to quantum state inputs.
  arXiv  Detail & Related papers  (2021-12-01T20:05:56Z)
• 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)
• 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)
• 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)

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.