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A constant number of random Clifford measurements allows the classical shadow protocol to perform direct fidelity estimation (DFE) with high precision. However, estimating properties of an unknown quantum state is expected to be more…

Quantum Physics · Physics 2025-09-17 Hyunho Cha , Jungwoo Lee

We present the first protocol allowing a classical computer to interactively verify the result of an efficient quantum computation. We achieve this by constructing a measurement protocol, which enables a classical verifier to use a quantum…

Quantum Physics · Physics 2023-12-11 Urmila Mahadev

Cryptography with quantum states exhibits a number of surprising and counterintuitive features. In a 2002 work, Barnum et al. argue that these features imply that digital signatures for quantum states are impossible (Barnum et al., FOCS…

Quantum Physics · Physics 2021-12-22 Gorjan Alagic , Tommaso Gagliardoni , Christian Majenz

Classification of quantum data is essential for quantum machine learning and near-term quantum technologies. In this paper, we propose a new hybrid quantum-classical framework for supervised quantum learning, which we call Variational…

Quantum Physics · Physics 2020-12-16 Guangxi Li , Zhixin Song , Xin Wang

We study classical simulation of quantum computation, taking the Gottesman-Knill theorem as a starting point. We show how each Clifford circuit can be reduced to an equivalent, manifestly simulatable circuit (normal form). This provides a…

Quantum Physics · Physics 2012-02-20 M. Van den Nest

Every quantum physical system can be considered the ''shadow'' of a special kind of classical system. The system proposed here is classical mainly because each observable function has a well precise value on each state of the system: an…

Quantum Physics · Physics 2007-05-23 Antonio Cassa

We study sequential quantum changepoint detection in settings where the pre- and post-change regimes are specified through constraints on the expectation values of a finite set of observables. We consider an architecture with separate…

Quantum Physics · Physics 2026-02-13 Matteo Zecchin , Osvaldo Simeone , Aaditya Ramdas

Extracting information efficiently from quantum systems is a major component of quantum information processing tasks. Randomized measurements, or classical shadows, enable predicting many properties of arbitrary quantum states using few…

Given copies of a quantum state $\rho$, a shadow tomography protocol aims to learn all expectation values from a fixed set of observables, to within a given precision $\epsilon$. We say that a shadow tomography protocol is triply efficient…

Quantum Physics · Physics 2025-03-28 Robbie King , David Gosset , Robin Kothari , Ryan Babbush

In this paper, we extend the protocol of classical verification of quantum computations (CVQC) recently proposed by Mahadev to make the verification efficient. Our result is obtained in the following three steps: $\bullet$ We show that…

Quantum Physics · Physics 2020-03-16 Nai-Hui Chia , Kai-Min Chung , Takashi Yamakawa

Recently, Google announced the first demonstration of quantum computational supremacy with a programmable superconducting processor. Their demonstration is based on collecting samples from the output distribution of a noisy random quantum…

Quantum Physics · Physics 2020-02-07 Scott Aaronson , Sam Gunn

We give a simple proof that it is impossible to guarantee the classicality of inputs into any mistrustful quantum cryptographic protocol. The argument illuminates the impossibility of unconditionally secure quantum implementations of…

Quantum Physics · Physics 2012-04-17 Adrian Kent

Shadow tomography via classical shadows is a state-of-the-art approach for estimating properties of a quantum state. We present a simplified, combinatorial analysis of a recently proposed instantiation of this approach based on the ensemble…

Quantum Physics · Physics 2022-08-01 Bryan O'Gorman

Efficient fidelity estimation of multiqubit quantum states is crucial to many applications in quantum information processing. However, to estimate the infidelity $\epsilon$ with multiplicative precision, conventional estimation protocols…

Quantum Physics · Physics 2025-12-01 Zhongyi Yang , Datong Chen , Zihao Li , Huangjun Zhu

We provide practical and powerful schemes for learning many properties of an unknown n-qubit quantum state using a sparing number of copies of the state. Specifically, we present a depth-modulated randomized measurement scheme that…

Classical shadows are a powerful method for learning many properties of quantum states in a sample-efficient manner, by making use of randomized measurements. Here we study the sample complexity of learning the expectation value of Pauli…

Quantum Physics · Physics 2023-06-13 Matteo Ippoliti , Yaodong Li , Tibor Rakovszky , Vedika Khemani

Quantum computers are believed to bring computational advantages in simulating quantum many body systems. However, recent works have shown that classical machine learning algorithms are able to predict numerous properties of quantum systems…

Quantum Physics · Physics 2024-12-23 Riccardo Molteni , Casper Gyurik , Vedran Dunjko

The classical knot recognition problem is the problem of determining whether the virtual knot represented by a given diagram is classical. We prove that this problem is in NP, and we give an exponential time algorithm for the problem.

Geometric Topology · Mathematics 2022-06-08 Kazuhiro Ichihara , Yuya Nishimura , Seiichi Tani

Measuring properties of quantum systems is a fundamental problem in quantum mechanics. We provide a simple method for estimating the expectation value of observables with an unknown quantum state. The idea is to use a data structure to…

Quantum Physics · Physics 2024-03-25 Naixu Guo , Feng Pan , Patrick Rebentrost

Random classical linear codes are widely believed to be hard to decode. While slightly sub-exponential time algorithms exist when the coding rate vanishes sufficiently rapidly, all known algorithms at constant rate require exponential time.…