Related papers: Lower Bounds for Learning Quantum States with Sing…
Quantum state tomography is the fundamental physical task of learning a complete classical description of an unknown state of a quantum system given coherent access to many identical samples of it. The complexity of this task is commonly…
We show that $\Omega(rd/\epsilon)$ copies of an unknown rank-$r$, dimension-$d$ quantum mixed state are necessary in order to learn a classical description with $1 - \epsilon$ fidelity. This improves upon the tomography lower bounds…
In this work, we show that the sample complexity required in quantum learning theory within a general parametric framework, is fundamentally governed by the inverse Fisher information matrix. More specifically, we derive upper and lower…
Given $n$ copies of an unknown quantum state $\rho\in\mathbb{C}^{d\times d}$, quantum state certification is the task of determining whether $\rho=\rho_0$ or $\|\rho-\rho_0\|_1>\varepsilon$, where $\rho_0$ is a known reference state. We…
Characterising large-scale quantum systems is central to fundamental physics and essential for applications of quantum technologies. While a full characterisation requires exponentially increasing resources, focusing on application-relevant…
Quantum-enhanced metrology aims to estimate an unknown parameter such that the precision scales better than the shot-noise bound. Single-shot adaptive quantum-enhanced metrology (AQEM) is a promising approach that uses feedback to tweak the…
Quantum state tomography is the problem of estimating a given quantum state. Usually, it is required to run the quantum experiment - state preparation, state evolution, measurement - several times to be able to estimate the output quantum…
Learning quantum state properties is both a fundamental and practical problem in quantum information theory. Classical shadows have emerged as an efficient method for estimating properties of unknown quantum states, with rigorous…
In this letter we revisit the problem of optimal design of quantum tomographic experiments. In contrast to previous approaches where an optimal set of measurements is decided in advance of the experiment, we allow for measurements to be…
We experimentally implement a machine-learning method for accurately identifying unknown pure quantum states. The method, called single-shot measurement learning, achieves the theoretical optimal accuracy for $\epsilon = O(N^{-1})$ in state…
Bell sampling is a simple yet powerful measurement primitive that has recently attracted a lot of attention, and has proven to be a valuable tool in studying stabiliser states. Unfortunately, however, it is known that Bell sampling fails…
We revisit the basic problem of quantum state certification: given copies of unknown mixed state $\rho\in\mathbb{C}^{d\times d}$ and the description of a mixed state $\sigma$, decide whether $\sigma = \rho$ or $\|\sigma -…
Advances in quantum technology require scalable techniques to efficiently extract information from a quantum system, such as expectation values of observables or its entropy. Traditional tomography is limited to a handful of qubits and…
The complete learning of an $n$-qubit quantum state requires samples exponentially in $n$. Several works consider subclasses of quantum states that can be learned in polynomial sample complexity such as stabilizer states or high-temperature…
The polynomial method by Beals, Buhrman, Cleve, Mosca, and de Wolf (FOCS 1998, J. ACM 2001), the adversary method by Ambainis (STOC 2000, J. Comput. Syst. Sci. 2002), and the compressed oracle method by Zhandry (CRYPTO 2019) have been shown…
Quantum learning encounters fundamental challenges when estimating non-linear properties, owing to the inherent linearity of quantum mechanics. Although recent advances in single-copy randomized measurement protocols have achieved optimal…
The problem of measuring a time-varying phase, even when the statistics of the variation is known, is considerably harder than that of measuring a constant phase. In particular, the usual bounds on accuracy - such as the $1/(4\bar{n})$…
We study the complexity of smoothed agnostic learning, recently introduced by~\cite{CKKMS24}, in which the learner competes with the best classifier in a target class under slight Gaussian perturbations of the inputs. Specifically, we focus…
Many prominent quantum computing algorithms with applications in fields such as chemistry and materials science require a large number of measurements, which represents an important roadblock for future real-world use cases. We introduce a…
We propose a learning method for estimating unknown pure quantum states. The basic idea of our method is to learn a unitary operation $\hat{U}$ that transforms a given unknown state $|\psi_\tau\rangle$ to a known fiducial state $|f\rangle$.…