Related papers: Instance-optimal high-precision shadow tomography …
We give the first tight sample complexity bounds for shadow tomography and classical shadows in the regime where the target error is below some sufficiently small inverse polynomial in the dimension of the Hilbert space. Formally we give a…
We study the problems of quantum tomography and shadow tomography using measurements performed on individual, identical copies of an unknown $d$-dimensional state. We first revisit a known lower bound due to Haah et al. (2017) on quantum…
We study single-copy shadow tomography in the adversarial robust setting, where the goal is to learn the expectation values of $M$ observables $O_1, \ldots, O_M$ with $\varepsilon$ accuracy, but $\gamma$-fraction of the outcomes can be…
We consider the classical shadows task for pure states in the setting of both joint and independent measurements. The task is to measure few copies of an unknown pure state $\rho$ in order to learn a classical description which suffices to…
Shadow tomography is a framework for constructing succinct descriptions of quantum states using randomized measurement bases, called classical shadows, with powerful methods to bound the estimators used. We recast existing experimental…
We revisit the problem of Pauli shadow tomography: given copies of an unknown $n$-qubit quantum state $\rho$, estimate $\text{tr}(P\rho)$ for some set of Pauli operators $P$ to within additive error $\epsilon$. This has been a popular…
Quantum state tomography is a fundamental problem in quantum computing. Given $n$ copies of an unknown $N$-qubit state $\rho \in \mathbb{C}^{d \times d},d=2^N$, the goal is to learn the state up to an accuracy $\epsilon$ in trace distance,…
We introduce the problem of *shadow tomography*: given an unknown $D$-dimensional quantum mixed state $\rho$, as well as known two-outcome measurements $E_{1},\ldots,E_{M}$, estimate the probability that $E_{i}$ accepts $\rho$, to within…
Quantum state tomography (QST) is one of the fundamental problems in quantum information. Among various metrics, sample complexity is widely used to evaluate QST algorithms. While multi-copy measurements are known to achieve optimal sample…
We describe a new shadow tomography algorithm that uses $n=\Theta(\sqrt{m}\log m/\epsilon^2)$ samples, for $m$ measurements and additive error $\epsilon$, which is independent of the dimension of the quantum state being learned. This stands…
We provide more sample-efficient versions of some basic routines in quantum data analysis, along with simpler proofs. Particularly, we give a quantum "Threshold Search" algorithm that requires only $O((\log^2 m)/\epsilon^2)$ samples of a…
We study the sample complexity of the classical shadows task: what is the fewest number of copies of an unknown state you need to measure to predict expected values with respect to some class of observables? Large joint measurements are…
Shadow tomography for quantum states provides a sample efficient approach for predicting the properties of quantum systems when the properties are restricted to expectation values of $2$-outcome POVMs. However, these shadow tomography…
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…
In quantum information theory, the accurate estimation of observables is pivotal for quantum information processing, playing a crucial role in compute and communication protocols. This work introduces a novel technique for estimating such…
Shadow tomography protocols have recently emerged as powerful tools for efficient quantum state learning, aiming to reconstruct expectation values of observables with fewer resources than traditional quantum state tomography. For the…
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…
This paper studies quantum supervised learning for classical inference from quantum states. In this model, a learner has access to a set of labeled quantum samples as the training set. The objective is to find a quantum measurement that…
The classical shadows protocol is an efficient strategy for estimating properties of an unknown state $\rho$ using a small number of state copies and measurements. In its original form, it involves twirling the state with unitaries from…
Shadow estimation is an efficient method for predicting many observables of a quantum state with a statistical guarantee. In the multi-shot scenario, one performs projective measurement on the sequentially prepared state for $K$ times after…