Related papers: Learning Distributions over Quantum Measurement Ou…
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…
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…
The problem of efficient quantum state learning, also called shadow tomography, aims to comprehend an unknown $d$-dimensional quantum state through POVMs. Yet, these states are rarely static; they evolve due to factors such as measurements,…
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…
Full quantum tomography of high-dimensional quantum systems is experimentally infeasible due to the exponential scaling of the number of required measurements on the number of qubits in the system. However, several ideas were proposed…
Predicting properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few…
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…
The ability of quantum computers to directly manipulate and analyze quantum states stored in quantum memory allows them to learn about aspects of our physical world that would otherwise be invisible given a modest number of measurements.…
Among recent insights into learning quantum states, online learning and shadow tomography procedures are notable for their ability to accurately predict expectation values even of adaptively chosen observables. In contrast to the state…
In this work, we initiate the study of learning quantum processes from quantum statistical queries. We focus on two fundamental learning tasks in this new access model: shadow tomography of quantum processes and process tomography with…
We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process…
Recent results have established dramatic advantages in learning properties of quantum states when a quantum computer is available to process or jointly measure multiple copies of the unknown quantum state. Learning tasks can be accomplished…
Quantum shadow tomography based on the classical shadow representation provides an efficient way to estimate properties of an unknown quantum state without performing a full quantum state tomography. In scenarios where estimating the…
Learning an unknown $n$-qubit quantum state $\rho$ is a fundamental challenge in quantum computing. Information-theoretically, it is known that tomography requires exponential in $n$ many copies of $\rho$ to estimate it up to trace…
Recently introduced shadow tomography protocols use classical shadows of quantum states to predict many target functions of an unknown quantum state. Unlike full quantum state tomography, shadow tomography does not insist on accurate…
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…
We develop a framework for learning properties of quantum states beyond the assumption of independent and identically distributed (i.i.d.) input states. We prove that, given any learning problem (under reasonable assumptions), an algorithm…
Quantum process tomography is a critical capability for building quantum computers, enabling quantum networks, and understanding quantum sensors. Like quantum state tomography, the process tomography of an arbitrary quantum channel requires…
Quantum state tomography is a fundamental task in quantum information science, enabling detailed characterization of correlations, entanglement, and electronic structure in quantum systems. However, its exponential measurement and…
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…