Related papers: Instance-optimal high-precision shadow tomography …
Classical shadow tomography has emerged as a powerful framework for predicting properties of quantum many-body systems with favorable sample complexity. Standard theoretical guarantees, however, rely on the assumption that experimental…
Classical shadow tomography provides an efficient method for predicting functions of an unknown quantum state from a few measurements of the state. It relies on a unitary channel that efficiently scrambles the quantum information of the…
We introduce a variational scheme inspired by classical shadow tomography to compute ground state correlations of quantum spin Hamiltonians. Shadow tomography allows for efficient reconstruction of expectation values of arbitrary…
Following the first paper on quantum algorithms for SDP-solving by Brand\~ao and Svore in 2016, rapid developments has been made on quantum optimization algorithms. Recently Brand\~ao et al. improved the quantum SDP-solver in the so-called…
We introduce a direct estimation framework for reconstructing multiple density matrix elements of an unknown quantum state using classical shadow tomography. Traditional direct measurement protocols (DMPs), while effective for individual…
We study quantum state testing where the goal is to test whether $\rho=\rho_0\in\mathbb{C}^{d\times d}$ or $\|\rho-\rho_0\|_1>\varepsilon$, given $n$ copies of $\rho$ and a known state description $\rho_0$. In practice, not all measurements…
A scalable Bayesian machine learning framework is introduced for estimating scalar properties of an unknown quantum state from measurement data, which bypasses full density matrix reconstruction. This work is the first to integrate the…
There has been a surge of progress in recent years in developing algorithms for testing and learning quantum states that achieve optimal copy complexity. Unfortunately, they require the use of entangled measurements across many copies of…
Instance shadow detection is a brand new problem, aiming to find shadow instances paired with object instances. To approach it, we first prepare a new dataset called SOBA, named after Shadow-OBject Association, with 3,623 pairs of shadow…
Shadow estimation is a method for deducing numerous properties of an unknown quantum state through a limited set of measurements, which suffers from noises in quantum devices. In this paper, we introduce an error-mitigated shadow estimation…
Classical shadow tomography is a powerful randomized measurement protocol for predicting many properties of a quantum state with few measurements. Two classical shadow protocols have been extensively studied in the literature: the…
We provide optimal lower bounds for two well-known parameter estimation (also known as statistical estimation) tasks in high dimensions with approximate differential privacy. First, we prove that for any $\alpha \le O(1)$, estimating the…
Obtaining precise estimates of quantum observables is a crucial step of variational quantum algorithms. We consider the problem of estimating expectation values of molecular Hamiltonians, obtained on states prepared on a quantum computer.…
Shadow estimation is a recent protocol that allows estimating exponentially many expectation values of a quantum state from ``classical shadows'', obtained by applying random quantum circuits and computational basis measurements. In this…
Informationally overcomplete POVMs are known to outperform minimally complete measurements in many tomography and estimation tasks, and they also leave a purely classical freedom in shadow tomography: the same observable admits infinitely…
Quantum process tomography (QPT) is crucial for advancing quantum technologies, including quantum computers, quantum networks and quantum sensors. Shadow process tomography (SPT) utilizes the Choi isomorphism to map QPT to shadow state…
We present shadow spectroscopy as a simulator-agnostic quantum algorithm for estimating energy gaps using very few circuit repetitions (shots) and no extra resources (ancilla qubits) beyond performing time evolution and measurements. The…
Classical Shadow Tomography (Huang, Kueng and Preskill, Nature Physics 2020) is a method for creating a classical snapshot of an unknown quantum state, which can later be used to predict the value of an a-priori unknown observable on that…
We present a two-step protocol for quantum measurement tomography that is light on classical co-processing cost and still achieves optimal sample complexity in the system dimension. Given measurement data from a known probe state ensemble,…
A common goal in the study of high dimensional and complex system is to model the system by a low order representation. In this letter we propose a general approach for assessing the quality of a reduced order model for high dimensional…