Related papers: Optimising shadow tomography with generalised meas…
We study the sample complexity of shadow tomography in the high-precision regime under realistic measurement constraints. Given an unknown $d$-dimensional quantum state $\rho$ and a known set of observables $\{O_i\}_{i=1}^m$, the goal is to…
Classical shadows are an efficient method for constructing an approximate classical description of a quantum state using very few measurements. In the paper we propose to enhance classical shadow methods using bootstrap resampling methods.…
A prime goal of quantum tomography is to provide quantitatively rigorous characterisation of quantum systems, be they states, processes or measurements, particularly for the purposes of trouble-shooting and benchmarking experiments in…
Quantum measurements are not deterministic. For this reason quantum measurements are repeated for a number of shots on identically prepared systems. The uncertainty in each measurement depends on the number of shots and the expected outcome…
Measurements are a vital part of any quantum computation, whether as a final step to retrieve results, as an intermediate step to inform subsequent operations, or as part of the computation itself (as in measurement-based quantum…
Smoothing is an estimation technique that takes into account both past and future observations, and can be more accurate than filtering alone. In this Letter, a quantum theory of smoothing is constructed using a time-symmetric formalism,…
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 optimal state determination (or tomography) is studied for a composite system of two qubits when measurements can be performed on one of the qubits and interactions of the two qubits can be implemented. The goal is to minimize the…
Classical shadows are a versatile tool to probe many-body quantum systems, consisting of a combination of randomised measurements and classical post-processing computations. In a recently introduced version of the protocol, the…
The method of classical shadows heralds unprecedented opportunities for quantum estimation with limited measurements [H.-Y. Huang, R. Kueng, and J. Preskill, Nat. Phys. 16, 1050 (2020)]. Yet its relationship to established quantum…
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…
Properties of quantum systems can be estimated using classical shadows, which implement measurements based on random ensembles of unitaries. Originally derived for global Clifford unitaries and products of single-qubit Clifford gates,…
The development of large-scale platforms for quantum information requires new methods for verification and validation of quantum behavior. Quantum tomography (QT) is the standard tool for diagnosing quantum states, process, and readout…
It is proposed a possible new approach of quantum measurements (QMS), disconnected of the traditional interpretation of uncertainty relations and independent of any appeal to the strange idea of collapse (reduction) of wave functions. The…
We present a robust shadow estimation protocol for wide classes of low-depth measurement circuits that mitigates noise as long as the effective measurement map including noise is locally unitarily invariant. This is in practice an excellent…
Boson is one of the most basic types of particles and preserves the commutation relation. An efficient way to measure a bosonic system is important not only for simulating complex physics phenomena of bosons (such as nuclei) on a qubit…
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…
The concept of randomized measurements on individual particles has proven to be useful for analyzing quantum systems and is central for methods like shadow tomography of quantum states. We introduce $\textit{collective}$ randomized…
We investigate the compression of quantum information with respect to a given set $\mathcal{M}$ of high-dimensional measurements. This leads to a notion of simulability, where we demand that the statistics obtained from $\mathcal{M}$ and an…
Quantum many-body systems provide a unique platform for exploring the rich interplay between chaos, randomness, and complexity. In a recently proposed paradigm known as deep thermalization, random quantum states of system A are generated by…