English
Related papers

Related papers: Optimal tradeoffs for estimating Pauli observables

200 papers

As quantum computers approach the fault tolerance threshold, diagnosing and characterizing the noise on large scale quantum devices is increasingly important. One of the most important classes of noise channels is the class of Pauli…

Quantum Physics · Physics 2021-02-17 Robin Harper , Wenjun Yu , Steven T. Flammia

We provide practical and powerful schemes for learning many properties of an unknown n-qubit quantum state using a sparing number of copies of the state. Specifically, we present a depth-modulated randomized measurement scheme that…

Estimating physical properties of quantum states from measurements is one of the most fundamental tasks in quantum science. In this work, we identify conditions on states under which it is possible to infer the expectation values of all…

Quantum Physics · Physics 2024-05-01 Cambyse Rouzé , Daniel Stilck França

The estimation of many-qubit observables is an essential task of quantum information processing. The generally applicable approach is to decompose the observables into weighted sums of multi-qubit Pauli strings, i.e., tensor products of…

Quantum Physics · Physics 2025-03-17 Liubov A. Markovich , Attaallah Almasi , Sina Zeytinoğlu , Johannes Borregaard

In standard optical tomographic methods, the off-diagonal elements of a density matrix $\rho$ are measured indirectly. Thus, the reconstruction of $\rho$, even if it is based on linear inversion, typically magnifies small errors in the…

Quantum Physics · Physics 2016-07-19 Karol Bartkiewicz , Antonín Černoch , Karel Lemr , Adam Miranowicz

As often emerges in various basic quantum properties such as R\'enyi and Tsallis entropies, the trace of quantum state powers $\text{tr}(\rho^q)$ has attracted a lot of attention. The recent work of Liu and Wang (SODA 2025) showed that,…

Quantum Physics · Physics 2026-04-03 Kean Chen , Yupan Liu , Qisheng Wang

We introduce a Pauli-measurement-based algorithm to certify the Schmidt number of $n$-qubit pure states. Our protocol achieves an average-case sample complexity of $\caO(\mathrm{poly}(n)\chi^2)$, a substantial improvement over the $\caO(2^n…

Quantum Physics · Physics 2026-01-19 Changhao Yi

We consider a quantum computation that only extracts one bit of information per $N$-qubit quantum state preparation. This is relevant for error mitigation schemes where the remainder of the system is measured to detect errors. We optimize…

Quantum Physics · Physics 2023-07-19 Stefano Polla , Gian-Luca R. Anselmetti , Thomas E. O'Brien

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…

Quantum Physics · Physics 2021-01-20 G. I. Struchalin , Ya. A. Zagorovskii , E. V. Kovlakov , S. S. Straupe , S. P. Kulik

Classically simulating the quantum contextual correlations produced by sequences of ideal measurements of compatible observables requires the measured system to have an internal memory. Computing the minimum amount of memory needed is, in…

Quantum Physics · Physics 2025-06-10 Stefan Trandafir , Colm Kelleher , Adán Cabello

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…

Quantum Physics · Physics 2024-08-07 Costin Bădescu , Ryan O'Donnell

Statistical verification of a quantum state aims to certify whether a given unknown state is close to the target state with confidence. So far, sample-optimal verification protocols based on local measurements have been found only for…

Quantum Physics · Physics 2020-12-08 Ninnat Dangniam , Yun-Guang Han , Huangjun Zhu

Estimating the expectation value of an operator corresponding to an observable is a fundamental task in quantum computation. It is often impossible to obtain such estimates directly, as the computer is restricted to measuring in a fixed…

In recent years there has been significant interest in understanding the statistical complexity of learning from quantum data under the constraint that one can only make unentangled measurements. While a key challenge in establishing tight…

Quantum Physics · Physics 2024-12-30 Sitan Chen , Weiyuan Gong , Zhihan Zhang

Model-independent estimation of the properties of quantum states is a central challenge in quantum technologies, as experimental imperfections, drifts, and imprecise models of the actual quantum dynamics inevitably hinder accurate…

We consider the problem of testing whether an unknown $n$-qubit quantum state $|\psi\rangle$ is a stabilizer state, with only single-copy access. We give an algorithm solving this problem using $O(n)$ copies, and conversely prove that…

Quantum Physics · Physics 2025-07-25 Marcel Hinsche , Jonas Helsen

Motivated by estimation of quantum noise models, we study the problem of learning a Pauli channel, or more generally the Pauli error rates of an arbitrary channel. By employing a novel reduction to the "Population Recovery" problem, we give…

Quantum Physics · Physics 2021-09-29 Steven T. Flammia , Ryan O'Donnell

The process of reconstructing quantum states from experimental measurements, accomplished through quantum state tomography (QST), plays a crucial role in verifying and benchmarking quantum devices. A key challenge of QST is to find out how…

Quantum Physics · Physics 2024-11-08 Zhen Qin , Casey Jameson , Zhexuan Gong , Michael B. Wakin , Zhihui Zhu

Inferring nonlinear features of quantum states is fundamentally important across quantum information science, but remains challenging due to the intrinsic linearity of quantum mechanics. It is widely recognized that quantum memory and…

Quantum Physics · Physics 2025-09-30 Qi Ye , Zhenhuan Liu , Dong-Ling Deng

Pauli-based computation (PBC) is a universal model for quantum computation with qubits where the input state is a magic (resource) state and the computation is driven by a sequence of adaptively chosen and compatible multiqubit Pauli…

Quantum Physics · Physics 2023-09-15 Filipa C. R. Peres