Related papers: Improved classical shadows from local symmetries i…
Pauli Measurements are the most important measurements in both theoretical and experimental aspects of quantum information science. In this paper, we explore the power of Pauli measurements in the state tomography related problems. Firstly,…
We consider the statistical problem of `compressive' estimation of low rank states with random basis measurements, where the estimation error is expressed terms of two metrics - the Frobenius norm and quantum infidelity. It is known that…
This paper presents an original ABC algorithm, "ABC Shadow", that can be applied to sample posterior densities that are continuously differentiable. The proposed method uses the ideas given by the auxiliary variable MH of (M\o ller and…
Measuring global quantum properties-such as the fidelity to complex multipartite states-is both an essential and experimentally challenging task. Classical shadow estimation offers favorable sample complexity, but typically relies on…
In light of recently proposed quantum algorithms that incorporate symmetries in the hope of quantum advantage, we show that with symmetries that are restrictive enough, classical algorithms can efficiently emulate their quantum counterparts…
Classical shadow tomography is a sample-efficient technique for characterizing quantum systems and predicting many of their properties. Circuit cutting is a technique for dividing large quantum circuits into smaller fragments that can be…
A bipartite state is classical with respect to party $A$ if and only if party $A$ can perform nondisruptive local state identification (NDLID) by a projective measurement. Motivated by this we introduce a class of quantum correlation…
Classicality associated with joint measurability of operators manifests through a valid classical joint probability distribution on measurement outcomes. For qudits in dimension $n$, where $n$ is prime or power of prime, we present a method…
Randomized measurement protocols, including classical shadows, entanglement tomography, and randomized benchmarking are powerful techniques to estimate observables, perform state tomography, or extract the entanglement properties of quantum…
Efficient measures to determine similarity of quantum states, such as the fidelity metric, have been widely studied. In this paper, we address the problem of defining a similarity measure for quantum operations that can be…
Classical shadows enable us to learn many properties of a quantum state $\rho$ with very few measurements. However, near-term and early fault-tolerant quantum computers will only be able to prepare noisy quantum states $\rho$ and it is thus…
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…
Boson sampling, a computational problem conjectured to be hard to simulate on a classical machine, is a promising candidate for an experimental demonstration of quantum advantage using bosons. However, inevitable experimental noise and…
The goal of qubit purification is to combine multiple noisy copies of an unknown pure quantum state to obtain one or more copies that are closer to the pure state. We show that a simple protocol based solely on random SWAP tests achieves…
In the problem of quantum state tomography, one is given $n$ copies of an unknown rank-$r$ mixed state $\rho \in \mathbb{C}^{d \times d}$ and asked to produce an estimator of $\rho$. In this work, we present the debiased Keyl's algorithm,…
Many hybrid quantum-classical algorithms for the application of ground state energy estimation in quantum chemistry involve estimating the expectation value of a molecular Hamiltonian with respect to a quantum state through measurements on…
Classifying phase transitions is a fundamental and complex challenge in condensed matter physics. This work proposes a framework for identifying quantum phase transitions by combining classical shadows with unsupervised machine learning. We…
Shadow estimation is a sample-efficient protocol for learning the properties of a quantum system using randomized measurements, but the current understanding of qudit shadow estimation is quite limited compared with the qubit setting. Here…
Classical shadow tomography provides a randomized scheme for approximating the quantum state and its properties at reduced computational cost with applications in quantum computing. In this Letter we present an algorithm for realizing fewer…
Nonclassicality cannot be a single-observable property since the statistics of any quantum observable is compatible with classical physics. We develop a general procedure to reveal nonclassical behavior from the joint measurement of…