Related papers: Learning Distributions over Quantum Measurement Ou…
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…
In quantum information theory, the accurate estimation of observables is pivotal for quantum information processing, playing a crucial role in compute and communication protocols. This work introduces a novel technique for estimating such…
Quantum machine learning has received significant attention in recent years, and promising progress has been made in the development of quantum algorithms to speed up traditional machine learning tasks. In this work, however, we focus on…
Extracting information efficiently from quantum systems is a major component of quantum information processing tasks. Randomized measurements, or classical shadows, enable predicting many properties of arbitrary quantum states using few…
We propose a learning method for estimating unknown pure quantum states. The basic idea of our method is to learn a unitary operation $\hat{U}$ that transforms a given unknown state $|\psi_\tau\rangle$ to a known fiducial state $|f\rangle$.…
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…
We prove the expected disturbance caused to a quantum system by a sequence of randomly ordered two-outcome projective measurements is upper bounded by the square root of the probability that at least one measurement in the sequence accepts.…
Learning properties of quantum states from measurement data is a fundamental challenge in quantum information. The sample complexity of such tasks depends crucially on the measurement primitive. While shadow tomography achieves…
Learning faithful representations of quantum states is crucial to fully characterizing the variety of many-body states created on quantum processors. While various tomographic methods such as classical shadow and MPS tomography have shown…
We give the first tight sample complexity bounds for shadow tomography and classical shadows in the regime where the target error is below some sufficiently small inverse polynomial in the dimension of the Hilbert space. Formally we give a…
Classical shadows constitute a protocol to estimate the expectation values of a collection of M observables acting on O(1) qubits of an unknown n-qubit state with a number of measurements that is independent of n and that grows only…
We show that measuring any two quantum states by a random POVM, under a suitable definition of randomness, gives probability distributions having total variation distance at least a universal constant times the Frobenius distance between…
Randomised measurements can efficiently characterise many-body quantum states by learning the expectation values of observables with low Pauli weights. In this paper, we generalise the theoretical tools of classical shadow tomography to the…
Gradient-based optimizers have been proposed for training variational quantum circuits in settings such as quantum neural networks (QNNs). The task of gradient estimation, however, has proven to be challenging, primarily due to distinctive…
Quantum tomography is a fundamental technique for characterizing, benchmarking, and verifying quantum states and devices. It plays a crucial role in advancing quantum technologies and deepening our understanding of quantum mechanics.…
Quantum noise constitutes a fundamental obstacle to realizing practical quantum technologies. To address the pivotal challenge of identifying quantum systems least affected by noise, we introduce the purest quantum state identification,…
Traditional quantum state tomography requires a number of measurements that grows exponentially with the number of qubits n. But using ideas from computational learning theory, we show that "for most practical purposes" one can learn a…
Quantum state tomography is a fundamental problem in quantum computing. Given $n$ copies of an unknown $N$-qubit state $\rho \in \mathbb{C}^{d \times d},d=2^N$, the goal is to learn the state up to an accuracy $\epsilon$ in trace distance,…
Pattern recognition is a central topic in Learning Theory with numerous applications such as voice and text recognition, image analysis, computer diagnosis. The statistical set-up in classification is the following: we are given an i.i.d.…
We introduce the concept of selective quantum state tomography or SQST, a tomographic scheme that enables a user to estimate arbitrary elements of an unknown quantum state using a fixed measurement record. We demonstrate how this may be…