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Rapid improvement in quantum hardware has opened the door to complex problems, but the precise characterization of quantum systems itself remains a challenge. To address this obstacle, novel tomography schemes have been developed that…
Quantum circuit partitioning (QCP) is a hybrid quantum-classical approach that aims to simulate large quantum systems on smaller quantum computers. A quantum computation is divided into smaller subsystems and results of measurements on…
Classical shadows are a powerful method for learning many properties of quantum states in a sample-efficient manner, by making use of randomized measurements. Here we study the sample complexity of learning the expectation value of Pauli…
Bell inequalities constitute a key tool in quantum information theory: they not only allow one to reveal nonlocality in composite quantum systems, but, more importantly, they can be used to certify relevant properties thereof. We provide a…
I explore the possibility that a quantum system S may be described completely by the combination of its standard quantum state $|\psi\rangle$ and a (hidden) quantum state $|\phi\rangle$ (that lives in the same Hilbert space), such that the…
We present a classification algorithm for quantum states, inspired by decision-tree methods. To adapt the decision-tree framework to the probabilistic nature of quantum measurements, we utilize conditional probabilities to compute…
Quantum Machine Learning models typically require expensive on-chip training procedures and often lack efficient gradient estimation methods. By employing Pauli propagation, it is possible to derive a symbolic representation of observables…
Despite the exponential overhead to describe general multi-qubit quantum states and processes, efficient methods for certain state families and operations have been developed and utilised. The stabilizer formalism and the Gottesman-Knill…
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…
Bell sampling is a simple yet powerful measurement primitive that has recently attracted a lot of attention, and has proven to be a valuable tool in studying stabiliser states. Unfortunately, however, it is known that Bell sampling fails…
Given many copies of an unknown quantum state $\rho$, we consider the task of learning a classical description of its principal eigenstate. Namely, assuming that $\rho$ has an eigenstate $|\phi\rangle$ with (unknown) eigenvalue $\lambda >…
We give an algorithm for pure state tomography with near-optimal copy and time complexity using only single-qubit measurements. Specifically, given $\widetilde{O}(2^n/\epsilon)$ copies of an unknown $n$-qubit pure state $|\psi\rangle$, the…
We study the problems of quantum tomography and shadow tomography using measurements performed on individual, identical copies of an unknown $d$-dimensional state. We first revisit a known lower bound due to Haah et al. (2017) on quantum…
We study classical shadows protocols based on randomized measurements in $n$-qubit entangled bases, generalizing the random Pauli measurement protocol ($n = 1$). We show that entangled measurements ($n\geq 2$) enable nontrivial and…
As quantum devices continue to grow in size but remain affected by noise, it is crucial to determine when and how they can outperform classical computers on practical tasks. A central piece in this effort is to develop the most efficient…
We examine the problem of finding the minimum number of Pauli measurements needed to uniquely determine an arbitrary $n$-qubit pure state among all quantum states. We show that only $11$ Pauli measurements are needed to determine an…
We extend the concept of probabilistic unambiguous discrimination of quantum states to quantum state estimation. We consider a scenario where the measurement device can output either an estimate of the unknown input state or an inconclusive…
The nonstabilizerness of quantum states is a necessary resource for universal quantum computation, yet its characterization is notoriously demanding. Quantifying nonstabilizerness typically requires an exponential number of measurements and…
We establish methods for quantum state tomography based on compressed sensing. These methods are specialized for quantum states that are fairly pure, and they offer a significant performance improvement on large quantum systems. In…
Quantum tomography is a crucial tool for characterizing quantum states and devices and estimating nonlinear properties of the systems. Performing full quantum state tomography on an $N_\mathrm{q}$ qubit system requires an exponentially…