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Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure…
We study the null space degeneracy of open quantum systems with multiple non-Abelian, strong symmetries. By decomposing the Hilbert space representation of these symmetries into an irreducible representation involving the direct sum of…
Hamiltonian learning is an important procedure in quantum system identification, calibration, and successful operation of quantum computers. Through queries to the quantum system, this procedure seeks to obtain the parameters of a given…
Extraspecial groups form a remarkable subclass of p-groups. They are also present in quantum information theory, in particular in quantum error correction. We give here a polynomial time quantum algorithm for finding hidden subgroups in…
Capturing the correlation emerging between constituents of many-body systems accurately is one of the key challenges for the appropriate description of various systems whose properties are underpinned by quantum mechanical fundamentals.…
One of the central issues in the hidden subgroup problem is to bound the sample complexity, i.e., the number of identical samples of coset states sufficient and necessary to solve the problem. In this paper, we present general bounds for…
This article is an expository account aimed at viewing entanglement in finite-dimensional quantum many-body systems as a phenomenon of global geometry. While the mathematics of general quantum states has been studied extensively, this…
Probabilistic (or Bayesian) modeling and learning offers interesting possibilities for systematic representation of uncertainty using probability theory. However, probabilistic learning often leads to computationally challenging problems.…
For many quantum systems intended for information processing, one detects the logical state of a qubit by integrating a continuously observed quantity over time. For example, ion and atom qubits are typically measured by driving a cycling…
One of the most important questions in quantum information theory is the so-called separability problem. It involves characterizing the set of separable (or, equivalently entangled) states among mixed states of a multipartite quantum…
Quantum metrology of an incoherent signal is a canonical sensing problem related to superresolution and noise spectroscopy. We show that quantum computing can accelerate searches for a weak incoherent signal when the signal and noise are…
A serious problem in learning probabilistic models is the presence of hidden variables. These variables are not observed, yet interact with several of the observed variables. Detecting hidden variables poses two problems: determining the…
Machine learning techniques have led to broad adoption of a statistical model of computing. The statistical distributions natively available on quantum processors are a superset of those available classically. Harnessing this attribute has…
We introduce a machine-learning approach for identifying hidden structural features of open quantum dynamics under restricted experimental access. Unlike most existing data-driven methods which focus on detection or prediction of dynamical…
The problem of quantum state filtering consists of determining whether an unknown quantum state, which is chosen from a known set of states, is either a particular, specified state, or not. We consider this problem for the case that the…
Quantum state filtering is a variant of the unambiguous state discrimination problem: the states are grouped in sets and we want to determine to which particular set a given input state belongs.The simplest case, when the N given states are…
Learning the structure of the entanglement Hamiltonian (EH) is central to characterizing quantum many-body states in analog quantum simulation. We describe a protocol where spatial deformations of the many-body Hamiltonian, physically…
Quantum graphical models (QGMs) extend the classical framework for reasoning about uncertainty by incorporating the quantum mechanical view of probability. Prior work on QGMs has focused on hidden quantum Markov models (HQMMs), which can be…
Drawing independent samples from a probability distribution is an important computational problem with applications in Monte Carlo algorithms, machine learning, and statistical physics. The problem can in principle be solved on a quantum…
This article surveys the state of the art in quantum computer algorithms, including both black-box and non-black-box results. It is infeasible to detail all the known quantum algorithms, so a representative sample is given. This includes a…