Related papers: The abelian state hidden subgroup problem: Learnin…
Quantum state tomography is an essential tool for the characterization and verification of quantum states. However, as it cannot be directly applied to systems with more than a few qubits, efficient tomography of larger states on mid-sized…
A symmetry of a state $\vert \psi \rangle$ is a unitary operator of which $\vert \psi \rangle$ is an eigenvector. When $\vert \psi \rangle$ is an unknown state supplied by a black-box oracle, the state's symmetries provide key physical…
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.…
The exponential scaling of the wave function is a fundamental property of quantum systems with far reaching implications in our ability to process quantum information. A problem where these are particularly relevant is quantum state…
Symmetry underlies many of the most effective classical and quantum learning algorithms, yet whether quantum learners can gain a fundamental advantage under symmetry-imposed structures remains an open question. Based on evidence that…
Stabilizer states constitute a set of pure states which plays a dominant role in quantum error correction, measurement--based quantum computation, and quantum communication. Central in these applications are the local symmetries of these…
Measurement correlations in quantum systems can exhibit non-local behavior, a fundamental aspect of quantum mechanics with applications such as device-independent quantum information processing. However, the explicit construction of local…
In quantum computing, knowing the symmetries a given system or state obeys or disobeys is often useful. For example, Hamiltonian symmetries may limit allowed state transitions or simplify learning parameters in machine learning…
Schr\"odinger's equation serves as a fundamental component in characterizing quantum systems, wherein both quantum state tomography and Hamiltonian learning are instrumental in comprehending and interpreting quantum systems. While numerous…
We define a quantum learning task called agnostic tomography, where given copies of an arbitrary state $\rho$ and a class of quantum states $\mathcal{C}$, the goal is to output a succinct description of a state that approximates $\rho$ at…
We give a pair of algorithms that efficiently learn a quantum state prepared by Clifford gates and $O(\log n)$ non-Clifford gates. Specifically, for an $n$-qubit state $|\psi\rangle$ prepared with at most $t$ non-Clifford gates, our…
Daniel Simon's 1994 discovery of an efficient quantum algorithm for solving the hidden subgroup problem (HSP) over Z_2^n provided one of the first algebraic problems for which quantum computers are exponentially faster than their classical…
We develop a method to deduce the symmetry properties of many-body Hamiltonians when they are prepared in Jordan-Wigner form for evaluation on quantum computers. Symmetries, such as point-group symmetries in molecules, are apparent in the…
Symmetries of the finite Heisenberg group represent an important tool for the study of deeper structure of finite-dimensional quantum mechanics. As is well known, these symmetries are properly expressed in terms of certain normalizer. This…
Learning probability distribution is an essential framework in classical learning theory. As a counterpart, quantum state learning has spurred the exploration of quantum machine learning theory. However, as dimensionality increases,…
In the context of finite Abelian groups two problems are presented and solved using quantum computing techniques. The first is the well--known Hidden Subgroup Problem, originally solved by Simon in a landmark work. The second is the Fully…
Amongst the most remarkable successes of quantum computation are Shor's efficient quantum algorithms for the computational tasks of integer factorisation and the evaluation of discrete logarithms. In this article we review the essential…
Quantum steering has attracted increasing research attention because of its fundamental importance, as well as its applications in quantum information science. Here we leverage the power of the deep learning model to infer the steerability…
Attempts to separate the power of classical and quantum models of computation have a long history. The ultimate goal is to find exponential separations for computational problems. However, such separations do not come a dime a dozen: while…
Preparation of a target quantum many-body state on quantum simulators is one of the significant steps in quantum science and technology. With a small number of qubits, a few quantum states, such as the Greenberger-Horne-Zeilinger state,…