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Hamiltonian locality testing and certification do not achieve the Heisenberg limit
Francisco Escudero Gutiérrez, Junseo Lee, Sebastian Zur
We establish lower bounds for Hamiltonian property testing with access to the time-evolution operator but not its inverse. Each experiment may query the time-evolution operator mul…
Optimal inequalities for completely bounded polynomials and the limitations of quantum query algorithms
Francisco Escudero Gutiérrez, Miquel Saucedo, Carlos Palazuelos
We consider the problem of establishing limitations on the power of quantum query algorithms via the completely bounded polynomial method. In particular, we prove several optimal f…
Certifying and learning local quantum Hamiltonians
Andreas Bluhm, Matthias C. Caro, Francisco Escudero Gutiérrez +4
In this work, we study the problems of certifying and learning quantum -local Hamiltonians, for a constant . Our main contributions are as follows: - Certification of Hamilto…
Certifying and learning quantum Ising Hamiltonians
Andreas Bluhm, Matthias C. Caro, Francisco Escudero Gutiérrez +2
In this work, we study the problems of certifying and learning quantum Ising Hamiltonians. Our main contributions are as follows: Certification of Ising Hamiltonians. We show that…
Nearly optimal algorithms to learn sparse quantum Hamiltonians in physically motivated distances
Amira Abbas, Nunzia Cerrato, Francisco Escudero Gutiérrez +3
We study the problem of learning Hamiltonians that are -sparse in the Pauli basis, given access to their time evolution. Although Hamiltonian learning has been extensively i…
Learning low-degree quantum objects
Srinivasan Arunachalam, Arkopal Dutt, Francisco Escudero Gutiérrez +1
We consider the problem of learning low-degree quantum objects up to -error in -distance. We show the following results: unknown -qubit degree- (in…
Simple algorithms to test and learn local Hamiltonians
Francisco Escudero Gutiérrez
We consider the problems of testing and learning an -qubit -local Hamiltonian from queries to its evolution operator with respect the 2-norm of the Pauli spectrum, or equival…
Influences of Fourier Completely Bounded Polynomials and Classical Simulation of Quantum Algorithms
Francisco Escudero Gutiérrez
We give a new presentation of the main result of Arunachalam, Briët and Palazuelos (SICOMP'19) and show that quantum query algorithms are characterized by a new class of polynomial…