arXiv subjects

Pablo Antonio Moreno Casares

Publications and source records attributed to Pablo Antonio Moreno Casares.

6 recordsLinked to original sources

arXiv2026

Capabilities Ain't All You Need: Measuring Propensities in AI

AI evaluation has primarily focused on measuring capabilities, with formal approaches inspired from Item Response Theory (IRT) being increasingly applied. Yet propensities - the tendencies of models to exhibit particular behaviours - play a central role in determining both performance and safety outcomes. However, traditional IRT describes a model's success on a task as a monotonic function of model capabilities and task demands, an approach unsuited to propensities, where both excess and deficiency can be problematic. Here, we introduce the first formal framework for measuring AI propensities by using a bilogistic formulation for model success, which attributes high success probability when the model's propensity is within an "ideal band". Further, we estimate the limits of the ideal band using LLMs equipped with newly developed task-agnostic rubrics. Applying our framework to six families of LLM models whose propensities are incited in either direction, we find that we can measure how much the propensity is shifted and what effect this has on the tasks. Critically, propensities estimated using one benchmark successfully predict behaviour on held-out tasks. Moreover, we obtain stronger predictive power when combining propensities and capabilities than either separately. More broadly, our framework showcases how rigorous propensity measurements can be conducted and how it yields gains over solely using capability evaluations to predict AI behaviour.

cs.LG↗

arXiv2024

Quantum simulation of time-dependent Hamiltonians via commutator-free quasi-Magnus operators

Hamiltonian simulation is arguably the most fundamental application of quantum computers. The Magnus operator is a popular method for time-dependent Hamiltonian simulation in computational mathematics, yet its usage requires the implementation of exponentials of commutators, which has previously made it unappealing for quantum computing. The development of commutator-free quasi-Magnus operators (CFQMs) circumvents this obstacle, at the expense of a lack of provable global numeric error bounds. In this work, we establish one such error bound for CFQM-based time-dependent quantum Hamiltonian simulation by carefully estimating the error of each step involved in their definition. This allows us to compare its cost with the alternatives, and show that CFQMs are often the most efficient product-formula technique available by more than an order of magnitude. As a result, we find that CFQMs may be particularly useful to simulate time-dependent Hamiltonians on early fault-tolerant quantum computers.

quant-ph↗

arXiv2024

Initial state preparation for quantum chemistry on quantum computers

Quantum algorithms for ground-state energy estimation of chemical systems require a high-quality initial state. However, initial state preparation is commonly either neglected entirely, or assumed to be solved by a simple product state like Hartree-Fock. Even if a nontrivial state is prepared, strong correlations render ground state overlap inadequate for quality assessment. In this work, we address the initial state preparation problem with an end-to-end algorithm that prepares and quantifies the quality of initial states, accomplishing the latter with a new metric -- the energy distribution. To be able to prepare more complicated initial states, we introduce an implementation technique for states in the form of a sum of Slater determinants that exhibits significantly better scaling than all prior approaches. We also propose low-precision quantum phase estimation (QPE) for further state quality refinement. The complete algorithm is capable of generating high-quality states for energy estimation, and is shown in select cases to lower the overall estimation cost by several orders of magnitude when compared with the best single product state ansatz. More broadly, the energy distribution picture suggests that the goal of QPE should be reinterpreted as generating improvements compared to the energy of the initial state and other classical estimates, which can still be achieved even if QPE does not project directly onto the ground state. Finally, we show how the energy distribution can help in identifying potential quantum advantage.

quant-ph↗

arXiv2023

Fault-tolerant quantum algorithms

The framework of this thesis is fault-tolerant quantum algorithms. Grover's algorithm and quantum walks are described in Chapter 2. We start by highlighting the central role that rotations play in quantum algorithms, explaining Grover's, why it is optimal, and how it may be extended. Key subroutines explained in this area are amplitude amplification and quantum walks, which will constitute useful parts of other algorithms. In the third chapter, in contrast, we turn to the exponential advantages promised by the Fourier transform in the context of the hidden subgroup problem. However, since this application is restricted to cryptography, we later explore its use in quantum linear algebra problems. Here we explain the development of the original quantum linear solver algorithm, its improvements, and finally the dequantization techniques that would often restrict the quantum advantage to polynomial. Chapter 4 is concerned with quantum simulation. We will review classical quantum chemistry techniques, and then focus on Hamiltonian simulation and ground state preparation as the key problems to be solved. Hamiltonian simulation, in particular, will enable the use of quantum phase estimation which computes the eigenvalues or energies of a given quantum state. Given the tradition of our group with error correction, we could not end this thesis without dedicating a final chapter to this topic. Here we explain the most important quantum error correction codes, the surface and color codes, and one extension of the latter, gauge color codes. They will show the complexity of implementing non-Clifford quantum gates, therefore validating their consideration as the bottleneck metric.

quant-ph↗

arXiv2020

Circuit implementation of bucket brigade qRAM for quantum state preparation

In this short review I aim to explain how we can construct a circuit implementation of the bucketbrigade qRAM first proposed in [1]. Used with classical data, this qRAM model can be used incombination with the quantum accessible data structure [2] to prepare arbitrary quantum statesquickly and repeatedly, once the data to be prepared is in memory

quant-ph↗

arXiv2018

A review on Loop Quantum Gravity

The aim of this dissertation is to review `Loop Quantum Gravity', explaining the main structure of the theory and indicating its main open issues. We will develop the two main lines of research for the theory: the canonical quantization (first two chapters) and spin foams (third). The final chapter will be devoted to studying some of the problems of the theory and what things remain to be developed. In chapter 3 we will also include an example of a simple calculation done in the frame of LQG: Schwarzschild black hole entropy.

gr-qc↗