arXiv subjects

Ruben Ibarrondo

Publications and source records attributed to Ruben Ibarrondo.

6 recordsLinked to original sources

arXiv2026

Convergence monitoring of quantum Gibbs samplers

Recent progress in fully quantum Markov chain Monte Carlo methods enables efficient Gibbs-state sampling on quantum computers [Chen et al., Nature 646, 561 (2025)]. Although rigorous worst-case bounds on mixing times remain largely inaccessible for classically intractable systems, experience from classical Monte Carlo suggests that convergence of relevant observables may nevertheless be rapid. This raises the practical question of how to diagnose convergence efficiently, i.e., with at most polynomial overhead. We propose a low-cost criterion for convergence monitoring that exploits the weak measurements inherent in quantum Gibbs samplers and their qubit-efficient variants [Ding et al., arXiv:2508.05703 (2025)]. Our approach is based on the observation that, at thermal equilibrium, the net energy flow between system and environment vanishes and energy-exchange statistics satisfy a balance condition. This condition appears in the distribution of (quasi-)frequencies extracted from the weak-measurement record and we use it to construct a Hamiltonian-agnostic stopping criterion based solely on data already generated by the sampler. We provide a statistical analysis, along with numerical and analytical studies to understand its performance, assumptions, and limitations.

quant-ph↗

arXiv2026

Contraction and Expansion Values of Quantum Channels

The contraction coefficient of the trace distance is a central tool in quantum information, quantifying how strongly a quantum channel degrades the distinguishability of states. However, being an extremal ratio, it captures only the most optimistic behaviour of the channel and is often trivial, even for very noisy channels. Moreover, a single scalar is poorly suited to describe how contraction accumulates under channel composition. In this work we introduce the \emph{contraction and expansion values}, two monotone sequences that refine the contraction and expansion coefficients in the same way singular values refine the operator norm. They arise from a min--max variational principle over subspaces of traceless Hermitian operators, admit an operational interpretation in terms of two state-discrimination games, and are shown to coincide with the Gel'fand or Bernstein numbers of the channel restricted to traceless operators. This identification places the sequences within Pietsch's theory of $s$-numbers and yields, in particular, bounds under channel composition that the contraction coefficient alone cannot provide. We establish their main structural properties and compute or estimate them for single-qubit channels, $d$-dimensional amplitude damping channels, and direct-sum channels.

quant-ph↗

arXiv2025

Average Contraction Coefficients of Quantum Channels

The data-processing inequality ensures quantum channels reduce state distinguishability, with contraction coefficients quantifying optimal bounds. However, these can be overly optimistic and not representative of the usual behavior. We study how noise contracts distinguishability of `typical' states, beyond the worst-case. To that end, we introduce and study a family of moments of contraction for quantum divergences, which interpolate between the worst-case contraction coefficient of a channel and its average behavior under a chosen ensemble of input states. We establish general properties of these moments, relate moments for different divergences, and derive bounds in terms of channel parameters like the entropy or purity of its Choi state. Focusing on the trace distance, we obtain upper and lower bounds on its average contraction under tensor-product noise channels, and prove that, depending on the local noise strength, there is a phase transition in the limit of many channel uses: below a critical error rate the average contraction remains near unity, whereas above it decays exponentially with system size. We extend these phase-transition phenomena to random quantum circuits with unital noise, showing that constant-depth noisy circuits do not shrink the trace distance on average, even when given highly entangled states as input. In contrast, even at $\log\log n$ depth, the average trace distance can become superpolynomially small. Finally, we explore moments of contraction for f-divergences and discuss applications to local differential privacy, demonstrating that noise regimes ensuring privacy can render outputs essentially indistinguishable on average. Thus, our results provide a fine-grained framework to quantify typical channel noise in quantum information and computation and unveil new phenomena in contraction coefficients, such as phase transitions for average contraction.

quant-ph↗

arXiv2025

Quantum approximated cloning-assisted density matrix exponentiation

Classical information loading is an essential task for many processing quantum algorithms, constituting a cornerstone in the field of quantum machine learning. In particular, the embedding techniques based on Hamiltonian simulation techniques enable the loading of matrices into quantum computers. A representative example of these methods is the Lloyd-Mohseni-Rebentrost protocol, which efficiently implements matrix exponentiation when multiple copies of a quantum state are available. However, this is a quite ideal set up, and in a realistic scenario, the copies are limited and the non-cloning theorem prevents from producing more exact copies in order to increase the accuracy of the protocol. Here, we propose a method to circumvent this limitation by introducing imperfect quantum copies, which significantly improve the performance of the LMR when the eigenvectors are known.

quant-ph↗

arXiv2022

Digital-analog co-design of the Harrow-Hassidim-Lloyd algorithm

The Harrow-Hassidim-Lloyd quantum algorithm was proposed to solve linear systems of equations $A\vec{x} = \vec{b}$ and it is the core of various applications. However, there is not an explicit quantum circuit for the subroutine which maps the inverse of the problem matrix $A$ into an ancillary qubit. This makes challenging the implementation in current quantum devices, forcing us to use hybrid approaches. Here, we propose a systematic manner to implement this subroutine, which can be adapted to other functions $f(A)$ of the matrix $A$, we present a co-designed quantum processor which reduces the depth of the algorithm, and we introduce its digital-analog implementation. The depth of our proposal scales with the precision $ε$ as $\mathcal{O}(ε^{-1})$, which is bounded by the number of samples allowed for a certain experiment. The co-design of the Harrow-Hassidim-Lloyd algorithm leads to a "kite-like" architecture, which allows us to reduce the number of required SWAP gates. Finally, merging a co-design quantum processor architecture with a digital-analog implementation contributes to the reduction of noise sources during the experimental realization of the algorithm.

quant-ph↗

arXiv2021

Forecasting Election Polls with Spin Systems

We show that the problem of political forecasting, i.e, predicting the result of elections and referendums, can be mapped to finding the ground state configuration of a classical spin system. Depending on the required prediction, this spin system can be a combination of XY, Ising and vector Potts models, always with two-spin interactions, magnetic fields, and on arbitrary graphs. By reduction to the Ising model our result shows that political forecasting is formally an NP-Hard problem. Moreover, we show that the ground state search can be recasted as Higher-order and Quadratic Unconstrained Binary Optimization (HUBO / QUBO) Problems, which are the standard input of classical and quantum combinatorial optimization techniques. We prove the validity of our approach by performing a numerical experiment based on data gathered from Twitter for a network of 10 people, finding good agreement between results from a poll and those predicted by our model. In general terms, our method can also be understood as a trend detection algorithm, particularly useful in the contexts of sentiment analysis and identification of fake news.

physics.soc-ph↗