arXiv subjects

Federico Tomás B. Pérez

Publications and source records attributed to Federico Tomás B. Pérez.

3 recordsLinked to original sources

arXiv2026

Optimal four-copy detection of the three-tangle and its fault-tolerant cost

The three-tangle, $τ_3$, is a measure of genuine tripartite entanglement that distinguishes GHZ-type from W-type entanglement in pure three-qubit states. Here, we identify the statistically optimal one-sided four-copy detector of the three-tangle and study its implementation cost. The optimal detector has click probability $τ_3^2/48$, while previous four-copy constructions achieve $τ_3^2/256$ and therefore require asymptotically $16/3$ times as many experimental repetitions. Using the representation-theoretic structure of the problem, we construct an ancilla-free implementation of the optimal detector using 15 CNOT gates, together with an 11-CNOT detector with click probability $τ_3^2/96$. These results reveal a tradeoff between statistical efficiency and implementation cost, since reducing the number of repetitions requires increasingly expensive circuits. We then show that this tradeoff persists once the circuits are encoded. In a fully fault-tolerant setting, the increased click probability comes with a substantial non-Clifford synthesis cost, while an early fault-tolerant implementation based on $T$ gates and STAR rotations reduces this overhead at the expense of additional encoded resources. We quantify these costs using both the Steane and $[[8,3,2]]$ codes, providing explicit resource estimates for implementing the optimal detector across different computational regimes.

quant-ph↗

arXiv2026

Generalized $m$-body mean-field projections for classical simulation of $d$-dimensional Heisenberg-picture dynamics

Classical simulation of quantum many-body dynamics is challenged by the rapid growth of operator complexity, particularly in higher dimensions where tensor-network methods become increasingly demanding. We develop state-adapted Pauli-weight propagation based on generalized $m$-body mean-field projections, which compress many-body observables into optimal low-body representations in a covariance geometry induced by the initial state. Combined with adaptive Krylov-like restricted Heisenberg dynamics, this provides an alternative to conventional Hilbert--Schmidt Pauli-weight truncation. We derive necessary and conditional sufficient bounds on low-body approximation accuracy using standard operator complexity measures and characterize possible dynamical failure mechanisms of the state-adapted method. Numerical benchmarks demonstrate substantial state-dependent accuracy gains, while identifying regimes of reduced accuracy or violations of Pauli spectral bounds. For a three-dimensional system of $80$ interacting spins, our method achieves strong body-order convergence, close agreement with independently converging tensor-network simulations, and substantially smaller sparse Pauli representations. These results establish state-adapted Pauli propagation as a promising approach to classical simulation of higher-dimensional coherent many-body dynamics.

quant-ph↗

arXiv2026

State-adapted generalized mean-field projections for Pauli propagation of Heisenberg dynamics

The Heisenberg picture can make quantum many-body simulation efficient when evolved observables admit compact operator representation within low-dimensional structures. Conventional Pauli-string propagation and truncation techniques exploit this structure, but in coherent Hamiltonian dynamics their error control is often heuristic and their stability can be poor. We introduce a state-adapted Krylov framework based on geometric generalized mean-field projections of many-body observables onto low-body operator subspaces. The resulting dynamics approximate expectation values, do not extend spatial support beyond that prescribed by Lieb-Robinson bounds, and compress high-body correlations onto their state-relevant low-body representatives rather than simply discarding them. We derive necessary operator-entanglement obstructions to low-body representation and conditional sufficient bounds on representation and dynamical errors involving nonstabilizerness and controlled high-body tails. Numerical benchmarks show improved, stable finite-$m$ hierarchies and simulations on large three-dimensional lattices, establishing a scalable state-adapted alternative to conventional Heisenberg-picture weight-truncation of Pauli strings.

quant-ph↗