arXiv subjects

Juan Garcia-Nila

Publications and source records attributed to Juan Garcia-Nila.

5 recordsLinked to original sources

arXiv2026

Thermodynamics of Ahn--Doherty--Landahl Continuous Quantum Error Correction

Continuous quantum error correction (CQEC) replaces discrete syndrome measurements and recovery operations with continuous syndrome extraction and real-time Hamiltonian feedback. Here we investigate the thermodynamic resources required by this process by formulating measurement-based continuous quantum error correction as an information engine. We distinguish the system-side power associated with energy transfer between the feedback field and the protected system from the controller-side power associated with the feedback Hamiltonian. The framework is first developed for the one-qubit Ahn-Doherty-Landahl (ADL) protocol and subsequently extended to the three-qubit repetition code under continuous stabilizer monitoring. Numerical simulations show that increasing the feedback strength improves the steady-state fidelity and reduces the conditional-state entropy, while both energetic contributions continue to increase in magnitude after the fidelity begins to saturate. These results expose a direct tradeoff between logical stabilization and the energetic resources required for continuous feedback, closely related to previously established energy--precision tradeoffs in quantum measurement and quantum-Zeno stabilization.

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arXiv2026

Holonomic quantum gates via continuous measurement in bosonic codes: GKP and cat states

We apply continuous measurement-based holonomic quantum computation (CMHQC) to bosonic quantum error-correcting codes and develop explicit protocols for both four-component cat codes and Gottesman-Kitaev-Preskill (GKP) codes. In this framework, a continuously monitored time-dependent codespace undergoes a closed trajectory on the Grassmannian manifold while Zeno confinement suppresses departures from the instantaneous code subspace. For cat codes, we construct a family of squeezed-cat trajectories whose projected Wilczek-Zee connection generates arbitrary logical Z rotations, including non-Clifford T-gates. For GKP codes, we introduce a translated-lattice trajectory that realizes the logical GKP T gate through a purely geometric holonomy. We derive the corresponding time-dependent projectors, analytically evaluate the projected connections, and show that the resulting holonomies reproduce the desired logical operations without Hamiltonian control. Furthermore, we analyze the error-correcting capabilities of the instantaneous codespaces by establishing dressed Knill-Laflamme conditions for the relevant bosonic error models and derive analytical estimates for leakage induced by finite-strength continuous measurements. Our results provide a concrete realization of measurement-induced holonomic control in experimentally relevant bosonic platforms and establish a full fault-tolerant logical gate implementation.

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arXiv2026

Continuous measurement-based holonomic quantum computation

We propose a scheme to generate holonomies using the Quantum Zeno effect, enabling logical unitary operations on quantum stabilizer codes purely through measurements. The quantum error-correcting code space is adiabatically rotated by measuring a succession of rotated stabilizer generators. When the rotation is sufficiently slow, the state remains confined to the instantaneous code space by the Zeno effect; otherwise, measurement-induced jumps can occur into a rotated orthogonal subspace. If the rotation completes a closed loop, the code state is transformed by a holonomy: a logical unitary transformation. We analytically derive the sequence of rotated stabilizer generators that produce a desired holonomy, and find the total time required to implement this procedure with a given success probability. If a measurement moves the state to the orthogonal subspace, we present a method to alter the path of the rotated observables to return the state either to the original code or the original error space with the desired holonomy; in the latter case, the holonomy is emulated. Finally, we establish conditions on the code and the measured observables that preserve the correctability of a given error set. When a code fails to meet the error-correcting conditions, our protocol can be applicable by augmenting the code with ancilla qubits.

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arXiv2026

Steering paths mid-flight for fault-tolerance in measurement-based holonomic gates

Continuous measurement-based holonomic quantum computation provides a route to universal logical computation in quantum error correcting codes. We introduce a fault-tolerant framework for implementing measurement-based holonomic gates that leverages continuous measurements with real-time feedback. We show that non-Markovian decoherence is intrinsically suppressed through the quantum Zeno effect, while Markovian errors are identified by the decoding of measurement records to reveal the rotated syndrome subspace populated during the evolution. This information enables steering holonomic paths mid-flight to ensure that the final evolution realizes the target logical gate. We further demonstrate that non-adiabatic effects give rise to measurement-induced errors, and we show that these can also be corrected by an analogous protocol. This approach relaxes the stringent adiabaticity requirement and enables faster implementation of holonomic gates.

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arXiv2024

Markovian and non-Markovian master equations versus an exactly solvable model of a qubit in a cavity

Quantum master equations are commonly used to model the dynamics of open quantum systems, but their accuracy is rarely compared with the analytical solution of exactly solvable models. In this work, we perform such a comparison for the damped Jaynes-Cummings model of a qubit in a leaky cavity, for which an analytical solution is available in the one-excitation subspace. We consider the non-Markovian time-convolutionless master equation up to the second (Redfield) and fourth orders as well as three types of Markovian master equations: the coarse-grained, cumulant, and standard rotating-wave approximation (RWA) Lindblad equations. We compare the exact solution to these master equations for three different spectral densities: impulse, Ohmic, and triangular. We demonstrate that the coarse-grained master equation outperforms the standard RWA-based Lindblad master equation for weak coupling or high qubit frequency (relative to the spectral density high-frequency cutoff $ω_c$), where the Markovian approximation is valid. In the presence of non-Markovian effects characterized by oscillatory, non-decaying behavior, the TCL approximation closely matches the exact solution for short evolution times (in units of $ω_c^{-1}$) even outside the regime of validity of the Markovian approximations. For long evolution times, all master equations perform poorly, as quantified in terms of the trace-norm distance from the exact solution. The fourth-order time-convolutionless master equation achieves the top performance in all cases. Our results highlight the need for reliable approximation methods to describe open-system quantum dynamics beyond the short-time limit.

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