arXiv subjects

F. A. Cárdenas-López

Publications and source records attributed to F. A. Cárdenas-López.

At least 19 recordsLinked to original sources

arXiv2026

Inertial Counterdiabatic Driving

We introduce an inertial counterdiabatic (CD) protocol that reformulates shortcut-to-adiabaticity design as a moving-frame diagonalization problem. The method employs the Magnus expansion to construct a variational propagator generated by an accessible CD ansatz. In the new rotating frame, the controls are optimized to suppress the off-diagonal Hamiltonian terms, and the CD terms are defined to counteract the corresponding inertial contribution. The propagator generated with the Magnus expansion naturally exploits additional control directions generated through its nested commutator, while the sequential design of the propagator introduces temporal nonlocality into the optimization. We benchmark the method on a two-qubit system and on the one-dimensional quantum Ising chain, where it consistently outperforms variational CD protocols based on action minimization. The largest improvements are observed near gap-closing regions, demonstrating the advantage of combining temporal and algebraic nonlocality for suppressing diabatic excitations.

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arXiv2026

Simple analytical flux-tuned iSWAP pulses for leakage suppression

Fast, high-fidelity two-qubit gates are a key requirement for fault-tolerant quantum computation. Tunable coupler architectures provide a flexible approach for implementing entangling gates through flux control with large on-off ratios, but fast flux modulation can induce diabatic transitions and population leakage to non-computational states, limiting gate performance. Here we present an analytical flux control method enabling derivative removal by adiabatic gate ($Φ$-DRAG) for suppressing leakage in flux tunable two-qubit gates. We show that $Φ$-DRAG differs fundamentally from conventional microwave implementations and derive modified flux modulation protocols that suppress leakage below $10^{-4}$ for fast entangling gates. The method remains effective across a range of asymmetry between qubit anharmonicities and different circuit parameters, enabling high-fidelity two-qubit gates within the fifteen nanosecond range.

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arXiv2026

Quantum circuit partition as a maze: emerging percolation transition via path finding

In quantum circuit optimization, circuit partitioning enables the optimization process to be parallelized across multiple devices. Each device is responsible for either reducing the number of selected gates or simplifying the local circuit structure. Most existing approaches to circuit partitioning are quantum-distribution-oriented and rely on splitting CNOT gates by introducing mid-circuit measurements and qubit resets. Currently, there is no criterion to determine how a circuit can be optimally partitioned without removing the CNOT gates for circuit optimization purposes. To address this challenge, we formalize the partition problem as a cutting path through a maze, where the CNOT gates represent the walls. We show that the existence of such a path separates quantum circuits into two classes through a percolation phase transition. In particular, it distinguishes a partitionable regime from a nonpartitionable one, arising from qubit permutations. Such permutations are generated by simulated annealing. We analyze its effect on the CNOT cluster from the perspective of network science and distribution analysis. Our results show that partitioning into two CNOT clusters is possible when the number of CNOTs is almost equal to the number of qubits. Based on this observation, we provide a scalable and practical criterion for identifying whether such a partition exists. Overall, our framework provides theoretical and numerical insight into circuit partitioning within quantum circuit optimization, forming the basis for algorithmic development.

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arXiv2026

Regularized Counterdiabatic Driving for the Quantum Rabi Model

Counter-diabatic (CD) driving provides a powerful route to fast and robust state preparation by suppressing diabatic excitations during finite-time evolution. Yet, deriving analytical CD protocols for complex systems remains challenging, motivating the development of variational approaches. These methods typically rely on minimizing trace-based functionals to construct approximate control Hamiltonians. However, in unbounded systems, such functionals can become ill-defined because of the unbounded bosonic Hilbert space, leading to divergent cost functions and unphysical variational coefficients. Here, we introduce a variational optimization framework equipped with physically motivated renormalization schemes that regularize the trace-based metric by restricting it to relevant displaced and low-energy subspaces. As a paradigmatic example, we apply our method to the quantum Rabi model beyond the dispersive approximation and identify two distinct CD contributions that couple the atomic degree of freedom to the position and momentum quadratures of the field. These terms suppress diabatic excitations across coupling regimes ranging from strong to deep-strong light--matter interaction. We further formulate a fidelity-based quantum optimal-control strategy that bypasses the limitations of trace-based variational methods. Finally, we show that the resulting CD terms can be implemented via Floquet engineering through parametric modulation of the native Hamiltonian. Our results demonstrate that CD driving can be consistently extended to continuous-variable systems with unbounded Hilbert spaces, providing a controlled and scalable framework for quantum control in strongly interacting light-matter platforms.

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arXiv2026

Robust multi-mode superconducting circuit optimized for quantum information processing

Multi-mode superconducting circuits offer a promising platform for engineering robust systems for quantum computation. Previous studies indicate that single-mode devices cannot be engineered to simultaneously exhibit resilience against multiple decoherence sources due to conflicting requirements. In contrast, multi-mode systems offer increased flexibility and have proven capable of overcoming these fundamental limitations. Here, we present a multi-mode device optimized for quantum information processing. It features an anharmonicity of a third of the qubit frequency and reduced energy dispersion caused by charge and magnetic flux fluctuations. It exhibits improvements over the fundamental errors limiting Transmon and Fluxonium coherence and control, achieving ratios between the total coherence time and the gate time $T_2/t_g$ one order of magnitude larger than Transmon and two times larger than Fluxonium for microwave charge drives, assuming equal dielectric and inductive loss quality factors and limited drive strength. It furthermore demonstrates robustness against fabrication errors, a major limitation in many proposed multi-mode devices.

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arXiv2025

Ultrafast Single Qubit Gates through Multi-Photon Transition Removal

One of the main enablers in quantum computing is having qubit control that is precise and fast. However, qubits typically have multilevel structures making them prone to unwanted transitions from fast gates. This leakage out of the computational subspace is especially detrimental to algorithms as it has been observed to cause long-lived errors, such as in quantum error correction. This forces a choice between either achieving fast gates or having low leakage. Previous works focus on suppressing leakage by mitigating the first to second excited state transition, overlooking multi-photon transitions, and achieving faster gates with further reductions in leakage has remained elusive. Here, we demonstrate single qubit gates with a total leakage error consistently below $2.0\times10^{-5}$, and obtain fidelities above $99.98\%$ for pulse durations down to 6.8 ns for both $X$ and $X/2$ gates. This is achieved by removing direct transitions beyond nearest-neighbor levels using a double recursive implementation of the Derivative Removal by Adiabatic Gate (DRAG) method, which we name the R2D method. Moreover, we find that at such short gate durations and strong driving strengths the main error source is from these higher order transitions. This is all shown in the widely-used superconducting transmon qubit, which has a weakly anharmonic level structure and suffers from higher order transitions significantly. We also introduce an approach for amplifying leakage error that can precisely quantify leakage rates below $10^{-6}$. The presented approach can be readily applied to other qubit types as well.

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arXiv2025

Universal pulses for superconducting qudit ladder gates

Qudits, generalizations of qubits to multi-level quantum systems, offer enhanced computational efficiency by encoding more information per lattice cell, avoiding costly swap operations and providing even exponential speedup in some cases. Utilizing the $d$-level manifold, however, requires high-speed gate operations because of the stronger decoherence at higher levels. While analytical control methods have proven effective for qubits in achieving fast gates with minimal control errors, their extension to qudits is nontrivial due to the increased complexity of the energy level structure arising from additional ancillary states. In this work, we present a universal pulse construction for generating rapid, high-fidelity unitary rotations between adjacent qudit levels, thereby providing a prescription for any gate in $SU(d)$. Control errors in these operations are effectively analyzed within a four-level subspace, including two leakage levels with approximately opposite detuning. By identifying the optimal degrees of freedom, we derive concise analytical pulse schemes that suppress multiple control errors and outperform existing methods. Remarkably, our approach achieves consistent coherent error scaling across all levels, approaching the quantum speed limit independently of parameter variations between levels. Validation on transmon circuits demonstrates significant improvements in gate fidelity for various qudit sizes aiming for $10^{-4}$ error. This method provides a scalable solution for improving qudit control and can be broadly applied to other quantum systems with ladder structures or operations involving multiple ancillary levels.

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arXiv2025

Resilient superconducting-element design with genetic algorithms

We present superconducting quantum circuits which exhibit atomic energy spectrum and selection rules as ladder and lambda three-level configurations designed by means of genetic algorithms. These heuristic optimization techniques are employed for adapting the topology and the parameters of a set of electrical circuits to find the suitable architecture matching the required energy levels and relevant transition matrix elements. We analyze the performance of the optimizer on one-dimensional single- and multi-loop circuits to design ladder ($Ξ$) and lambda ($Λ$) three-level system with specific transition matrix elements. As expected, attaining both the required energy spectrum and the needed selection rules is challenging for single-loop circuits, but they can be accurately obtained even with just two loops. Additionally, we show that our multi-loop circuits are robust under random fluctuation in their circuital parameters, i.e. under eventual fabrication flaws. Developing an optimization algorithm for automatized circuit quantization opens an avenue to engineering superconducting circuits with specific symmetry to be used as modules within large-scale setups, which may allow us to mitigate the well-known current errors observed in the first generation of quantum processors.

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arXiv2024

Optimal Control for Open Quantum System in Circuit Quantum Electrodynamics

We propose a quantum optimal control framework based on the Pontryagin Maximum Principle to design energy- and time-efficient pulses for open quantum systems. By formulating the Langevin equation of a dissipative LC circuit as a linear control problem, we derive optimized pulses with exponential scaling in energy cost, outperforming conventional shortcut-to-adiabaticity methods such as counter-diabatic driving. When applied to a resonator dispersively coupled to a qubit, these optimized pulses achieve an excellent signal-to-noise ratio comparable to longitudinal coupling schemes across varying critical photon numbers. Our results provide a significant step toward efficient control in dissipative open systems and improved qubit readout in circuit quantum electrodynamics.

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arXiv2024

Microwave Quantum Memcapacitor Effect

Developing the field of neuromorphic quantum computing necessitates designing scalable quantum memory devices. Here, we propose a superconducting quantum memory device in the microwave regime, termed as a microwave quantum memcapacitor. It comprises two linked resonators, the primary one is coupled to a Superconducting Quantum Interference Device, which allows for the modulation of the resonator properties through external magnetic flux. The auxiliary resonator, operated through weak measurements, provides feedback to the primary resonator, ensuring stable memory behaviour. This device operates with a classical input in one cavity while reading the response in the other, serving as a fundamental building block toward arrays of microwave quantum memcapacitors. We observe that a bipartite setup can retain its memory behaviour and gains entanglement and quantum correlations. Our findings pave the way for the experimental implementation of memcapacitive superconducting quantum devices and memory device arrays for neuromorphic quantum computing.

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arXiv2023

Shortcuts to adiabaticity in superconducting circuits for fast multi-partite state generation

Shortcuts to adiabaticity provides a flexible method to accelerate and improve a quantum control task beyond adiabatic criteria. Here we propose the reverse-engineering approach to design the longitudinal coupling between a set of qubits coupled to several field modes, for achieving a fast generation of multi-partite quantum gates in photonic or qubit-based architecture. We show that the enhancing generation time is at the nanosecond scale that does not scale with the number of system components. In addition, our protocol does not suffer noticeable detrimental effects due to the dissipative dynamics. Finally, the possible implementation is discussed with the state-of-the-art circuit quantum electrodynamics architecture.

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arXiv2023

Charge qubits in the USC regime for quantum state transfer

We study the feasibility of reaching the ultrastrong (USC) and deep-strong coupling (DSC) regimes of light-matter interaction, in particular at resonance condition, with a superconducting charge qubit, also known as Cooper-Pair box (CPB). We numerically show that by shunting the charge qubit with a high-impedance LC-circuit, one can maximally reach both USC and DSC regimes exceeding the classical upper bound $|g|\leq \sqrt{ω_qω_r}/2$ between two harmonic systems with frequencies $ω_q$ and $ω_r$. As an application, we propose a hybrid system consisting of two CPBs ultrastrongly coupled to an LC-oscillator as a mediator device that catalyzes a quantum state transfer protocol between a pair of transmon qubits, with all the parties subjected to local thermal noise. We demonstrate that the QST protocol maximizes its efficiency when the mediator operates in the USC regime, exhibiting comparable times with proposals relying on highly coherent and controllable mediators requiring state-preparation or post-selection. This work opens the door for studying light-matter interactions beyond the quantum Rabi model at extreme coupling strengths, providing a new building block for applications within quantum computation and quantum information processing.

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arXiv2023

Embedded Quantum Correlations in thermalized quantum Rabi systems

We study the quantum correlations embedded in open quantum Rabi systems. Specifically, we study how the quantum correlation depends on the coupling strength, number of qubits, and reservoir temperatures. We numerically calculate the quantum correlations of up to three qubits interacting with a single field mode. We find that the embedded quantum correlations exhibit a maximum for a given coupling strength, which depends inversely on the number of subsystems and the reservoir temperature. We explore how this feature affects the performance of a many-qubit Otto heat engine, finding numerical evidence of a direct correspondence between the minimum of the extractable work and the maximum of the embedded quantum correlations in the qubit-cavity bi-partition. Furthermore, as we increase the number of qubits, the maximum extractable work is reached at smaller values of the coupling strength. This work could help design more sophisticated quantum heat engines that rely on many-body systems with embedded correlations as working substances.

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arXiv2022

Shortcuts to Adiabaticity for Fast Qubit Readout in Circuit Quantum Electrodynamics

We propose how to engineer the longitudinal coupling to accelerate the measurement of a qubit longitudinally coupled to a cavity, motivated by the concept of shortcuts to adiabaticity. Different modulations are inversely designed from two methods of inverse engineering and counter-diabatic driving, for achieving larger values of the signal-to-noise ratio (SNR) at nanosecond scale. By comparison, we demonstrate that our protocols outperform the usual periodic modulations on the pointer state separation and SNR. Finally, we show a possible implementation considering state-of-the-art circuit quantum electrodynamics architecture, estimating the minimal time allowed for the measurement process.

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arXiv2022

Tripartite entanglement in quantum memristors

We study the entanglement and memristive properties of three coupled quantum memristors. We consider quantum memristors based on superconducting asymmetric SQUID architectures which are coupled via inductors. The three quantum memristors are arranged in two different geometries: linear and triangular coupling configurations. We obtain a variety of correlation measures, including bipartite entanglement and tripartite negativity. We find that, for identical quantum memristors, entanglement and memristivity follow the same behavior for the triangular case and the opposite one in the linear case. Finally, we study the multipartite correlations with the tripartite negativity and entanglement monogamy relations, showing that our system has genuine tripartite entanglement. Our results show that quantum correlations in multipartite memristive systems have a non-trivial role and can be used to design quantum memristor arrays for quantum neural networks and neuromorphic quantum computing architectures.

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arXiv2019

Enhanced Quantum Synchronization via Quantum Machine Learning

We study the quantum synchronization between a pair of two-level systems inside two coupled cavities. By using a digital-analog decomposition of the master equation that rules the system dynamics, we show that this approach leads to quantum synchronization between both two-level systems. Moreover, we can identify in this digital-analog block decomposition the fundamental elements of a quantum machine learning protocol, in which the agent and the environment (learning units) interact through a mediating system, namely, the register. If we can additionally equip this algorithm with a classical feedback mechanism, which consists of projective measurements in the register, reinitialization of the register state and local conditional operations on the agent and environment subspace, a powerful and flexible quantum machine learning protocol emerges. Indeed, numerical simulations show that this protocol enhances the synchronization process, even when every subsystem experience different loss/decoherence mechanisms, and give us the flexibility to choose the synchronization state. Finally, we propose an implementation based on current technologies in superconducting circuits.

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arXiv2018

Parity-assisted generation of nonclassical states of light in circuit quantum electrodynamics

We propose a method to generate nonclassical states of light in multimode microwave cavities. Our approach considers two-photon processes that take place in a system composed of two extended cavities and an ultrastrongly coupled light-matter system. Under specific resonance conditions, our method generates, in a deterministic manner, product states of uncorrelated photon pairs, Bell states, and W states. We demonstrate improved generation times when increasing the number of multimode cavities, and prove the generation of genuine multipartite entangled states when coupling an ancillary system to each cavity. Finally, we discuss the feasibility of our proposal in circuit quantum electrodynamics.

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arXiv2018

Multiqubit and multilevel quantum reinforcement learning with quantum technologies

We propose a protocol to perform quantum reinforcement learning with quantum technologies. At variance with recent results on quantum reinforcement learning with superconducting circuits, in our current protocol coherent feedback during the learning process is not required, enabling its implementation in a wide variety of quantum systems. We consider diverse possible scenarios for an agent, an environment, and a register that connects them, involving multiqubit and multilevel systems, as well as open-system dynamics. We finally propose possible implementations of this protocol in trapped ions and superconducting circuits. The field of quantum reinforcement learning with quantum technologies will enable enhanced quantum control, as well as more efficient machine learning calculations.

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