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Fundamentos de cúbits transmon para ingenierías

Cruz Trejo Said Carbot, Ojeda Guillén Didider

Published May 7, 2025• 0 citations
Publisher

Abstract

In this research, we explore the operation of the transmon qubit, a key superconducting architecture in quantum computing. To do so, we address fundamental concepts such as the quantum anharmonic oscillator, Cooper pairs, quantum tunneling, Josephson junctions (JJ), SQUID devices, and the Cooper pair box. The purpose is to provide a rigorous yet accessible introduction, specifically aimed at engineering professionals, that explains the operational principles of the transmon without requiring advanced knowledge of theoretical physics.

DOI
10.5281/zenodo.19710485

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Quantum mechanics and superconductivity are intimately connected on many levels. Quantum mechanics is needed to understand why a metal is a metal. The BCS condensate of Cooper pairs would not exist without quantum mechanics, nor could Cooper pairs tunnel through the barriers of Josephson junctions. The name SQUID is the abbreviation of superconducting quantum interference device. Yet another level of quantumness has been added in the last two decades. It turns out to be possible to design and fabricate superconducting objects that have macroscopic dimensions and properties, but behave as if they are single quantum particles. Amplitude and phase of the superconducting wavefunction act as conjugate quantum variables. Practical devices and circuits make use of Josephson junctions to reach the parameter values that are needed, but there is a clear distinction from the Josephson electronics circuits in the other chapters of this book. The latter may, in this context, well be referred to as being classical.

CRC Press eBooks•Nov 11, 2011•4 citations
In this research, we explore the operation of the transmon qubit, a key superconducting architecture in quantum computing. To do so, we address fundamental concepts such as the quantum anharmonic oscillator, Cooper pairs, quantum tunneling, Josephson junctions (JJ), SQUID devices, and the Cooper pair box. The purpose is to provide a rigorous yet accessible introduction, specifically aimed at engineering professionals, that explains the operational principles of the transmon without requiring advanced knowledge of theoretical physics.
Short dephasing times pose one of the main challenges in realizing a quantum computer. Different approaches have been devised to cure this problem for superconducting qubits, a prime example being the operation of such devices at optimal working points, so-called sweet spots. This latter approach led to significant improvement of T2T_2T2​ times in Cooper pair box qubits [D. Vion et al., Science 296, 886 (2002)]. Here, we introduce a new type of superconducting qubit called the transmon. Unlike the charge qubit, the transmon is designed to operate in a regime of significantly increased ratio of Josephson energy and charging energy EJ/ECE_J/E_CEJ​/EC​. The transmon benefits from the fact that its charge dispersion decreases exponentially with EJ/ECE_J/E_CEJ​/EC​, while its loss in anharmonicity is described by a weak power law. As a result, we predict a drastic reduction in sensitivity to charge noise relative to the Cooper pair box and an increase in the qubit-photon coupling, while maintaining sufficient anharmonicity for selective qubit control. Our detailed analysis of the full system shows that this gain is not compromised by increased noise in other known channels.
As superconducting circuits emerge as a leading platform for scalable quantum information processing, building comprehensive bridges from the foundational principles of macroscopic quantum phenomena to the architecture of modern quantum devices is increasingly essential for introducing new researchers to the field. This tutorial provides a self-contained, pedagogical introduction to superconducting quantum circuits at the undergraduate level. Beginning with an overview of superconductivity and the Josephson effect, the tutorial systematically develops the quantization of microwave circuits into the framework of circuit quantum electrodynamics (cQED). The transmon qubit is then introduced as a state-of-the-art application, with a detailed derivation of its Hamiltonian and its interaction with control and readout circuitry. The theoretical formalism is consolidated through a numerical simulation of vacuum Rabi oscillations in a driven transmon-resonator system, a canonical experiment that demonstrates the coherent energy exchange characteristic of the strong coupling regime. This work serves as a foundational guide and first point of contact, equipping students and researchers with the conceptual and mathematical tools necessary to understand and engineer superconducting quantum hardware.
Abstract Superconductivity manifests macroscopic quantum phenomena. A superconducting circuit composed of Josephson junctions, Cooper pair boxes, and rf-/dc-SQUID, properly miniaturized, becomes quantized and demonstrates Rabi oscillations and entanglement. In this paper, we offer an overview of this approach. We begin with an introduction of the history and elementary theory of superconductivity. Then we describe the building blocks of superconducting classical circuits and derive their canonical quantizations. The set-up of qubits and superconducting quantum logic gates are then examined. Finally, ways to make measurements are discussed.
This thesis explores novel strategies for advancing superconducting quantum computing through a series of experimental investigations and device innovations. Grounded in the development of circuit quantum electrodynamics, the work addresses the challenges posed by the limitations of coherent control, coherence time and scaling of superconducting qubits. Focusing on transmon qubits, the thesis first reviews the foundational principles of circuit quantum electrodynamics and the critical role of the transmon in achieving robust qubit performance. Three experimental studies form the core of this work. The first study demonstrates a universal quantum gate set for strongly coupled transmons. By exploiting the residual ZZ interaction, the work introduces a novel two-axis gate protocol for single-qubit operations and implements both CZ and CNOT gates with high fidelities, highlighting the potential for fast, low-error quantum operations in the strong coupling regime. The second study investigates a dual-rail qubit architecture using parametrically coupled transmons, showcasing a hardware-efficient approach to quantum error correction. This experiment converts single-photon loss errors into detectable erasures and leverages mid-circuit detection to enhance qubit coherence, thereby advancing fault-tolerant quantum computing schemes in the NISQ era. The final study focuses on the development of merged-element transmons (MET) and their FinMET variants. By integrating the Josephson junction and shunt capacitor into a single trilayer device, these innovations achieve a dramatic reduction in device footprint while addressing loss channels through advanced materials engineering, ultimately paving the way for scalable, high-coherence quantum circuits. Collectively, these contributions demonstrate significant progress in quantum gate design, error mitigation, and qubit architecture, offering promising routes toward the realization of largescale, fault-tolerant quantum computers
Quantum mechanics and superconductivity are intimately connected on many levels. Quantum mechanics is needed to understand why a metal is a metal. The BCS condensate of Cooper pairs would not exist without quantum mechanics, nor could Cooper pairs tunnel through the barriers of Josephson junctions. The name SQUID is the abbreviation of superconducting quantum interference device. Yet another level of quantumness has been added in the last two decades. It turns out to be possible to design and fabricate superconducting objects that have macroscopic dimensions and properties, but behave as if they are single quantum particles. Amplitude and phase of the superconducting wavefunction act as conjugate quantum variables. Practical devices and circuits make use of Josephson junctions to reach the parameter values that are needed, but there is a clear distinction from the Josephson electronics circuits in the other chapters of this book. The latter may, in this context, well be referred to as being classical.