Thèse un Routeur Quantique Basé sur une Architecture Hybride Spin-Circuit Supraconducteur H/F - Doctorat.Gouv.Fr

Établissement : Université Paris-Saclay GS Physique École doctorale : Physique en Ile de France Laboratoire de recherche : CEA/SPEC - Service de Physique de l'Etat Condensé Direction de la thèse : Emmanuel FLURIN ORCID 0000000213678967 Début de la thèse : 2026-10-01 Date limite de candidature : 2026-05-30T23:59:59 Une mémoire vive quantique adressable aléatoirement (QRAM) est une mémoire quantique dans laquelle on peut lire ou écrire de l'information quantique dans une superposition de cellules mémoire. Un tel dispositif est particulièrement puissant pour la mise en oeuvre d'une multitude d'algorithmes quantiques, notamment l'algorithme de recherche de Grover, la chimie quantique, la cryptographie quantique et l'apprentissage automatique quantique, et il est considéré par beaucoup comme un élément essentiel de l'ordinateur quantique du futur. Sa réalisation s'est toutefois révélée difficile en raison de la complexité de l'adressage quantique d'un support de stockage quantique.

L'objectif principal de ce projet de doctorat sera d'utiliser des techniques récemment développées de détection de spin unique, de spectroscopie et de contrôle cohérent afin de démontrer un routeur quantique, la cellule élémentaire d'une QRAM, à partir de spins électroniques et nucléaires dans l'état solide. Ce projet développera de nouvelles architectures de dispositifs supraconducteurs et explorera des régimes jusqu'ici inaccessibles de couplage entre des circuits mésoscopiques et des défauts paramagnétiques individuels. Cela constituera la réalisation d'une nouvelle architecture de traitement de l'information quantique et ouvrira la voie à des expériences fondamentales passionnantes sur l'interaction lumière-matière dans une plateforme inédite. In a classical random-access memory (RAM), the goal is to store and retrieve information from an array of memory cells on demand and in any order. A QRAM is the quantum analogue of this architecture: a branching structure of quantum routers enables access to an array of quantum memory cells. Quantum information is stored in the memory, and the routing of information through the tree of quantum routers is itself quantum. This means that one can choose to read from or write to a superposition of memory cells, depending on the states of the quantum routers.

Many proposals for QRAM have been put forward using platforms such as optical systems [14], Rydberg atoms [15], hybrid acoustic devices [16,17], photonic integrated circuits [18], and superconducting qubits [8]. Despite its importance for many proposed quantum algorithms [2-7], and although recent progress has been made [16,19], with storage of quantum information under classical addressing having been demonstrated [20-23], there has been only one demonstration of a true QRAM [10]. Significant challenges related to storage time, fidelity, and scalability therefore remain.

As a platform for quantum information processing, defect spins in crystals offer particularly long coherence times, potentially very high qubit density and connectivity, and natural confinement within the crystal lattice. They therefore constitute a compelling platform for realizing the unit cell of a QRAM-a quantum router-using an efficient routing protocol.

In recent work carried out by the Quantronics group at CEA Saclay [12,13], a planar niobium superconducting resonator was patterned onto the surface of an erbium-doped CaWO crystal, as shown in Fig. 1(a,b), and cooled to 10 mK in a dilution refrigerator. The coupling between the resonator and the Er spins was sufficiently strong that the spins decayed predominantly via microwave fluorescence into the resonator through the Purcell effect [24]. Fluorescence from individual Er defects within the crystal was detected using a single microwave photon detector (SMPD).

Spin-1/2 183W nuclei are naturally present in CaWO with a natural abundance of 14%, meaning that there is roughly a one-in-three probability that a given Er site will have one 183W nucleus in the same unit cell, and a one-in-four probability of having two such
183W spins. One Er defect was found to be coupled to two nearby 183W nuclei, giving rise to the energy-level structure shown in Fig. 1(c). The presence of these nuclear spins was detected by observing the nuclear-spin-dependent frequency shift of the Er spin, as shown in Fig. 1(d). A quantum non-demolition (QND) measurement of the nuclear spin state can therefore be performed by detecting the fluorescence frequency of the Er spin; readout histograms illustrating this are shown in Fig. 1(e). The core goal of this PhD project will be to demonstrate the unit cell of a QRAM using electron and nuclear spins. This will require numerous technical developments. Key prerequisites include spin-resonator coupling greater than 50 kHz and microsecond-timescale tuning of spin frequencies.

To achieve the necessary coupling between spin and resonator, with g0 > 50 kHz, new ultra-low-impedance multilayer superconducting resonators have already been designed, fabricated, and successfully tested in the Quantronics group, and are expected to demonstrate the requisite coupling in the coming months. Microsecond-timescale tuning of individual spins will also be required. Devices with electric-field bias gates will be used to achieve spin-frequency tuning of approximately 500 kHz on a sub-microsecond timescale; such devices have already been developed and are currently undergoing preliminary testing.

In the first year of the project, the goal will be to work with a postdoctoral researcher to finalize these two technical developments and combine them in a single device based on Er:CaWO4. Single-spin resonance with g0 > 50 kHz will be demonstrated, along with fast tuning of multiple individual Er spins.

In the second year, these developments will be leveraged to demonstrate a CSWAP gate between two individual Er spins. First, a SWAP gate will be used to demonstrate entanglement between two distant Er spins, as shown in Fig. 2b. The protocol will then be extended to include additional 183W nuclear spins coupled to the two single Er spins. These will be used as control and storage qubits. This system will then be used to demonstrate the generation of a three-qubit GHZ state with a single CSWAP gate.

The goal for the later stages of the project is to demonstrate concatenated CSWAP gates, as shown in Fig. 2c. This will involve further extending the experiment to include a third Er spin. The concatenated CSWAP gates will be used to create a GHZ state between two Er spins and a 183W spin, thereby realizing a quantum router. This will demonstrate the ability to build a QRAM unit cell in Er:CaWO4. These experiments will yield multiple individually high-impact results, culminating in the demonstration of a QRAM unit cell with seconds-long storage time.

This work will constitute a proof of principle for a quantum router using spins in the solid state, and will represent a key milestone toward realizing an operational QRAM. These experiments will explore new control techniques and a new regime of coupling between individual spins and superconducting devices. This PhD project forms part of a broader effort to build a QRAM based on a hybrid spin-superconducting circuit architecture. The core component of a QRAM is a quantum router. This device takes an input qubit and an address qubit, and swaps the state of the input qubit into one of two output qubits depending on the state of the control qubit. The resulting operation can be understood as a concatenation of two CSWAP gates. To build a QRAM, such quantum routers are connected together to form a branching structure. A scheme for realizing this architecture is presented in Fig. 2(a). In this approach, we use a series of coupled Er spins, each associated with a nearby 183W spin. Within each quantum-router unit cell (indicated by a dashed box), an Er spin serves as the input qubit, while its nearby 183W spin acts as the control qubit. At the base of the tree, W spins are used as storage qubits.

Er:CaWO4 is an attractive candidate for implementing a QRAM for several reasons. The g-factor of Er defects in CaWO4 can reach 8.38 depending on the orientation of the applied field, whereas the free-electron g-factor is approximately 2, as is the case for the majority of paramagnetic spin species studied in EPR. A large g-factor is advantageous because it increases the spin-resonator coupling strength, g0. CaWO4 is also valuable as a largely spin-free substrate: the only commonly occurring spinful isotope is 183W, with a natural abundance of 14%. As previous experiments have shown, these 183W nuclei can be used as qubits with coherence times on the order of seconds, and they provide a natural means of implementing the routing operation required for a QRAM. Building on the experimental toolbox already established for controlling this system, this PhD project will develop the platform toward more advanced quantum experiments.

The scheme presented in Fig. 2(a) requires coupling three Er spins to one another in order to realize a single quantum router. This has not yet been demonstrated. We aim to achieve Er-Er coupling through a virtual-photon interaction mediated by the superconducting resonator, in a manner analogous to virtual-photon gates in superconducting circuits [25] and hybrid quantum-dot devices [26]. In this scheme, two Er spins coupled to the same resonator are brought into resonance with one another while the resonator is detuned from both by a frequency , as shown in Fig. 2(b). Under these conditions, the spins exchange a virtual microwave photon through the resonator at a rate J = g0²/, where g0 is the coupling of each individual Er spin to the resonator, assuming both spins have approximately the same coupling strength. Provided that , where is the resonator bandwidth, the resonator itself remains unpopulated and therefore does not contribute significantly to decoherence during the interaction. This enables a resonator-mediated SWAP interaction between two physically distant Er spins.

To use this gate as a CSWAP, we will identify two Er spins, denoted qubits A and B. Qubit A will be chosen to have a single adjacent 183W spin, which will act as the control qubit. As shown in previous experiments [12], the frequency of qubit A depends on the state of this control qubit. As a result, the resonance condition required to realize a SWAP operation between A and B becomes conditional on the state of the control qubit, thereby implementing a CSWAP gate.

To realize two concatenated CSWAP operations, we will introduce a third Er spin, denoted qubit C, as shown in Fig. 2(c). The qubits will be tuned such that the resonance condition for a SWAP between A and B is satisfied when the control qubit is in the state, whereas if it is in the state, A and C are brought into resonance instead. This realizes two concatenated CSWAP operations in a single step.

Dans ce projet, l'ensemble du système est quantique : les spins électroniques et nucléaires individuels dans le solide, leurs interactions mutuelles, le résonateur supraconducteur utilisé pour médier et lire ces interactions, ainsi que la chaîne de mesure micro-onde quantique participent tous à l'expérience en tant qu'objets quantiques. Un tel projet requiert donc un ou une candidate disposant d'une solide formation en physique quantique, ainsi que d'un goût prononcé pour la physique expérimentale à l'interface entre la physique des spins, les circuits supraconducteurs, l'électronique micro-onde, la mesure quantique et le traitement quantique de l'information.

La personne recherchée devra être à l'aise avec les notions de dynamique de spin, de cohérence et de contrôle de qubits, et manifester un intérêt marqué pour le développement et la mise en oeuvre d'expériences cryogéniques de pointe. Une appétence pour le travail pluridisciplinaire sera essentielle, car le projet combine des éléments de physique de la matière condensée, d'électronique micro-onde, de nanofabrication, de spectroscopie et d'ingénierie quantique. Une expérience préalable dans un ou plusieurs de ces domaines serait appréciée, mais la curiosité, la rigueur scientifique et l'enthousiasme à apprendre de nouvelles techniques seront tout aussi importants.