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Coherent Flux Qubits for Quantum Annealing

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Universitat de Barcelona. Facultat de Física

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[eng] Quantum annealing is a heuristic analog quantum algorithm that promises potential quantum speedup over classical algorithms for a huge variety of optimization problems. Current existing annealers, despite their technical complexity and large qubit number, in the several thousands, display very short coherence times, making the annealing process incoherent.

The main goal of this thesis is to initiate an alternative path towards building coherent quantum annealers based on superconducting flux qubits. In this thesis, many techniques and methods have been established, and the results obtained represent the first coherent control of superconducting qubits in the QCT group, and, in general, in Southern Europe.

An uncoupled flux qubit device is designed to benchmark qubit coherence that will be used as the building block for future iterations of coherent quantum annealers. The Hamiltonian design of the flux qubits is focused on reducing the persistent current to reduce flux noise susceptibility. The processor is designed so that common coherence benchmarking experiments, such as T1 and T2 measurements, are performed. The physical design has been iterated to understand the role the qubit loop configurations and the qubit frequency have on the coherence times.

The flux qubits are measured inside a dilution refrigerator, where special focus is put on magnetic shielding. Spectroscopy measurements provide initial information on the qubit parameters and quality.  Coherent control of flux qubits is achieved in the form of coherent Rabi oscillations, which constitutes one of the most important results of this thesis. Rabi oscillations are repeated for many flux operation points to understand the noise mechanisms. Decay times of 40us are shown, which are among the best results for flux qubits. However, the qubit coherence is low, leading to coherence times shorter than 20ns, probably because of flux noise. Moreover, due to device imperfections, the qubits could not be characterized at their optimal coherence conditions, which otherwise corresponds to the initial configuration for quantum annealing. In summary, the coherence results of the flux qubits measured represent an important benchmark in the development of a coherent quantum annealer and provide very valuable information on how to improve the flux qubits for future iterations of quantum annealing processors.

As an initial ramp-up phase of this thesis work, experiments with transmons qubits, which are a very well established technology, were performed to develop the time-domain measurement techniques in the newly established QCT lab, and to set a superconducting quantum computing setup ready to perform quantum algorithms. Indeed, a Universal Approximant algorithm was executed on a single transmon qubit to experimentally prove the approximation capabilities of a single-qubit quantum algorithm.

In parallel to the development of qubit experiments, intrinsic properties of thin-film aluminum has been studied, being the most common material for building superconducting qubit circuits. The magnetic penetration depth of thin film superconducting aluminum has been studied as a function of the film thickness. This calibration, not previously performed in the literature, is especially relevant for the design of flux-sensitive devices, such as flux qubits. The penetration depth is closely related to the so-called kinetic inductance, which is a significant portion of the total inductance in superconductors. This study allows for a better design determination of the inductance in superconducting circuits. Moreover, it points to the possibility of a change in superconductivity type in aluminum in the typical range of thicknesses used in superconducting circuit experiments.

Finally, and in relation to improving the qubit readout fidelity, through a brief stay in NTT (Japan) a quantum-limited amplifier has been redesigned to improve its usability. The quantum-limited amplifier is theoretically identical as one already developed by Arpit Ranadive from the Grenoble team led by Dr. Nicolas Roch, a collaborator of the QCT group, which consists on an array of Superconducting Nonlinear Asymmetric Inductive eLement (SNAIL). The SNAIL circuit is identical to that of the flux qubit, but operated in a different regime. The work developed here will be continued with the fabrication of the actual devices.

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[cat] El "quantum annealing" és un algorisme quàntic analògic heurístic que ofereix una possible avantatge quàntica sobre els algorismes clàssics per a una àmplia gamma de problemes d'optimització. Malgrat la complexitat tècnica i el considerable nombre de qubits en els processadors de "quantum annealing" existents, aquests mostren temps de coherència molt curts, resultant en un procés d'annealing incoherent.

La tesi té com a objectiu principal obrir un camí alternatiu cap a la construcció de "quantum annealers" coherents basats en "flux qubits" superconductors. S'han establert diverses tècniques i mètodes, i els resultats obtinguts representen el primer control coherent de qubits superconductors al grup QCT i, en general, al sud d'Europa.

S'ha dissenyat un dispositiu de "flux qubits" desacoblat per mesurar la coherència dels qubits, que s'utilitzaran com a component bàsic per a futures iteracions de "quantum annealers" coherents. Els flux qubits es mesuren dins d'un refrigerador de dilució, prestant especial atenció a l'aïllament magnètic. El control coherent dels qubits de flux s'aconsegueix mitjançant oscil·lacions de Rabi coherents, repetides en diversos punts d'operació del flux magnètic per comprendre els mecanismes del soroll. S'han observat temps de decaïment de 40 us, que es troben entre els millors resultats per a "flux qubits". No obstant això, la coherència del qubit és baixa, la qual cosa resulta en temps de coherència inferiors a 20 ns, probablement a causa del soroll magnètic. A causa d'imperfeccions en el dispositiu, els qubits no van poder ser caracteritzats en condicions òptimes de coherència, que correspondrien a la configuració inicial per a "quantum annealing". En resum, els resultats de coherència mesurats en els qubits de flux representen un avenç important en el desenvolupament d'un "quantum annealer" coherent i ofereixen informació valuosa sobre com millorar els qubits de flux per a futures iteracions de processadors.

Paral·lelament al desenvolupament d'experiments amb qubits, s'han estudiat les propietats intrínseques de capes primes d'alumini, el material més comú per construir circuits de qubits superconductors. S'ha investigat la profunditat de penetració magnètica de l'alumini superconductor de capa prima en funció de l'ample de la capa. Aquesta calibració, que no s'havia realitzat prèviament a la literatura, és especialment rellevant per al disseny de dispositius sensibles al flux, com els "flux qubits".

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Coherent Flux Qubits for Quantum Annealing