Noise-tolerant quantum speedups in quantum annealing without fine tuning

Quantum annealing is a powerful alternative model for quantum computing, which can succeed in the presence of environmental noise even without error correction. However, despite great effort, no conclusive proof of a quantum speedup (relative to state of the art classical algorithms) has been shown for these systems, and rigorous theoretical proofs of a quantum advantage generally rely on exponential precision in at least some aspects of the system, an unphysical resource guaranteed to be scrambled by random noise. In this work, we propose a new variant of quantum annealing, called RFQA, which can maintain a scalable quantum speedup in the face of noise and modest control precision. Specifically, we consider a modification of flux qubit-based quantum annealing which includes random, but coherent, low-frequency oscillations in the directions of the transverse field terms as the system evolves. We show that this method produces a quantum speedup for finding ground states in the Grover problem and quantum random energy model, and thus should be widely applicable to other hard optimization problems which can be formulated as quantum spin glasses. Further, we show that this speedup should be resilient to two realistic noise channels ($1/f$-like local potential fluctuations and local heating from interaction with a finite temperature bath), and that another noise channel, bath-assisted quantum phase transitions, actually accelerates the algorithm and may outweigh the negative effects of the others. The modifications we consider have a straightforward experimental implementation and could be explored with current technology.Comment: 21 pages, 7 figure

Qubit measurement and coupling strategies and their applications

A quantum computer can reduce the amount of computational effort for selected applications exponentially by taking advantage of quantum mechanical phenomena of nature. For the realization of a real-world quantum computer, among other things, optimized qubit measurements and qubit coupling schemes are indispensable. This dissertation uses theoretical tools to develop novel measurement and coupling strategies in different superconducting qubit architectures. In a first part of the thesis a protocol for multi-qubit parity measurements of Transmon qubit registers is presented, which takes advantage of the nonlinear energy level structure to strongly increase contrast, while at the same time achieving high fidelities and being quantum non-demolishing. The second part focuses on superconducting flux qubits, which are promising for adiabatic quantum computing. First a novel indirect flux qubit measurement protocol is introduced, which provides the ability to measure in a fixed basis, the persistent current basis, independent of the qubit energy eigenbasis. Second it is shown that the limitation of natural interactions to pairwise interactions can be overcome by using a nonlinear coupler and four flux qubits. The achieved four local interactions between the qubits are proven to be in the strong coupling regime and even exceed the two local ones for the right system parameters.Ein Quantencomputer besitzt das Potenzial den Rechenaufwand für bestimmte Aufgaben gegenüber einem klassischen Computer exponentiell zu reduzieren, indem er sich quantenmechanischer Phänomene der Natur bedient. Zur Realisierung eines echten Quantencomputers sind, neben anderen Bestandteilen, optimierte Mess- und Kopplungsschemata für Qubits unabdingbar. Diese Dissertation befasst sich damit theoretische Mittel zu nutzen, um neue Mess- und Kopplunsstrategien in verschiedenen supraleitenden Qubitarchitekturen zu entwickeln. In dem ersten Teil der Arbeit wird ein neues Protokoll zur Paritätsmessung von Registern aus Transmon Qubits vorgestellt, welches die nichtlineare Energiestruktur ausnutzt, um den Kontrast der Messung stark zu erhöhen und zudem sowohl einen hohe Messgüte aufweist als auch QND ist. Der zweite Teil fokussiert sich auf supraleitende Flussqubits, die vor allem beim adiabatischen Quantencomputer genutzt werden. Zuerst wird ein neues, indirektes Messprotokol vorgestellt, welches die Möglichkeit bietet in einer festen Basis, der Dauerstrombasis, unabhängig von der jeweiligen Energieeigenbasis, zu messen. Danach wird gezeigt, dass die Einschränkung von natürlichen Wechselwirkungen auf paarweise Wechselwirkung überwunden werden kann, indem man vier Flussqubits mittels eines nichtlinearen Kopplers verknüpft. Die erreichten Viererwechselwirkungen zwischen den Qubits sind im Regime starker Kopplung und können für die richtigen Systemparameter die paarweisen Wechselwirkungen überschreiten

Digital quantum simulations of spin models with superconducting circuits

143 p.A lo largo de la historia, el ser humano, consciente de su incapacidad natural para realizar diversas tareas, ha utilizado herramientas que le han permitido afrontar de forma cada vez más satisfactoria los problemas de cada época. Estos avances que van desde las lanzas prehistóricas para cazar mamuts hasta los aviones actuales para llegar al otro lado del mundo en cuestión de horas, han provisto a los humanos de habilidades que la naturaleza no nos ha brindado. No es distinto el caso particular de la computación. Desde niños hemos aprendido a hacer uso de elementos más allá de nuestra mente analítica para la realización de todo tipo de cálculos. Contar con los dedos, utilizar un ábaco o un papel y un lápiz, y en última instancia hacer uso de un ordenador son solo algunos ejemplos de ello. Hay quien podría pensar erróneamente que los superordenadores con tecnología puntera son capaces de resolver los problemas computacionales más complejos pero la verdad es que posiblemente nunca lleguen a conseguirlo

Out-of-equilibrium many-body quantum systems with respect to adiabatic quantum computing through the lens of the Pechukas–Yukawa framework

We investigate the theoretical description of adiabatic quantum computing (AQC) algorithms using the evolution of the Hamiltonian eigenvalues in the framework of the Pechukas–Yukawa formalism, exactly mapping the eigenvalues to the dynamics of a fictitious one-dimensional classical gas with cubic repulsion. We exploit the properties of the Pechukas-Yukawa model to describe the behaviour of quantum algorithms used in AQC. Specifically, we derive the non-equilibrium nonstationary statistical mechanics of the Pechukas–Yukawa gas based on the Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) chain of equations with the goal of increasing the efficiency of direct numerical simulation. We extended our research to consider the impacts of level crossings and avoided crossings to evaluate the compatibility of the Pechukas–Yukawa formalism and the Landau–Zener description of these occurrences. This is valuable to the investigation of decoherence in a quantum system and carries scope for research on the description of state dynamics through the energy level dynamics. We relate the evolution of a quantum state of a system under external perturbation to that of its energy levels. Using this relationship, we produced a cumulant expansion with improved efficiency compared to traditional methods of approximate quantum state evolution description. It is especially significant for the investigation of decoherence in an evolving quantum system.</div

Quantum Information in Rydberg-Dressed Atoms

In any physical platform, two ingredients are essential for quantum information processing: single-qubit control, and entangling interactions between qubits. Neutral atoms can be individually controlled with high fidelity and are resilient to environmental noise, making them attractive candidates for implementing quantum information protocols. However, achieving strong interactions remains a major obstacle. One way to increase the interaction strength between neutral atoms is to excite them into high-lying Rydberg states, which exhibit large electric dipole moments (and by extension, strong electric dipole-dipole interactions). By slowly ramping up the Rydberg level coupling in a system, one can dress\u27\u27 the atomic ground states with some Rydberg character; this maps the Rydberg dipole interaction to an effective interaction between ground states. Such Rydberg-dressed interaction is the focus of this dissertation. After describing the physics of the Rydberg-dressed interaction, we propose three protocols that demonstrate its versatility and provide a framework for considering some of the details of realistic implementation. In all three cases, Rydberg dressing --- along with some form of single-atom control --- is used to generate highly entangled states of interest. Our first proposal relates to the adiabatic model of quantum computing, in which solutions to problems are encoded in the ground states of carefully engineered Hamiltonians. The Rydberg-dressed interaction can provide nonlinear Hamiltonian terms, allowing us to encode NP-hard and other interesting problems. We model this protocol in the presence of decoherence, and find that computational fidelities of ~0.98 for four atoms should be possible with currently realistic experimental parameters. Our second proposal is also related to quantum computing, this time in the circuit model. The Rydberg-dressed interaction can be used to generate a controlled-NOT logic gate which, when interwoven with single-qubit gates, can perform universal quantum computation. Experimentally, noise due to atomic thermal motion has been a primary limitation on the fidelities of these gates. We show that a Doppler-free setup, with counterpropagating lasers, effectively suppresses this type of noise, allowing simulated fidelities of up to ~0.998 per gate. Such strong suppression is only possible because the Doppler-free configuration can harness the natural robustness of adiabatic dressing; other gate schemes using, e.g., resonant pulses, do not exhibit the same degree of improvement. Finally, we consider exploiting the many-body character of the Rydberg-dressed interaction to generate collective entanglement in mesoscopic ensembles of neutral atoms. An atomic ensemble uniformly illuminated by a single Rydberg-exciting laser is isomorphic to the well-known Jaynes-Cummings model. In addition to adapting generic Jaynes-Cummings entanglement protocols developed in other platforms, one can apply microwaves to drive entanglement in a way that is unique to the atomic platform. We prove that by allowing the microwave phase to vary in time, one can generate arbitrary symmetric states of the ensemble. While this method compares favorably with other entanglement protocols in many ways, the required frequency of phase switching presents a fundamental limitation on its effectiveness. To mitigate this, we propose a variant scheme in which parameters are chosen to only allow excitations within the system\u27s dressed-ground subspace; this effectively cuts phase switching demands in half. All three protocols serve to illustrate the power of the Rydberg-dressed interaction and suggest directions for future study