Engineering a Quantum Many-body Hamiltonian with Trapped Ions

While fault-tolerant quantum computation might still be years away, analog quantum simulators offer a way to leverage current quantum technologies to study classically intractable quantum systems. Cutting edge quantum simulators such as those utilizing ultracold atoms are beginning to study physics which surpass what is classically tractable. As the system sizes of these quantum simulators increase, there are also concurrent gains in the complexity and types of Hamiltonians which can be simulated. In this work, I describe advances toward the realization of an adaptable, tunable quantum simulator capable of surpassing classical computation. We simulate long-ranged Ising and XY spin models which can have global arbitrary transverse and longitudinal fields in addition to individual transverse fields using a linear chain of up to 24 Yb+ 171 ions confined in a linear rf Paul trap. Each qubit is encoded in the ground state hyperfine levels of an ion. Spin-spin interactions are engineered by the application of spin-dependent forces from laser fields, coupling spin to motion. Each spin can be read independently using state-dependent fluorescence. The results here add yet more tools to an ever growing quantum simulation toolbox. One of many challenges has been the coherent manipulation of individual qubits. By using a surprisingly large fourth-order Stark shifts in a clock-state qubit, we demonstrate an ability to individually manipulate spins and apply independent Hamiltonian terms, greatly increasing the range of quantum simulations which can be implemented. As quantum systems grow beyond the capability of classical numerics, a constant question is how to verify a quantum simulation. Here, I present measurements which may provide useful metrics for large system sizes and demonstrate them in a system of up to 24 ions during a classically intractable simulation. The observed values are consistent with extremely large entangled states, as much as ~95% of the system entangled. Finally, we use many of these techniques in order to generate a spin Hamiltonian which fails to thermalize during experimental time scales due to a meta-stable state which is often called prethermal. The observed prethermal state is a new form of prethermalization which arises due to long-range interactions and open boundary conditions, even in the thermodynamic limit. This prethermalization is observed in a system of up to 22 spins. We expect that system sizes can be extended up to 30 spins with only minor upgrades to the current apparatus. These results emphasize that as the technology improves, the techniques and tools developed here can potentially be used to perform simulations which will surpass the capability of even the most sophisticated classical techniques, enabling the study of a whole new regime of quantum many-body physics.

Quantum Gate and Quantum State Preparation through Neighboring Optimal Control

Successful implementation of fault-tolerant quantum computation on a system of qubits places severe demands on the hardware used to control the many-qubit state. It is known that an accuracy threshold Pa exists for any quantum gate that is to be used for such a computation to be able to continue for an unlimited number of steps. Specifically, the error probability Pe for such a gate must fall below the accuracy threshold: Pe < Pa. Estimates of Pa vary widely, though Pa ∼ 10−4 has emerged as a challenging target for hardware designers. I present a theoretical framework based on neighboring optimal control that takes as input a good quantum gate and returns a new gate with better performance. I illustrate this approach by applying it to a universal set of quantum gates produced using non-adiabatic rapid passage. Performance improvements are substantial comparing to the original (unimproved) gates, both for ideal and non-ideal controls. Under suitable conditions detailed below, all gate error probabilities fall by 1 to 4 orders of magnitude below the target threshold of 10−4. After applying the neighboring optimal control theory to improve the performance of quantum gates in a universal set, I further apply the general control theory in a two-step procedure for fault-tolerant logical state preparation, and I illustrate this procedure by preparing a logical Bell state fault-tolerantly. The two-step preparation procedure is as follow: Step 1 provides a one-shot procedure using neighboring optimal control theory to prepare a physical qubit state which is a high-fidelity approximation to the Bell state |β01⟩ = 1/√2(|01⟩ + |10⟩). I show that for ideal (non-ideal) control, an approximate |β01⟩ state could be prepared with error probability ϵ ∼ 10−6 (10−5) with one-shot local operations. Step 2 then takes a block of p pairs of physical qubits, each prepared in |β01⟩ state using Step 1, and fault-tolerantly prepares the logical Bell state for the C4 quantum error detection code.

ENZYME-FREE UBIQUITIN LIGATION. FROM NATIVE CHEMICAL LIGATION AND SPIN LABELING TO DIMERIZATION BY INTER-UBIQUITIN MIMICKING LINKAGE AND PH-DEPENDENT CONFORMATIONAL SWITCH

The delicate balance between the production and disposal of proteins is vital for the changes required in the cell to respond to given stimulus. Ubiquitination is a protein modification with a range of signaling outcomes when ubiquitin is attached to a protein through a highly ordered enzymatic cascade process. Understanding ubiquitination is a growing field and nowadays the application of chemical reactions allows the isolation of quantitative materials for structural studies. Therefore, in this dissertation it is described some of these suitable chemical methodologies to produce an isopeptide bond toward the polymerization of ubiquitin bypassing the enzymatic control with the purpose of showing if these chemical modifications have a direct impact on the structure of ubiquitin. First, the possibility of incorporating non-natural lysine analogs known as mercaptolysines into the polypeptide chain of Ubiquitin was explored when they were attached to ubiquitin by native chemical ligation at its C terminus. The sulfhydryl group was used for the attachment of a paramagnetic label to map the surface of ubiquitin. Second, the condensation catalyzed by silver nitrate was used for the dimer assembly. In particular, the main focus was on examining whether orthogonal protection and deprotection of each monomer have an impact on the reaction yield, since the synthetic strategy has been previously attempted successfully. Third, the formation of ubiquitin dimers was approached by building an inter-ubiquitin linkage mimicking the isopeptide bond with two approaches, the classic disulfide exchange as well as the thiol-ene click reaction by thermal initiation in aqueous conditions. After assembling the dimeric units, they were studied by Nuclear Magnetic Resonance, in order to establish a conformational state profile which depends on the pH conditions. The latter is a very important concept since some ligands have a preferred affinity when the protein-protein hydrophobic patches are in close proximity.