One of the useful applications of a quantum computer is quantum simulation. While the quest for a universal quantum computer is still undergoing research, analog quantum simulators can study specific quantum models that are classically challenging or even intractable. These quantum simulators provide the opportunity to test particular quantum models and scale up the system size to gain insight into more exciting physics. The analog quantum simulator featured in this thesis is a cryogenic trapped-ion system. It serves the purpose of a large-scale quantum simulation by reducing the background pressure for storing a large ion chain with a long lifetime. This work presents the construction and characterization of this cryogenic apparatus and its performance as a trapped-ion quantum simulator. Quantum information is encoded in the atomic state of the ion chain. The entangling operation in trapped ions uses the collective motion of the ion chain for quantum simulation. Therefore, it is imperative to develop a cooling mechanism to prepare the ion chain to near motional ground-state for achieving high fidelity operations. Here, with this system, we explore another ground-state cooling mechanism with electromagnetically induced transparency (EIT) in a four-level system (171Yb+). EIT cooling allows simultaneous ground-state cooling across a bandwidth of motional modes, which it is useful in a large ion chain. Finally, we report the observation of magnetic domain-wall confinement in interacting spins chains. Such confinement is analogous to the color confinement in quantum chromodynamics (QCD), where hadrons are produced by quark confinement. We study the implications of such confinement in many-body spin system by observing the information propagation after applying a quantum quench of the confinement Hamiltonian. We also measure the excitation energy of domain-wall bound states from non-equilibrium quench dynamics. At the end of this experiment, we explore the number of domain wall excitations created with different quench parameters, which can be challenging to model with classical computers.
Trapped-ion systems are among the most promising hardware candidates for large scale quantum computing and quantum simulation. In order to scale up such devices, it is necessary to engineer extreme-high vacuum (XHV) environments to prevent background gas from disrupting the ion crystal. Here we present a new cryogenic ion trapping system designed for long time storage of large ion chains. Our apparatus is based on a segmented-blade ion trap enclosed in a 4 K cryostat, which enables us to routinely trap and hold over 100 171 Yb + ions for hours in a linear configuration, due to low background gas pressure from differential cryo-pumping. We characterize the XHV cryogenic environment measuring pressures below by recording both inelastic and elastic collisions between the ion chain and the molecular background gas. We also demonstrate coherent one and two-qubit operations and nearly equidistant ion spacing for chains of up to 44 ions using anharmonic axial potentials, in order to enable better detection and single ion addressing in large ion arrays. We anticipate that this reliable production and lifetime enhancement of large linear ion chains will enable quantum simulation of models that are intractable with classical computer modeling.
While realizing a fully functional quantum computer presents a long term technical goal, in the present, there are small to mid-sized quantum simulators (up to
∼100 qubits), that are capable of approaching specialized problems. The quantum simulator discussed here uses trapped ions to act as qubits and is housed in a cryogenically cooled vacuum chamber in order to reduce the background pressure, thereby increasing ion chain length and life-time. The details of performance and characterization of this cryogenic apparatus are discussed, and this system is used to study many-body dephasing in a finite-sized quantum spin system. How a closed quantum many-body system relaxes and dephases as a function of time is important to understand when dealing with many-body spin systems. In this work, the first experimental observation of persistent temporal fluctuations after a quantum quench is presented with a tunable long-range interacting transverse-field Ising Hamiltonian. The fluctuations in the average magnetization of a finite-size system of spin-
1/2 particles are measured presenting a direct measurement of relaxation dynamics in a non-integrable system. This experiment is in the regime where the properties of the system are closely related to the integrable Hamiltonian with global coupling. The system size is varied in order to investigate the dependence on finite-size scaling, and the system size scaling exponent extracted from the measured fluctuations is consistent with theoretical prediction.