Atom-ion quantum gate

We study ultracold collisions of ions with neutral atoms in traps. Recently, ultracold atom-ion systems are becoming available in experimental setups, where their quantum states can be coherently controlled. This allows for an implementation of quantum information processing combining the advantages of charged and neutral particles. The state-dependent dynamics that is a necessary ingredient for quantum computation schemes is provided in this case by the short-range interaction forces depending on hyperfine states of both particles. In this work we develop a theoretical description of spin-state-dependent trapped atom-ion collisions in the framework of a Multichannel Quantum Defect Theory (MQDT) and formulate an effective single channel model that reduces the complexity of the problem. Based on this description we simulate a two-qubit phase gate between a Ba135+ ion and a Rb87 atom using a realistic combination of the singlet and triplet scattering lengths. We optimize and accelerate the gate process with the help of optimal control techniques. Our result is a gate fidelity 0.999 within 350 microseconds.Comment: 15 pages, submitted to Phys. Rev. A, added references to Section I, corrected typos, improved Section II

Compressive gate set tomography

Flexible characterization techniques that identify and quantify experimental imperfections under realistic assumptions are crucial for the development of quantum computers. Gate set tomography is a characterization approach that simultaneously and self-consistently extracts a tomographic description of the implementation of an entire set of quantum gates, as well as the initial state and measurement, from experimental data. Obtaining such a detailed picture of the experimental implementation is associated with high requirements on the number of sequences and their design, making gate set tomography a challenging task even for only two qubits. In this work, we show that low-rank approximations of gate sets can be obtained from significantly fewer gate sequences and that it is sufficient to draw them randomly. Such tomographic information is needed for the crucial task of dealing with coherent noise. To this end, we formulate the data processing problem of gate set tomography as a rank-constrained tensor completion problem. We provide an algorithm to solve this problem while respecting the usual positivity and normalization constraints of quantum mechanics by using second-order geometrical optimization methods on the complex Stiefel manifold. Besides the reduction in sequences, we demonstrate numerically that the algorithm does not rely on structured gate sets or an elaborate circuit design to robustly perform gate set tomography and is therefore more broadly applicable than traditional approaches.Comment: 14+12 pages, several figures and diagram

Towards optical quantum information processing using Rydberg dark-state polaritons

This thesis proposes a novel method to implement universal quantum gates for photonic qubits using the strong dipole-dipole interactions present in a cold gas of Rydberg atoms and the control offered by microwave fields. By means of electromagnetically induced transparency (EIT) we store the information encoded in photonic qubits as Rydberg excitations, and then couple these to neighbouring states using microwaves. Microwaves alter the range of the dipole-dipole interactions between the excitations, and a suitable geometrical arrangement of the excitations in the cloud leads to a controlled $\pi$ phase shift in the system's wavefunction, the basis of the universal gates proposed. After processing, the excitations in the medium are later retrieved as photons. A theoretical description of the implementation of a 2-qubit universal gate is presented and a numerical analysis shows the feasibility of its implementation in a cold cloud of Rubidium atoms. A scheme is also proposed to construct more general gates with applications in quantum information processing. These schemes have been made possible by the analysis of recent experiments performed in the group. This analysis is repeated here, along with the characterization of parts of the detection system required to obtain them

Localized Excitation of Single Atom to a Rydberg State with Structured Laser Beam for Quantum Information

Sufficient control over the excitation of the Rydberg atom as a quantum memory is crucial for the fast and deterministic preparation and manipulation of the quantum information. Considering the Laguerre-Gaussian (LG) beam spatial features, localized excitation of a four-level atom to a highly excited Rydberg state is presented. The position-dependent AC-Stark shift of the first and Rydberg state in the effective quadrupole two-level description of a far-detuned three-photon Rydberg excitation results in a steep trapping potential for Rydberg state. The transfer of optical orbital angular momentum from LG beam to the Rydberg state via quadrupole transition in the last Rydberg excitation process offers a long-lived and controllable qudit quantum memory. The effective quadrupole Rabi frequency is presented as a function of ratio of the first to Rydberg excitation laser beam waist and the center of mass position inside the trap. It depicts high accuracy of detecting Rydberg atom at the center of the trap, which can pave the way for implementation of high-fidelity qudit gate

Extending scientific computing system with structural quantum programming capabilities

We present a basic high-level structures used for developing quantum programming languages. The presented structures are commonly used in many existing quantum programming languages and we use quantum pseudo-code based on QCL quantum programming language to describe them. We also present the implementation of introduced structures in GNU Octave language for scientific computing. Procedures used in the implementation are available as a package quantum-octave, providing a library of functions, which facilitates the simulation of quantum computing. This package allows also to incorporate high-level programming concepts into the simulation in GNU Octave and Matlab. As such it connects features unique for high-level quantum programming languages, with the full palette of efficient computational routines commonly available in modern scientific computing systems. To present the major features of the described package we provide the implementation of selected quantum algorithms. We also show how quantum errors can be taken into account during the simulation of quantum algorithms using quantum-octave package. This is possible thanks to the ability to operate on density matrices

Quantum Dot Cellular Automata Check Node Implementation for LDPC Decoders

The quantum dot Cellular Automata (QCA) is an emerging nanotechnology that has gained significant research interest in recent years. Extremely small feature sizes, ultralow power consumption, and high clock frequency make QCA a potentially attractive solution for implementing computing architectures at the nanoscale. To be considered as a suitable CMOS substitute, the QCA technology must be able to implement complex real-time applications with affordable complexity. Low density parity check (LDPC) decoding is one of such applications. The core of LDPC decoding lies in the check node (CN) processing element which executes actual decoding algorithm and contributes toward overall performance and complexity of the LDPC decoder. This study presents a novel QCA architecture for partial parallel, layered LDPC check node. The CN executes Normalized Min Sum decoding algorithm and is flexible to support CN degree dc up to 20. The CN is constructed using a VHDL behavioral model of QCA elementary circuits which provides a hierarchical bottom up approach to evaluate the logical behavior, area, and power dissipation of the whole design. Performance evaluations are reported for the two main implementations of QCA i.e. molecular and magneti