Micro-Fabricated Surface Trap and Cavity Integration for Trapped Ion Quantum Computing

Atomic ions trapped in micro-fabricated surface traps can be utilized as a physical platform with which to build a quantum computer. They possess many of the desirable qualities of such a device, including high fidelity state preparation and readout, universal logic gates, long coherence times, and can be readily entangled with each other through photonic interconnects. The use of optical cavities integrated with trapped ion qubits as a photonic interface presents the possibility for order of magnitude improvements in performance in several key areas of their use in quantum computation. The first part of this thesis describes the design and fabrication of a novel surface trap for integration with an optical cavity. The trap is custom made on a highly reflective mirror surface and includes the capability of moving the ion trap location along all three trap axes with nanometer scale precision. The second part of this thesis demonstrates the suitability of small micro-cavities formed from laser ablated fused silica substrates with radii of curvature in the 300-500 micron range for use with the mirror trap as part of an integrated ion trap cavity system. Quantum computing applications for such a system include dramatic improvements in the photonic entanglement rate up to 10 kHz, the qubit measurement time down to 1 microsecond, and the measurement error rates down to the 10e-5 range. The final part of this thesis details a performance simulator for exploring the physical resource requirements and performance demands to scale such a quantum computer to sizes capable of performing quantum algorithms beyond the limits of classical computation.

Quantum computing and post-quantum cryptography

One of the main practical implications of quantum mechanical theory is quantum computing, and therefore the quantum computer. Quantum computing (for example, with Shor’s algorithm) challenges the computational hardness assumptions, such as the factoring problem and the discrete logarithm problem, that anchor the safety of cryptosystems. So the scientific community is studying how to defend cryptography; there are two defense strategies: the quantum cryptography (which involves the use of quantum cryptographic algorithms on quantum computers) and the post-quantum cryptography (based on classical cryptographic algorithms, but resistant to quantum computers). For example, National Institute of Standards and Technology (NIST) is collecting and standardizing the post-quantum ciphers, as it established DES and AES as symmetric cipher standards, in the past. In this thesis an introduction on quantum mechanics was given, in order to be able to talk about quantum computing and to analyze Shor’s algorithm. The differences between quantum and post-quantum cryptography were then analyzed. Subsequently the focus was given to the mathematical problems assumed to be resistant to quantum computers. To conclude, post-quantum digital signature cryptographic algorithms selected by NIST were studied and compared in order to apply them in today’s life.

A study of the relaxation dynamics in a quadrupolar NMR system using Quantum State Tomography

This article reports a relaxation study in an oriented system containing spin 3/2 nuclei using quantum state tomography (QST). The use of QST allowed evaluating the time evolution of all density matrix elements starting from several initial states. Using an appropriated treatment based on the Redfield theory, the relaxation rate of each density matrix element was measured and the reduced spectral densities that describe the system relaxation were determined. All the experimental data could be well described assuming pure quadrupolar relaxation and reduced spectral densities corresponding to a superposition of slow and fast motions. The data were also analyzed in the context of Quantum Information Processing, where the coherence loss of each qubit of the system was determined using the partial trace operation. (C) 2008 Elsevier Inc. All rights reserved.

Study of charge, spin, and structural orderings in quantum materials using nuclei and muons as local probes

Quantum Materials are many body systems displaying emergent phenomena caused by quantum collective behaviour, such as superconductivity, charge density wave, fractional hall effect, and exotic magnetism. Among quantum materials, two families have recently attracted attention: kagome metals and Kitaev materials. Kagome metals have a unique crystal structure made up of triangular lattice layers that are used to form the kagome layer. Due to superconductivity, magnetism, and charge ordering states such as the Charge Density Wave (CDW), unexpected physical phenomena such as the massive Anomalous Hall Effect (AHE) and possible Majorana fermions develop in these materials. Kitaev materials are a type of quantum material with a unique spin model named after Alexei Kitaev. They include fractional fluctuations of Majorana fermions and non-topological abelian anyons, both of which might be used in quantum computing. Furthermore, they provide a realistic framework for the development of quantum spin liquid (QSL), in which quantum fluctuations produce long-range entanglements between electronic states despite the lack of classical magnetic ordering. In my research, I performed several nuclear magnetic resonance (NMR), nuclear quadrupole resonance (NQR), and muon spin spectroscopy (µSR) experiments to explain and unravel novel phases of matter within these unusual families of materials. NMR has been found to be an excellent tool for studying these materials’ local electronic structures and magnetic properties. I could use NMR to determine, for the first time, the structure of a novel kagome superconductor, RbV3Sb5, below the CDW transition, and to highlight the role of chemical doping in the CDW phase of AV3Sb5 superconductors. µSR has been used to investigate the effect of doping on kagome material samples in order to study the presence and behaviour of an anomalous phase developing at low temperatures and possibly related to time-reversal symmetry breaking.

Hyperfine interactions in silicon quantum dots

A fundamental interaction for electrons is their hyperfine interaction (HFI) with nuclear spins. HFI is well characterized in free atoms and molecules, and is crucial for purposes from chemical identification of atoms to trapped ion quantum computing. However, electron wave functions near atomic sites, therefore HFI, are often not accurately known in solids. Here we perform an all-electron calculation for conduction electrons in silicon and obtain reliable information on HFI. We verify the outstanding quantum spin coherence in Si, which is critical for fault-tolerant solid state quantum computing.

NMR analog of Bell's inequalities violation test

In this paper, we present an analog of Bell's inequalities violation test for N qubits to be performed in a nuclear magnetic resonance (NMR) quantum computer. This can be used to simulate or predict the results for different Bell's inequality tests, with distinct configurations and a larger number of qubits. To demonstrate our scheme, we implemented a simulation of the violation of the Clauser, Horne, Shimony and Holt (CHSH) inequality using a two-qubit NMR system and compared the results to those of a photon experiment. The experimental results are well described by the quantum mechanics theory and a local realistic hidden variables model (LRHVM) that was specifically developed for NMR. That is why we refer to this experiment as a simulation of Bell's inequality violation. Our result shows explicitly how the two theories can be compatible with each other due to the detection loophole. In the last part of this work, we discuss the possibility of testing some fundamental features of quantum mechanics using NMR with highly polarized spins, where a strong discrepancy between quantum mechanics and hidden variables models can be expected.

Fault-tolerant quantum computation with cluster states

The one-way quantum computing model introduced by Raussendorf and Briegel [Phys. Rev. Lett. 86, 5188 (2001)] shows that it is possible to quantum compute using only a fixed entangled resource known as a cluster state, and adaptive single-qubit measurements. This model is the basis for several practical proposals for quantum computation, including a promising proposal for optical quantum computation based on cluster states [M. A. Nielsen, Phys. Rev. Lett. (to be published), quant-ph/0402005]. A significant open question is whether such proposals are scalable in the presence of physically realistic noise. In this paper we prove two threshold theorems which show that scalable fault-tolerant quantum computation may be achieved in implementations based on cluster states, provided the noise in the implementations is below some constant threshold value. Our first threshold theorem applies to a class of implementations in which entangling gates are applied deterministically, but with a small amount of noise. We expect this threshold to be applicable in a wide variety of physical systems. Our second threshold theorem is specifically adapted to proposals such as the optical cluster-state proposal, in which nondeterministic entangling gates are used. A critical technical component of our proofs is two powerful theorems which relate the properties of noisy unitary operations restricted to act on a subspace of state space to extensions of those operations acting on the entire state space. We expect these theorems to have a variety of applications in other areas of quantum-information science.

Quantum control and quantum entanglement

We discuss quantum error correction for errors that occur at random times as described by, a conditional Poisson process. We shoo, how a class of such errors, detected spontaneous emission, can be corrected by continuous closed loop, feedback.

Quantum nonlocality, cryptography and complexity

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

Quantum control of electromagnetically induced transparency dispersion via atomic tunneling in a double-well Bose-Einstein condensate

Electromagnetically induced transparency (EIT) is an important tool for controlling light propagation and nonlinear wave mixing in atomic gases with potential applications ranging from quantum computing to table top tests of general relativity. Here we consider EIT in an atomic Bose-Einstein condensate (BEC) trapped in a double-well potential. A weak probe laser propagates through one of the wells and interacts with atoms in a three-level Lambda configuration. The well through which the probe propagates is dressed by a strong control laser with Rabi frequency Omega(mu), as in standard EIT systems. Tunneling between the wells at the frequency g provides a coherent coupling between identical electronic states in the two wells, which leads to the formation of interwell dressed states. The macroscopic interwell coherence of the BEC wave function results in the formation of two ultranarrow absorption resonances for the probe field that are inside of the ordinary EIT transparency window. We show that these new resonances can be interpreted in terms of the interwell dressed states and the formation of a type of dark state involving the control laser and the interwell tunneling. To either side of these ultranarrow resonances there is normal dispersion with very large slope controlled by g. We discuss prospects for observing these ultranarrow resonances and the corresponding regions of high dispersion experimentally.

Experimental requirements for Grover's algorithm in optical quantum computation

The field of linear optical quantum computation (LOQC) will soon need a repertoire of experimental milestones. We make progress in this direction by describing several experiments based on Grover's algorithm. These experiments range from a relatively simple implementation using only a single nonscalable controlled- NOT (CNOT) gate to the most complex, requiring two concatenated scalable CNOT gates, and thus form a useful set of early milestones for LOQC. We also give a complete description of basic LOQC using polarization-encoded qubits, making use of many simplifications to the original scheme of Knill, Laflamme, and Milburn [E. Knill, R. Laflamme, and G. J. Milburn, Nature (London) 409, 46 (2001)].

Testing integrability with a single bit of quantum information

We show that deterministic quantum computing with a single bit can determine whether the classical limit of a quantum system is chaotic or integrable using O(N) physical resources, where N is the dimension of the Hilbert space of the system under study. This is a square-root improvement over all known classical procedures. Our study relies strictly on the random matrix conjecture. We also present numerical results for the nonlinear kicked top.

Gates for the kane quantum computer in the presence of dephasing

In this paper we investigate the effect of dephasing on proposed quantum gates for the solid-state Kane quantum computing architecture. Using a simple model of the decoherence, we find that the typical error in a controlled-NOT gate is 8.3x10(-5). We also compute the fidelities of Z, X, swap, and controlled Z operations under a variety of dephasing rates. We show that these numerical results are comparable with the error threshold required for fault tolerant quantum computation.

Optical quantum computation using cluster states

We propose an approach to optical quantum computation in which a deterministic entangling quantum gate may be performed using, on average, a few hundred coherently interacting optical elements (beam splitters, phase shifters, single photon sources, and photodetectors with feedforward). This scheme combines ideas from the optical quantum computing proposal of Knill, Laflamme, and Milburn [Nature (London) 409, 46 (2001)], and the abstract cluster-state model of quantum computation proposed by Raussendorf and Briegel [Phys. Rev. Lett. 86, 5188 (2001)].

Quantum-gate characterization in an extended Hilbert space

We describe an approach for characterizing the process performed by a quantum gate using quantum process tomography, by first modeling the gate in an extended Hilbert space, which includes nonqubit degrees of freedom. To prevent unphysical processes from being predicted, present quantum process tomography procedures incorporate mathematical constraints, which make no assumptions as to the actual physical nature of the system being described. By contrast, the procedure presented here assumes a particular class of physical processes, and enforces physicality by fitting the data to this model. This allows quantum process tomography to be performed using a smaller experimental data set, and produces parameters with a direct physical interpretation. The approach is demonstrated by example of mode matching in an all-optical controlled-NOT gate. The techniques described are general and could be applied to other optical circuits or quantum computing architectures.