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.

Measuring entangled qutrits and their use for quantum bit commitment

We produce and holographically measure entangled qudits encoded in transverse spatial modes of single photons. With the novel use of a quantum state tomography method that only requires two-state superpositions, we achieve the most complete characterization of entangled qutrits to date. Ideally, entangled qutrits provide better security than qubits in quantum bit commitment: we model the sensitivity of this to mixture and show experimentally and theoretically that qutrits with even a small amount of decoherence cannot offer increased security over qubits.

Foundations of quantum technology

Recent progress in fabrication and control of single quantum systems presage a nascent technology based on quantum principles. We review these principles in the context of specific examples including: quantum dots, quantum electromechanical systems, quantum communication and quantum computation.

Quantum computing and polynomial equations over the finite field Z(2)

What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field Z(2). This connection allows simple proofs to be given for two known relationships between quantum and classical complexity classes, namely BQP subset of P-#P and BQP subset of PP.

Characterization of complex quantum dynamics with a scalable NMR information processor

We present experimental results on the measurement of fidelity decay under contrasting system dynamics using a nuclear magnetic resonance quantum information processor. The measurements were performed by implementing a scalable circuit in the model of deterministic quantum computation with only one quantum bit. The results show measurable differences between regular and complex behavior and for complex dynamics are faithful to the expected theoretical decay rate. Moreover, we illustrate how the experimental method can be seen as an efficient way for either extracting coarse-grained information about the dynamics of a large system or measuring the decoherence rate from engineered environments.

Classical simulation of quantum many-body systems with a tree tensor network

We show how to efficiently simulate a quantum many-body system with tree structure when its entanglement (Schmidt number) is small for any bipartite split along an edge of the tree. As an application, we show that any one-way quantum computation on a tree graph can be efficiently simulated with a classical computer.

Quantum optical systems for the implementation of quantum information processing

We review the field of quantum optical information from elementary considerations to quantum computation schemes. We illustrate our discussion with descriptions of experimental demonstrations of key communication and processing tasks from the last decade and also look forward to the key results likely in the next decade. We examine both discrete (single photon) type processing as well as those which employ continuous variable manipulations. The mathematical formalism is kept to the minimum needed to understand the key theoretical and experimental results.

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.

Nanofiber control of ultracold quantum gases

While a great amount of attention is being given to the development of nanodevices, both through academic research and private industry, the field is still on the verge. Progress hinges upon the development of tools and components that can precisely control the interaction between light and matter, and that can be efficiently integrated into nano-devices. Nanofibers are one of the most promising candidates for such purposes. However, in order to fully exploit their potential, a more intimate knowledge of how nanofibers interact with single neutral atoms must be gained. As we learn more about the properties of nanofiber modes, and the way they interface with atoms, and as the technology develops that allows them to be prepared with more precisely known properties, they become more and more adaptable and effective. The work presented in this thesis touches on many topics, which is testament to the broad range of applications and high degree of promise that nanofibers hold. For immediate use, we need to fully grasp how they can be best implemented as sensors, filters, detectors, and switches in existing nano-technologies. Areas of interest also include how they might be best exploited for probing atom-surface interactions, single-atom detection and single photon generation. Nanofiber research is also motivated by their potential integration into fundamental cold atom quantum experiments, and the role they can play there. Combining nanofibers with existing optical and quantum technologies is a powerful strategy for advancing areas like quantum computation, quantum information processing, and quantum communication. In this thesis I present a variety of theoretical work, which explores a range of the applications listed above. The first work presented concerns the use of the evanescent fields around a nanofiber to manipulate an existing trapping geometry and therefore influence the centre-of-mass dynamics of the atom. The second work presented explores interesting trapping geometries that can be achieved in the vicinity of a fiber in which just four modes are allowed to propagate. In a third study I explore the use of a nanofiber as a detector of small numbers of photons by calculating the rate of emission into the fiber modes when the fiber is moved along next to a regularly separated array of atoms. Also included are some results from a work in progress, where I consider the scattered field that appears along the nanofiber axis when a small number of atoms trapped along that axis are illuminated orthogonally; some interesting preliminary results are outlined. Finally, in contrast with the rest of the thesis, I consider some interesting physics that can be done in one of the trapping geometries that can be created around the fiber, here I explore the ground states of a phase separated two-component superfluid Bose-Einstein condensate trapped in a toroidal potential.

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.

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.

Circuit Quantum Electrodynamics with Transmon Qubits in the Ultrastrong Coupling Regime

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Performance Analysis of Topological Quantum Error Correcting Codes

In the last few years there has been a great development of techniques like quantum computers and quantum communication systems, due to their huge potentialities and the growing number of applications. However, physical qubits experience a lot of nonidealities, like measurement errors and decoherence, that generate failures in the quantum computation. This work shows how it is possible to exploit concepts from classical information in order to realize quantum error-correcting codes, adding some redundancy qubits. In particular, the threshold theorem states that it is possible to lower the percentage of failures in the decoding at will, if the physical error rate is below a given accuracy threshold. The focus will be on codes belonging to the family of the topological codes, like toric, planar and XZZX surface codes. Firstly, they will be compared from a theoretical point of view, in order to show their advantages and disadvantages. The algorithms behind the minimum perfect matching decoder, the most popular for such codes, will be presented. The last section will be dedicated to the analysis of the performances of these topological codes with different error channel models, showing interesting results. In particular, while the error correction capability of surface codes decreases in presence of biased errors, XZZX codes own some intrinsic symmetries that allow them to improve their performances if one kind of error occurs more frequently than the others.

Engineering interactions for quasiperfect transfer of polariton states through nonideal bosonic networks of distinct topologies

We present a scheme for quasiperfect transfer of polariton states from a sender to a spatially separated receiver, both composed of high-quality cavities filled by atomic samples. The sender and the receiver are connected by a nonideal transmission channel -the data bus- modelled by a network of lossy empty cavities. In particular, we analyze the influence of a large class of data-bus topologies on the fidelity and transfer time of the polariton state. Moreover, we also assume dispersive couplings between the polariton fields and the data-bus normal modes in order to achieve a tunneling-like state transfer. Such a tunneling-transfer mechanism, by which the excitation energy of the polariton effectively does not populate the data-bus cavities, is capable of attenuating appreciably the dissipative effects of the data-bus cavities. After deriving a Hamiltonian for the effective coupling between the sender and the receiver, we show that the decay rate of the fidelity is proportional to a cooperativity parameter that weighs the cost of the dissipation rate against the benefit of the effective coupling strength. The increase of the fidelity of the transfer process can be achieved at the expense of longer transfer times. We also show that the dependence of both the fidelity and the transfer time on the network topology is analyzed in detail for distinct regimes of parameters. It follows that the data-bus topology can be explored to control the time of the state-transfer process.

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.