Browsing by Subject "Quantum physics"

Ion traps are a leading candidate for scaling quantum computers. The component technologies can be difficult to integrate and manufacture. Experimental systems are also subject to mechanical drift creating a large maintenance overhead. A full system redesign with stability and scalability in mind is presented. The center of our approach is a compact cryogenic ion trap package (trap cryopackage). A surface trap is mounted to a modified ceramic pin grid array (CPGA) this is enclosed using a copper lid. The differentially pumped trap cryopackage has all necessary optical feedthroughs and an ion source (ablation target). The lid pressure is held at ultra-high vacuum (UHV) by cryogenic sorption pumping using carbon getter. We install this cryopackage into a commercial low-vibration closed-cycle cryostat which sits inside a custom monolithic enclosure. The system is tested and trapped ions are found to have common mode heating rate on the order of 10 quanta/s. The modular optical setup provides for a couterpropagating single qubit coherence time of 527 ms. We survey a population of FM two-qubit gates (gate times 120 μs - 450 μs) and find an average gate fidelity of 98\%. We study the gate survey with quantum Monte Carlo simulation and find that our two-qubit gate fidelity is limited by low frequency (30 Hz - 3 kHz) coherent electrical noise on our motional modes.

In this thesis I discuss an alternative approach for investigating quarkonium production in hadron colliders. I present a complete framework for developing observables for studies of charmonium states produced within a jet. My work is based on the use of effective field theories of quantum chromodynamics that allow for the approximate factorization of jet cross sections in perturbative calculable terms and universal non-perturbative functions that are extracted from data. Particularly in this thesis I explore the factorization approach of non-relativistic quantum chromodynamics and soft-collinear effective theory. The fragmenting jet functions play central role in factorization theorems for cross sections for identified hadrons within jets. This cross sections can depend on the hadron-jet energy ratio and possibly on other jet observables. I expand this concept to jet-shape observables known as angularities and introduce the transverse momentum dependent fragmenting jet functions. Applications of these advanced methods to J/ψ production from gluon fragmentation in electron-positron annihilation are presented and I develop the tools for expanding this work in hadron colliders. Additionally, I compare predictions for J/ψ production in jets, based on the framework of fragmenting jet functions, against recent experimental data from the LHCb collaboration.

Lindblad equations, since introduced in 1976 by Lindblad, and by Gorini, Kossakowski, and Sudarshan, have received much attention in many areas of scientific research. Around the past fifty years, many properties and structures of Lindblad equations have been discovered and identified. In this dissertation, we study Lindblad equations from three aspects: (I) physical perspective; (II) numerical perspective; and (III) information theory perspective.

In Chp. 2, we study Lindblad equations from the physical perspective. More specifically, we derive a Lindblad equation for a simplified Anderson-Holstein model arising from quantum chemistry. Though we consider the classical approach (i.e., the weak coupling limit), we provide more explicit scaling for parameters when the approximations are made. Moreover, we derive a classical master equation based on the Lindbladian formalism.

In Chp. 3, we consider numerical aspects of Lindblad equations. Motivated by the dynamical low-rank approximation method for matrix ODEs and stochastic unraveling for Lindblad equations, we are curious about the relation between the action of dynamical low-rank approximation and the action of stochastic unraveling. To address this, we propose a stochastic dynamical low-rank approximation method. In the context of Lindblad equations, we illustrate a commuting relation between the dynamical low-rank approximation and the stochastic unraveling.

In Chp. 4, we investigate Lindblad equations from the information theory perspective. We consider a particular family of Lindblad equations: primitive Lindblad equations with GNS-detailed balance. We identify Riemannian manifolds in which these Lindblad equations are gradient flow dynamics of sandwiched Rényi divergences. The necessary condition for such a geometric structure is also studied. Moreover, we study the exponential convergence behavior of these Lindblad equations to their equilibria, quantified by the whole family of sandwiched Rényi divergences.

This thesis aims to present methods for characterizing and mitigating errors in quantum computers. We begin by providing a historical overview of computing devices and the evolution of quantum information. The basics of characterizing noise in quantum computers and the utilization of quantum control and error mitigation techniques to reduce the impact of noise on performance are also discussed. In the initial part of the thesis, we focus on a particularly detrimental type of time-dependent errors and derive theoretical limits of a closed-loop feedback based quantum control protocol for their mitigation. Two different protocols, one suitable for fault-tolerant systems and another for near-term devices, are presented and their performance is demonstrated through numerical simulations. Additionally, we explore the mitigation of coherent noise at the circuit level through the use of the hidden inverses protocol with results from experiments conducted at Duke University, Sandia National Laboratories, and IBM. Finally, we propose a scalable error characterization procedure for large quantum systems, which is tested through numerical simulations to highlight its sensitivity to various sources of noise. Crucially, this protocol does not require access to ideal classical simulation of quantum circuits unlike other benchmarks such as quantum volume or cross entropy benchmarks.

Quantum information science strives to leverage the quantum-mechanical nature of our universe in order to achieve large improvements in certain information processing tasks. Such tasks include quantum communications and fault-tolerant quantum computation. In this dissertation, we make contributions to both of these applications.

In deep-space optical communications, the mathematical abstraction of the binary phase shift keying (BPSK) modulated pure-loss optical channel is called the pure-state channel. It takes classical inputs and delivers quantum outputs that are pure (qubit) states. To achieve optimal information transmission, if classical error-correcting codes are employed over this channel, then one needs to develop receivers that collectively measure all output qubits in order to optimally identify the transmitted message. In general, it is hard to determine these optimal collective measurements and even harder to realize them in practice. So, current receivers first measure each qubit channel output and then classically post-process the measurements. This approach is sub-optimal. We investigate a recently proposed quantum algorithm for this task, which is inspired by classical belief-propagation algorithms, and analyze its performance on a simple $5$-bit code. We show that the algorithm makes optimal decisions for the value of each bit and it appears to achieve optimal performance when deciding the full transmitted message. We also provide explicit circuits for the algorithm in terms of standard gates. For deep-space optical communications, this suggests a near-term quantum advantage over the aforementioned sub-optimal scheme. Such a communication advantage appears to be the first of its kind.

Quantum error correction is vital to building a universal fault-tolerant quantum computer. An $[\![ n,k,d ]\!]$ quantum error-correcting code (QECC) protects $k$ information (or logical) qubits by encoding them into quantum states of $n > k$ physical qubits such that any undetectable error must affect at least $d$ physical qubits. In this dissertation we focus on stabilizer QECCs, which are the most widely used type of QECCs. Since we would like to perform universal (i.e., arbitrary) quantum computation on the $k$ logical qubits, an important problem is to determine fault-tolerant $n$-qubit physical operations that induce the desired logical operations. Our first contribution here is a systematic algorithm that can translate a given logical Clifford operation on a stabilizer QECC into all (equivalence classes of) physical Clifford circuits that realize that operation. We exploit binary symplectic matrices to make this translation efficient and call this procedure the Logical Clifford Synthesis (LCS) algorithm.

In order to achieve universality, a quantum computer also needs to implement at least one non-Clifford logical operation. We develop a mathematical framework for a large subset of diagonal (unitary) operations in the Clifford hierarchy, and we refer to these as Quadratic Form Diagonal (QFD) gates. We show that all $1$- and $2$-local diagonal gates in the hierarchy are QFD, and we rigorously derive their action on Pauli matrices. This framework of QFD gates includes many non-Clifford gates and could be of independent interest. Subsequently, we use the QFD formalism to characterize all $[\![ n,k,d ]\!]$ stabilizer codes whose code subspaces are preserved under the transversal action of $T$ and $T^{-1}$ gates on the $n$ physical qubits. The $T$ and $T^{-1}$ gates are among the simplest non-Clifford gates to engineer in the lab. By employing a ``reverse LCS'' strategy, we also discuss the logical operations induced by these physical gates. We discuss some important corollaries related to triorthogonal codes and the optimality of CSS codes with respect to $T$ and $T^{-1}$ gates. We also describe a few purely-classical coding problems motivated by physical constraints arising from fault-tolerance. Finally, we discuss several examples of codes and determine the logical operation induced by physical $Z$-rotations on a family of quantum Reed-Muller codes. A conscious effort has been made to keep this dissertation self-contained, by including necessary background material on quantum information and computation.

The challenge of quantum computing is to combine error resilience with universal computation. Diagonal gates such as the transversal T gate play an important role in implementing a universal set of quantum operations. We introduce a framework that describes the process of preparing a code state, applying a diagonal physical gate, measuring a code syndrome, and applying a Pauli correction that may depend on the measured syndrome (the average logical channel induced by an arbitrary diagonal gate). The framework describes the interaction of code states and physical gates in terms of generator coefficients determined by the induced logical operator. The interaction of code states and diagonal gates depends on the signs of Z-stabilizers in the CSS code, and the proposed generator coefficient framework explicitly includes this degree of freedom. We derive necessary and sufficient conditions for an arbitrary diagonal gate to preserve the code space of a stabilizer code, and provide an explicit expression of the induced logical operator. When the diagonal gate is a quadratic form diagonal gate, the conditions can be expressed in terms of divisibility of weights in the two classical codes that determine the CSS code. These codes find applications in magic state distillation and elsewhere. When all the signs are positive, we characterize all possible CSS codes, invariant under transversal Z-rotation through π/2^l, that are constructed from classical Reed-Muller codes by deriving the necessary and sufficient constraints on the level l. According to the divisibility conditions, we construct new families of CSS codes using cosets of the first order Reed-Muller code defined by quadratic forms. The generator coefficient framework extends to arbitrary stabilizer codes but the more general class of non-degenerate stabilizer codes does not bring advantages when designing the code parameters.

Relying on the generator coefficient framework, we introduce a method of synthesizing CSS codes that realizes a target logical diagonal gate at some level l in the Clifford hierarchy. The method combines three basic operations: concatenation, removal of Z-stabilizers, and addition of X-stabilizers. It explicitly tracks the logical gate induced by a diagonal physical gate that preserves a CSS code. The first step is concatenation, where the input is a CSS code and a physical diagonal gate at level l inducing a logical diagonal gate at the same level. The output is a new code for which a physical diagonal gate at level l+1 induces the original logical gate. The next step is judicious removal of Z-stabilizers to increase the level of the induced logical operator. We identify three ways of climbing the logical Clifford hierarchy from level l to level l+1, each built on a recursive relation on the Pauli coefficients of the induced logical operators. Removal of Z-stabilizers may reduce distance, and the purpose of the third basic operation, addition of X-stabilizers, is to compensate for such losses. Our approach to logical gate synthesis is demonstrated by two proofs of concept: the [[2^(l+1) − 2, 2, 2]] triorthogonal code family, and the [[2^m, (m choose r) , 2^(min{r, m-r})]] quantum Reed-Muller code family.

Due to recent experimental progress on highly controllable quantum systems, increasing attention has been paid to open quantum systems, where driving and dissipation can lead to undesirable decoherence but may also stabilize interesting states and lead to new physics. Theoretically speaking, the generator of the dynamics (called the Liouvillian) for open quantum systems is non-Hermitian, giving rise to phenomena not allowed in closed systems.This dissertation mainly studies dissipative phase transitions in open systems where the steady state undergoes a non-analytic change at the transition point. We apply various analytic methods to investigate different open many-body models. (i) We study open systems where the Liouvillian can be brought into a block-triangular form. This allows us to bound the spectral gap from below, showing that, in a large class of systems, dissipative phase transitions are impossible. (ii) We perform perturbative treatment to spin-1/2 systems with a large dephasing channel and study the non-Hermitian skin effect in such systems. (iii) We establish the solvability of quadratic open systems using the third-quantization technique. With this, we further investigate quadratic fermionic and bosonic systems respectively. We find that criticality is not allowed for quadratic fermionic systems while we find examples of bosonic criticality for d>=2 dimensional quadratic systems. We also establish a proposition stating that without symmetry constraints beyond invariance under single-particle basis and particle-hole transformations, all gapped Liouvillians belong to the same phase. (iv) We employ Keldysh field theory to study dissipative Bose-Einstein condensation. With the one-loop renormalization group calculation, we elucidate the universality class to which this phase transition belongs. (v) We study the mathematical structure of the Liouvillian and establish an algebraic condition for the irreducibility of the Liouvillian. Irreducibility will lead to the uniqueness and faithfulness of the steady state.

Open quantum systems refer to quantum systems that couple with their surrounding environment. They are ubiquitous, especially for quantum devices. Due to coupling with the external environment, the dynamics of open quantum systems becomes non-unitary, which leads to additional complexity and novel possibilities compared to the unitary dynamics of closed systems. The study of open quantum systems is therefore of both theoretical and practical interest.

In this dissertation, using paradigmatic models of (Markovian) open quantum systems, I study three aspects of open quantum systems: (i) measurement of emitted particles from an open quantum system, to probe its dynamics; (ii) quantum entanglement in open quantum systems, which demonstrates the significance of information gained from measurement; and (iii) quantum critical phenomena in an open quantum many-body system. The first part is of importance for probing dynamics of open quantum systems and for engineering quantum states of emitted particles using engineered open quantum systems. The second part is from the quantum information point of view, which clearly demonstrates the subtle relation between quantum entanglement of mixed states and measurement in open quantum systems. An entanglement generation protocol is provided, which can be useful for quantum information processing. The last part is concerned with open quantum many-body physics, which demonstrates the basic mechanism behind phase transitions in open quantum systems. The differences and similarities between Lindbladian and Hamiltonian phase transitions are shown from various perspectives.

Quantum entanglement lies at the heart of modern physics and pervades various research fields. In the field of quantum many-body physics, celebrated area and log-area laws have been established for the entanglement entropy of ground states. However, there exists a long-standing question regarding the transition of eigenstate entanglement entropy from the ground state to the highly excited states. Our study fills this gap and elucidates a crossover behavior with universal scaling properties. In the study of quantum matters, knowledge about the entanglement structure can be used to guide the design of tensor network state simulations. For example, we may iteratively eliminate short-range entanglement in a so-called entanglement renormalization scheme so that the entangled ground state is mapped to a product state and then resolved exactly. This idea can be adapted to hybrid quantum-classical algorithms and speed up the simulation of strongly correlated quantum many-body systems.

In the first part of this dissertation, we investigate eigenstate entanglement scaling in quantum many-body systems and characterize the crossover from the ground-state entanglement regime at low energies and small subsystem sizes to extensive volume laws at high energies or large subsystem sizes. We first establish a weak eigenstate thermalization hypothesis (ETH) for translation-invariant systems, argue that the entanglement entropies of (almost) all energy eigenstates are described by a single crossover function whenever the (weak) ETH applies, and point out the universal scaling properties in the quantum critical regime. We then comprehensively confirm these scaling properties by analyzing large classes of quantum many-body systems. Particularly, we give the eigenstate entanglement scaling functions in analytical form for critical one-dimensional systems based on conformal field theory and for $d$-dimensional fermionic systems with Fermi surfaces. For $d=1,2,3$ non-interacting fermions, the scaling functions are numerically verified, and for $d=1,2,3$ harmonic lattice models (free scalar field theory), they are numerically determined. ETH is confirmed with Monte Carlo methods by sampling energy eigenstates or squeezed states for fermions or bosons with $d=1,2$. We also probe and confirm the described scaling properties and the applicability of the ETH in integrable and non-integrable interacting spin-1/2 chains by using exact diagonalization. All the evidence appearing here strongly suggests the existence of crossover functions. Their transition from ground-state scaling to extensive scaling, as well as the universal scaling properties in quantum-critical regimes, are generic.

In the second part of this dissertation, we present a quantum-classical tensor network state algorithm for condensed matter systems. First, we describe this algorithm, which is based on the multi-scale entanglement renormalization ansatz (MERA) and gradient-based optimizations. Due to its narrow causal cone, the algorithm can be implemented on noisy intermediate-scale quantum (NISQ) devices and still describe large systems. We show that the number of required qubits is independent of the system size, increasing only to logarithmic scaling when using quantum amplitude estimation to speed up gradient evaluations. Translational invariance can be used to make the computational cost square-logarithmic with respect to the system size and to describe the thermodynamic limit. The method is particularly attractive for ion-trap devices with ion shuttling capabilities. We then demonstrate it numerically for MERA with Trotterized disentanglers and isometries and find that the computational cost of such MERA quantum eigensolvers is substantially lower than that of the corresponding classical algorithms. In particular, numerical results in various strongly-correlated quantum magnet models show that it has a polynomial quantum advantage over the classical approach. In the experimental implementation, small angles in the employed two-qubit quantum gates are advantageous. We find that, by adding an angle penalty term to the energy functional, the average absolute values of the angles can be moderately reduced without significantly affecting the energy accuracies. Finally, we propose that the Trotter-type circuit in each tensor can be replaced by a parallel random circuit. However, this replacement does not seem to result in further gains as long as the tensor-network bond dimensions are small.

Quantum communication protocols, such as quantum key distribution (QKD), are practically important in the dawning of a new quantum information age where quantum computers can perform efficient prime factorization to render public key cryptosystems obsolete. QKD is a communication scheme that utilizes the quantum state of a single photons to transmit information, such as a cryptographic key, that is robust against adversaries including those with a quantum computer. In this thesis I describe the contributions that I have made to the development of high-rate, free-space quantum communication systems.

My effort is focused on building a robust quantum receiver for a high-dimensional time-phase QKD protocol where the data is encoded and secured using a single photon's timing and phase degrees of freedom. This type of communication protocol can encode information in a high-dimensional state, allowing the transmission of $>1$ bit per photon. To realize a successful implementation of the protocol a high-performance single-photon detection system must be constructed. My contribution to the field begins with the development of low-noise, low-power cryogenic amplifiers for a detection system using superconducting nanowire single-photon detectors (SNSPDs). Detector characteristics such as maximum count rate and timing resolution are heavily influenced by the design of the read-out circuits that sense and amplify the detection signal. I demonstrate a read-out system with a maximum count rate $>20\,$million counts-per-second and timing resolution as high as $35$\,ps. These results are achieved while maintaining a low power dissipation $<3$\,mW at 4\,K operation, enabling a scalable read-out circuit strategy.

A second contribution I make to the development of detection systems utilizing SNSPDs is extending the superb performance of these detectors to include photon number resolving capabilities. I demonstrate that SNSPDs exhibit multi-photon detection up to four photons where the absorbed photo number is encoded in the rise time of the electrical waveform generated by the detector. Additionally, our experiment agrees well with the predictions of a universal model for turn-on dynamics of SNSPDs. A feature our multi-photon detection system demonstrates high resolution between $n=1$ and $n>1$ photons with a bit-error-rate (BER) of $4.2\times10^{-4}$.

Finally, I extend the utility of the time-phase QKD protocol to free-space applications. Atmospheric turbulences cause spatial mode scrambling of the optical beam during transmission. Therefore, the quantum receiver, and most importantly the time-delay interferometer needed for the measurement of a phase encoding of a single photon, must support many spatial modes. I construct and characterize an interferometer with a 5\,GHz free spectral range that has a wide field-of-view and is passively a-thermal. The results of interferometer characterization are highlighted by a $>99\,\%$ single-mode, and $>98\,\%$ multi-mode interference visibility with negligible dependence on the spatial mode structure of the input beam and modest temperature fluctuations. Additionally, the interferometer displays a small path-length shift of 130\,nm/$^{\,\circ}$C, allowing for great thermal stability with modest temperature control.

The framework of quantum field theory (QFT) underlies our modern understanding of both particle physics and condensed matter physics. Despite its importance, precise quantitative calculations in strongly-coupled theories in QFTs have generally only been possible through non-perturbative lattice Monte Carlo (MC) methods. Traditionally, such lattice MC methods proceed by starting from a lattice regularization of the continuum QFT of interest, which has the same (possibly infinite dimensional) local Hilbert space at each lattice site as the continuum QFT. In this thesis, we explore an alternative regularization where the local Hilbert space is also replaced by a smaller finite dimensional Hilbert space. Motivated by the appeal of such models for near-term quantum computers, we dub this approach qubit regularization. Using this approach, in this thesis, we present three main results. First, we develop a qubit-regularization for the O(N) nonlinear sigma model (NLSM) in D $\geq$ 3 spacetime dimensions. We show using numerical lattice calculations that the O(N ) qubit model lies in the correct universality class for N = 2, 4, 6, 8, and reproduces the universal physics of the O(N) Wilson-Fisher (WF) fixed point in D = 3 spacetime dimensions by computing some well-known critical exponents. Next, we explore sectors of large global charges of the O(N) WF conformal field theory (CFT) using the O(N) qubit model. This allows us to test the predictions of a recently proposed large-charge effective field theory (EFT) and extract the two leading low-energy constants (LECs) in the EFT. Performing computations for N = 2, 4, 6, 8, we are also able to quantitatively test predictions of a recent large-N analysis in the large-charge sectors. Finally, we show that our qubit approach can also be used to study the few-body physics of non-relativistic particles. In particular, we consider a system of two species of mass-imbalanced fermions in $1 + 1$ dimensions. We compute the ground state energies for a range of mass-imbalances and interaction strengths, and uncover some problems with recent results obtained from the Complex Langevin (CL) method for the same system.

Experimental systems that trap single, neutral atoms have recently emerged as a promising platform for experiments in a range of disciplines such as quantum information science, quantum simulation and fundamental light-atom interaction. In this thesis, I build such a system and use it to trap and study a single, neutral atom of 87Rb. I confront and overcome several experimental challenges while designing and building the system. For example, I develop a MOT of unusual geometry with which to load the single-atom trap and also a detection scheme that robustly detects the trapped atom nondestructively, that is, without pushing it out of the trap. The result of this design and construction process is a system that stably traps a single atom in an optical dipole trap. I achieve trap lifetimes of over 1 minute in the absence of near-resonant laser light.

In addition to the experimental apparatus, I develop a thorough rate-equation model to predict the population dynamics of the trapped atom's internal quantum state when probed by near-resonant light. This model gives unique insight into the influence of the atom's internal dynamics on the detected scattering rate. I use this model to predict several important experimental parameters and compare it to the experimental data. This allows me to characterize the parameters that govern how the atom interacts with near-resonant laser light and how that interaction affects the experimental data. For example, I perform an absolute calibration of the collection efficiency of the experimental system, a first for a single, neutral-atom trap.

Using these experimental and modeling tools, I investigate the scattering rate of an atom in the presence of near-resonant linearly-polarized laser light. This is of great interest to the field because it is used to measure the atom's internal quantum state, in a process known as quantum-state readout. Fast and accurate quantum-state readout is crucial to the success of many protocols in quantum information science and quantum simulation. Using the tools described here, I achieve quantum-state readout with an average fidelity of 97.6±0.2% using a linearly-polarized probe beam. The readout requires a measurement time of 160±20 μs, and the atom remains in the trap after the readout in 97.1±0.1% of the trials. I use linearly-polarized light instead of circularly-polarized light because it makes the readout less sensitive to the atom's occupation of a specific magnetic sublevel, and hence does not require sublevel-specific state preparation. It also allows for a more flexible experimental geometry. This is the fastest and highest-fidelity nondestructive readout of a single neutral atom performed with a linearly-polarized probe beam reported to date.

In addition, I identify a decay in the atom's scattering rate over the course of the readout time that limits the quantum-state readout fidelity. I investigate possible sources of this decay using the rate-equation model and a model of the readout protocol, and I conclude that it is likely caused by a combination of Raman transitions and heating. The heating is related to the near-resonant probe light and also to the optical dipole trap that holds the atom. I discuss ways that this decay can be avoided, but point out that these possible solutions result in longer readout times. This investigation has applications across a wide variety of experiments that require fast quantum-state readout.

Fault-tolerant quantum computation requires the measurements of error syndromes and logical operators in a way that minimizes undesired correlated errors on the quantum data. This thesis explores possible forms for performing these measurements. Our first result aims at minimizing the number of ancilla qubits for syndrome measurement. We show that on a generalized surface code family known as 2D compass codes, each stabilizer check can be fault-tolerantly measured witha single ancilla qubit, regardless of the weight of the check. Our result infers that large ancilla blocks are not always necessary for performing stabilizer measure- ments of high weight. We then look at another regime where ancilla size is less of a concern. We show a simple framework that bridges Shor- and Steane-style ancillas, which are arguably the smallest and biggest ancilla constructions for syndrome measurements respectively. Our framework enables intermediate-size ancillas whose preparations are easier than Steane-style ancilla, while being more robust against measurement errors compared to Shor’s construction. We further show that our new constructions could be useful for future quantum computers with long coherence time. Our final result look at how the framework for constructing syndrome measurement circuits can be modified to perform logical operator measurements. While Shor- and Steane-style ancilla can be used for logical measurements, they have impractical time and space overhead when applied to large quantum codes. We show that on a quantum low-density-parity-check code family called hyperbolic surface codes, intermediate ancilla can be constructed such that no repetitive logical measurements are required for boosting the accuracy. In addition, these ancilla blocks can be directly prepared without postselection or state distillation.

The trapped atomic ion qubits feature desirable properties for use in a quantum computer such as long coherence times, high qubit readout fidelity, and universal logic gates. While these essential properties have been demonstrated, the ability to scale a trapped ion quantum system has not yet been shown. The challenge of scaling the system calls for methods to realize high-fidelity logic gates in scalable trap structures. Surface electrode ion traps, that are microfabricated from a silicon substrate, provide a scalable platform for trapping ion qubits only if high-fidelity operations are achievable in these structures. Here, we present a system for trapping and manipulating ions in a scalable surface trap. Trapping times exceeding 20 minutes without laser cooling, and heating rates as low as 0.8 quanta/ms indicate stable trapping conditions in these microtraps. Coherence times of more than one second verify adequate qubit and control field stability. We demonstrate low-error single-qubit gates performed using stimulated Raman transitions driven by lasers that are tightly focused on the ion qubit. Digital feedback loops are implemented to control the driving field's amplitude and frequency. Gate errors are measured using a randomized benchmarking protocol for single qubit gates, where residual amplitude error in the control beam is compensated using various pulse sequence techniques. Using pulse compensation, we demonstrate single qubit gates with an average error per randomized Clifford group gate of $3.6(3)\times10^{-4}$, which is below the fault-tolerant threshold for some error-correction schemes.

There is currently a great interest in using high-dimensional (dimension d>2) quantum states for various communication and computational tasks. High-dimensional quantum states provide an efficient and robust means of encoding information, where each photon can encode a maximum of log_2(d) bits of information. One application where this becomes a significant advantage is quantum key distribution (QKD), which is a communication technique that relies on the quantum nature of photonic states to share a classical secret key between two remote users in the presence of a powerful eavesdropper. High-dimensional QKD protocols are believed to overcome some of the practical challenges of the conventional qubit-based (d = 2) protocols, such as the long recovery time of the single-photon detectors, or the low error tolerance to quantum channel noise.

In this thesis, I demonstrate experimentally and theoretically various novel QKD protocols implemented with high-dimensional quantum photonic states, where the information is encoded using the temporal and phase degrees of freedom. One challenging aspect of high-dimensional time-phase QKD protocols is that the measurement of the phase states requires intricate experimental setups, involving time-delay interferometers, fiber Bragg gratings, or a combination of electro-optic modulators and fiber Bragg gratings, among others. Here, I explore two different measurement schemes, one involving a tree of delay line interferometers, and the other using a quantum-controlled technique, where the measurement of the phase states is performed by interfering an incoming quantum state with another locally generated quantum state. Using the interferometric method (quantum-controlled) and a d = 4 (d = 8) encoding scheme, I achieve a secret key rate of 26.2 +/- 2.8 (16.6 +/- 1.0) Mbps at a 4 (3.2) dB channel loss. Overall, the secret key rates achieved in this thesis are a few folds improvement compared to the other state-of-the-art high-rate QKD systems.

Finally, I consider the possibility of an eavesdropper attacking the high-dimensional quantum states using a universal quantum cloning machine, where she uses weak coherent states of different mean photon numbers (decoy-state technique) to estimate the single-photon fidelity. I show that an eavesdropper can estimate the unknown quantum states in the channel with a degraded but optimal cloning fidelity. Specifically, I find that the upper bound of the cloning fidelity decreases from 0.834 +/- 0.003 at d= 2 to 0.639 +/- 0.003 at d = 6, thereby providing evidence for two conclusions. First, the decoy-state technique can be used to extract single-photon contribution from intricate weak coherent states based two-photon experiments. Second, high-dimensional quantum photonic states are more robust compared to the d = 2 quantum states.

A quantum circuit is a widely used model for quantum computation. It consists of quantum registers, which we refer to as qubits, and quantum gates. To build a large-scale trapped ion quantum computer, the performance of executing quantum circuits is a bottleneck. Atomic ions are great qubit candidates. However, high-fidelity two-qubit gates extending over all qubits with individual control in a large-scale trapped-ion system have not been achieved. Moreover, coherent gate errors in deep quantum circuits exaggerate the error since they accumulate quadratically. This thesis presents the effort to build a trapped-ion quantum computing system that possesses individual qubit control, scalable high-fidelity two-qubit gates, and the capability to run quantum circuits with multiple qubits. This thesis shows that we realize and characterize high-fidelity two-qubit gates in a system with up to 4 ions using radial modes. The ions are individually addressed by two tightly focused beams steered using micro-electromechanical system (MEMS) mirrors. We accomplish the highest two-qubit gate fidelity using radial motional modes to date. Two methods of robust frequency-modulated two-qubit gate pulse design are introduced. With the state-of-the-art scalable two-qubit gates, we propose a compilation technique, which we refer to as hidden inverses, that creates circuits robust to residual coherent errors. We present experimental data showing that hidden inverses suppress both overrotation and phase misalignment errors in our trapped-ion system, resulting in improved quantum circuit performance.

Trapped ions provide a promising platform to build a practical quantum computer. Scaling the high performance of small systems to longer ion chains is a technical endeavor that benefits from both better hardware system design and gate-level control techniques. In this thesis, I discuss our work on building a small-scale trapped-ion quantum computing system that features stable laser beam control, low-crosstalk individual addressing and capability to implement high-fidelity multi-qubit gates.

We develop control techniques to extend the pack-leading fidelity of entangling gates in two-ion systems to longer chains. A major error source limiting entangling gate fidelities in ion chains is crosstalk between target and neighboring spectator qubits. We propose and demonstrate a crosstalk suppression scheme that eliminates all first-order crosstalk utilizing only local control of target qubits, as opposed to an existing scheme which requires control over all neighboring qubits. Using the scheme, we achieve a $99.5\%$ gate fidelity in a 5-ion chain. Complex quantum circuits can benefit from native multi-qubit gates such as the $N$-Toffoli gate, which substantially reduce the overhead cost from performing universal decomposition into single- and two-qubit gates. We take advantage of novel performance benefits of long ion chains to realize scalable Cirac-Zoller gates, which uses a simple pulse sequence to efficiently implement $N$-Toffoli gates. We demonstrate the Cirac-Zoller 3- and 4-Toffoli gates in a five-ion chain with higher fidelities than previous results using trapped ions. We also present the first experimental realization of a 5-Toffoli gate.

Solving the time-independent Schrödinger equation for the electronic structure Hamiltonian in quantum chemistry is hoped to be one problem where quantum computers may provide an early advantage over classical computers. The basic intuition behind this is that quantum computers are able to prepare states with an exponentially large number of probability amplitudes with a linear number of qubits, whereas classical methods must introduce approximations and heuristics to avoid the need to store and perform operations on such exponentially large states. We address two challenges that occur within the context of developing algorithms for solving the electronic structure problem on quantum computers: 1. developing methods which not only find the ground state, but also excited states and; 2. contending with the basis set truncation error which requires the use of large numbers of qubits using conventional methods. We first develop the quantum Orbital Minimization Method (qOMM) and show through numerical simulations using Qiskit that it is able to converge much more quickly to a set of low-lying excited states than another method, the Subspace Search Variational Quantum Eigensolver (SSVQE) which has appeared in the literature in recent years. We then develop the optimal orbital variational quantum eigensolver (OptOrbVQE) algorithm and numerically simulate it using Qiskit to show that it can often achieves lower basis set truncation error in the ground state energy than methods using larger, conventional basis sets. We then generalize this method to find excited states in optimized basis sets and demonstrate analogous results to the ground state case through numerical simulations in Qiskit.

This dissertation addresses challenges in quantum computing with trapped ions, including system integration of the trapped ion hardware, heating-induced decoherence, and efficient cooling mechanisms, by investigating multi-species or isotope ion chains with sympathetic cooling techniques. The study explores loading ion chains with 174Yb and 138Ba species, using an Nd:YAG ablation laser for isotope-selective trapping. A detail of the design of a compact room-temperature trapped ion system is presented, comprising an ultra-high vacuum (UHV) package, a micro-fabricated surface trap, and a small form-factor ion pump, demonstrating trapping of 174Yb+ ions and achieving a suitable vacuum level. A detailed ion chain cooling model based on sympathetic cooling addresses the heating problem of 171Yb+ qubits on a two-dimensional surface trap, revealing the crucial role of the mass ratio between cooling and qubit ions in the sympathetic cooling dynamics. The dissertation further delves into the implementation of sympathetic cooling in trapped ion systems, successfully cooling qubit 171Yb+ ions using 172Yb+ or 174Yb+ ions as cooling ions, reducing motional heating and decoherence without direct interaction with qubits. In summary, this dissertation contributes to developing and optimizing compact trapped ion systems for quantum computing, providing insights on multi-species ion chains, sympathetic cooling techniques, and ion chain cooling models to enhance trapped ion quantum computing performance and fidelity.

Strong coupling between light and matter has been demonstrated both in classical

cavity quantum electrodynamics (QED) systems and in more recent circuit-QED

experiments. This enables the generation of strong nonlinear photon-photon interactions

at the single-photon level, which is of great interest for the observation

of quantum nonlinear optical phenomena, the control of light quanta in quantum

information protocols such as quantum networking, as well as the study of

strongly correlated quantum many-body systems using light. Recently, strong

coupling has also been realized in a variety of one-dimensional (1D) waveguide-

QED experimental systems, which in turn makes them promising candidates for

quantum information processing. Compared to cavity-QED systems, there are

two new features in waveguide-QED: the existence of a continuum of states and

the restricted 1D phase space, which together bring in new physical effects, such

as the bound-state effects. This thesis consists of two parts: 1) understanding the

fundamental interaction between local quantum objects, such as two-level systems

and four-level systems, and photons confined in the waveguide; 2) exploring

its implications in quantum information processing, in particular photonic

quantum computation and quantum key distribution.

First, we demonstrate that by coupling a two-level system (TLS) or three/fourlevel

system to a 1D continuum, strongly-correlated photons can be generated

inside the waveguide. Photon-photon bound states, which decay exponentially as a function of the relative coordinates of photons, appear in multiphoton scattering

processes. As a result, photon bunching and antibunching can be observed

in the photon-photon correlation function, and nonclassical light source can be

generated on demand. In the case of an N-type four-level system, we show

that the effective photon-photon interaction mediated by the four-level system,

gives rise to a variety of nonlinear optical phenomena, including photon blockade,

photon-induced tunneling, and creation of single-photon states and photon

pairs with a high degree of spectral entanglement, all in the absence of a cavity.

However, to enable greater quantum networking potential using waveguide-

QED, it is important to study systems having more than just one TLS/qubit.

We develop a numerical Green function method to study cooperative effects in

a system of two qubits coupled to a 1D waveguide. Quantum beats emerge in

photon-photon correlations, and persist to much longer time scales because of

non-Markovian processes. In addition, this system can be used to generate a

high-degree of long-distance entanglement when one of the two qubits is driven

by an on-resonance laser, further paving the way toward waveguide-QED-based

quantum networks.

Furthermore, based on our study of light-matter interactions in waveguide-

QED, we investigate its implications in quantum information processing. First,

we study quantum key distribution using the sub-Possonian single photon source

obtained by scattering a coherent state off a two-level system. The rate for key

generation is found to be twice as large as for other sources. Second, we propose

a new scheme for scalable quantum computation using flying qubits--propagating

photons in a one-dimensional waveguide--interacting with matter qubits. Photonphoton

interactions are mediated by the coupling to a three- or four-level system,

based on which photon-photon -phase gates (Controlled-NOT) can be implemented for universal quantum computation. We show that high gate fidelity is

possible given recent dramatic experimental progress in superconducting circuits

and photonic-crystal waveguides. The proposed system can be an important

building block for future on-chip quantum networks.