A large-scale quantum computer will have the ability to solve many computational problems beyond the capabilities of today's most powerful computers. Significant efforts to build such a computer are underway, many of which are small prototypes that are believed to be extensible to larger systems. Such systems, like the one in this thesis built off of 171Yb+ ions, are enticing scientific endeavors for their potential to inform the production of large-scale systems, as well as the interesting experiments they can perform. In this work, experimental research is presented on both topics: scalability as well as compelling computations. The first half of this thesis discusses building and optimizing a quantum computer to have high-fidelity qubit operations. An experimental architecture that allows for individual addressing and individual detection of qubits is presented alongside a discussion of errors and error-reduction. We derive the coherent manipulation of qubits using Raman lasers for rotational gates and the criteria necessary for multi-qubit entangling gates. Methods for efficiently fulfilling these criteria are presented with experimental data. Lastly, we consider coherence-related properties of the system necessary to perform these operations and how they can be experimentally improved. The second half of the thesis features three experimental applications of the quantum computer: quantifying quantum scrambling, applying a quantum error correction code, and measuring Renyi entropy. Quantum scrambling is the coherent delocalization of information through a quantum system and is notably difficult to quantify experimentally. We present an efficient scheme to measure it using quantum teleportation. Quantum error correction is a set of techniques for mitigating the effect of imperfect operations performed on a quantum computer, and we demonstrate some of these techniques in order to fault-tolerantly prepare a logical qubit. Lastly, \renyi entropy is an information theoretic quantity that can be used to directly quantify the amount of entanglement in a system. We present a method for measuring it efficiently using a quantum gate known as a Fredkin gate.
A large-scale quantum computer will have the ability to solve many computational problems beyond the capabilities of today's most powerful computers. Significant efforts to build such a computer are underway, many of which are small prototypes that are believed to be extensible to larger systems. Such systems, like the one in this thesis built off of 171Yb+ ions, are enticing scientific endeavors for their potential to inform the production of large-scale systems, as well as the interesting experiments they can perform. In this work, experimental research is presented on both topics: scalability as well as compelling computations. The first half of this thesis discusses building and optimizing a quantum computer to have high-fidelity qubit operations. An experimental architecture that allows for individual addressing and individual detection of qubits is presented alongside a discussion of errors and error-reduction. We derive the coherent manipulation of qubits using Raman lasers for rotational gates and the criteria necessary for multi-qubit entangling gates. Methods for efficiently fulfilling these criteria are presented with experimental data. Lastly, we consider coherence-related properties of the system necessary to perform these operations and how they can be experimentally improved. The second half of the thesis features three experimental applications of the quantum computer: quantifying quantum scrambling, applying a quantum error correction code, and measuring Renyi entropy. Quantum scrambling is the coherent delocalization of information through a quantum system and is notably difficult to quantify experimentally. We present an efficient scheme to measure it using quantum teleportation. Quantum error correction is a set of techniques for mitigating the effect of imperfect operations performed on a quantum computer, and we demonstrate some of these techniques in order to fault-tolerantly prepare a logical qubit. Lastly, \renyi entropy is an information theoretic quantity that can be used to directly quantify the amount of entanglement in a system. We present a method for measuring it efficiently using a quantum gate known as a Fredkin gate.
Quantum computers promise to solve models of important physical processes, optimize complex cost functions, and challenge cryptography in ways that are intractable using current computers. In order to achieve these promises, quantum computers must both increase in size and decrease error rates. To increase the system size, we report on the design, construction, and operation of an integrated trapped ion quantum computer consisting of a chain of 15 171Yb+ ions with all-to-all connectivity and high-fidelity gate operations. In the process, we identify a physical mechanism that adversely affects gate fidelity in long ion chains. Residual heating of the ions from noisy electric fields creates decoherence due to the weak confinement of the ions transverse to a focused addressing laser. We demonstrate this effect in chains of up to 25 ions and present a model that accurately describes the observed decoherence. To mitigate this noise source, we first propose a new sympathetic cooling scheme to periodically re-cool the ions throughout a quantum circuit, and then demonstrate its capability in a proof-of-concept experiment. One path to suppress error rates in quantum computers is through quantum error correction schemes that combine multiple physical qubits into logical qubits that robustly store information within an entangled state. These extra degrees of freedom enable the detection and correction of errors. Fault-tolerant circuits contain the spread of errors while operating the logical qubit and are essential for realizing error suppression in practice. We demonstrate fault-tolerant preparation, measurement, rotation, and stabilizer measurement of a distance-3 Bacon-Shor logical qubit in our quantum computer. The result is an encoded logical qubit with error rates lower than the error of the entangling operations required to operate it.
Quantum computing represents an exciting frontier in the realm of information processing; it is a promising technology that may provide future advances in a wide range of fields, from quantum chemistry to optimization problems. This thesis discusses experimental results for several quantum algorithms performed on a programmable quantum computer consisting of a linear chain of five or seven trapped 171Yb+ atomic clock ions with long coherence times and high gate fidelities. We execute modular one- and two-qubit computation gates through Raman transitions driven by a beat note between counter-propagating beams from a pulsed laser. The system's individual addressing capability provides arbitrary single-qubit rotations as well as all possible two-qubit entangling gates, which are implemented using a pulse-segmentation scheme. The quantum computer can be programmed from a high-level interface to execute arbitrary quantum circuits, and comes with a toolbox of many important composite gates and quantum subroutines. We present experimental results for a complete three-qubit Grover quantum search algorithm, a hallmark application of a quantum computer with a well-known speedup over classical searches of an unsorted database, and report better-than-classical performance. The algorithm is performed for all 8 possible single-result oracles and all 28 possible two-result oracles. All quantum solutions are shown to outperform their classical counterparts. Performing parallel operations will be a powerful capability as deeper circuits on larger, more complex quantum computers present new challenges. Here, we perform a pair of 2-qubit gates simultaneously in a single chain of trapped ions. We employ a pre-calculated pulse shaping scheme that modulates the phase and amplitude of the Raman transitions to drive programmable high-fidelity 2-qubit entangling gates in parallel by coupling to the collective modes of motion of the ion chain. Ensuring the operation yields only spin-spin interactions between the desired pairs, with neither residual spin-motion entanglement nor crosstalk spin-spin entanglement, is a nonlinear constraint problem, and pulse solutions are found using optimization techniques. As an application, we demonstrate the quantum full adder using a depth-4 circuit requiring the use of parallel 2-qubit operations.
The field of quantum computing has been developing rapidly over the last decades, driven by the belief that quantum computing can provide computational advantage over devices of other computational paradigms. However, the aspect of scaling quantum computing hardware systems to sizes where computational advantage can be achieved remains the cornerstone problem of the field. This thesis constitutes a step in the path towards scalable quantum systems. Specifically, the thesis describes the commissioning and operation of a trapped-ion quantum computing setup with modular design assembled in two 19-inch racks. The setup functions as a standalone device without a need for any special external infrastructure. The setup is capable of operating with 16 qubits in a highly-automated way with the ability to access the setup through a hardware-agnostic high-level interface. Details required for working with a 16-ion chain and the prospects of scaling the system further are discussed throughout the work. The setup's performance is demonstrated via experimental implementation of quantum error correction, a major milestone on the way to scalable and practically-useful quantum computing. Various quantum error correction primitives were performed with logical qubits encoded using color codes. The primitives include encoding of the logical states, direct implementation of logical Clifford gates, and implementation of logical non-Clifford gates via magic state injection and code switching. These results represent one of the first experimental logical-level manipulations with encoded qubits.
Quantum computing will be one of the most incredible breakthroughs in science and technology of our generation. Although the ultimate goal of building quantum computers that hold thousands of error-corrected qubits is still beyond our reach, we have made substantial progress. Compared with the first-generation prototypes, holding a few qubits with gate errors of several percent, the latest generation systems can apply more than a hundred gates (with fidelities above 99%) to tens of fully connected qubits. This thesis focuses on the applications of such state-of-the-art ion-trap quantum computers. The latest generation ion-trap quantum computers have become complex enough that automation is necessary for optimal operations. We present a full-stack automation scheme implemented on a system at the University of Maryland. With the automation scheme, the system can operate without human interference for a few days. With automation, such systems can efficiently demonstrate different categories of applications. We present the experimental study of several hybrid algorithms aiming for generation modeling and efficient quantum state preparation. We also present a gate-based digital quantum simulation with the trotterization method. Our result accurately reproduced all the features expected from running the algorithms. Verifying quantum computations with classical simulation is getting increasingly challenging as quantum computers evolve. We present two approaches to validate quantum computations. First, we demonstrate a method based on random measurement for comparing the results from different quantum computers. Our comparison captures the similarities between quantum computers made with the same technology. We then present experimental works in verifying quantum advantage classically with interactive protocols. We show that our results, at scale with real-time interaction, can demonstrate quantum advantages.
This thesis describes experimental work on implementing single and two qubit gates in ¹7¹Yb+ ions using methods suitable for a large scale quantum computer. By combining a magnetic field gradient with microwave and radiofrequency radiation, the spin and motional states of the ions are coupled which allows multi-qubit operations to be performed, as well as providing individual addressing of ions in frequency space. A dressed state qubit is used which exhibits an increase of over two orders of magnitude in the coherence time for a qubit that it is sensitive to the magnetic field gradient. Using this system, single qubit gates are characterised using the technique of randomised benchmarking, resulting in a measured average error per gate of 9(3)x10¯4. A new type of two qubit gate is experimentally demonstrated, which in comparison to a standard two qubit gate shows significantly increased resilience to two major sources of gate infidelity: heating of the motional mode of the ions during gate operations, and incorrectly set gate field frequencies. These types of errors are expected to become increasingly important with the move towards quantum processors with large numbers of qubits. Using this same technique, a two qubit gate is also demonstrated at a higher initial temperature with a significantly improved fidelity compared to standard methods. These gate techniques are used to demonstrate work towards implementing positiondependent quantum logic, a method which could remove the correlation between the number of ions and the number of gate fields required in a large scale quantum computing architecture. A method to move the dressed state qubit through a magnetic field gradient while preserving quantum information is demonstrated, as well as a method to optimise the phase of a two qubit gate of unknown phase in order to implement a CNOT logic gate. This provides a path forwards to demonstrating a CNOT gate using position-dependent quantum logic.
Realising large-scale quantum computation in the near future will require increasing the number of low-error two-qubit gates that can be implemented on a quantum computer before decoherence. One of the biggest challenges facing current trapped ion quantum computers is implementing high-speed two-qubit operations, whilst increasing the number of qubits. One of the most promising proposals for overcoming current limitations is the use of ultra-fast pulses to implement fast two-qubit gates between nearest-neighbour pairs of ions. In this thesis, I investigate these ‘fast gates’ in two-dimensional arrays of microtraps, each containing a single ion. I argue that two-dimensional architectures allow for a significant reduction in the number of two-qubit gates required for a particular computation, as compared to one-dimensional ion chains. I demonstrate this reduction for a quantum simulation of a 40-mode Fermi-Hubbard Hamiltonian. I develop an efficient scheme that allows fast gates to be numerically optimised for two-dimensional geometries. I find that this optimisation scheme is capable of designing gates that are faster, higher fidelity, and require lower laser repetition rates. Using this scheme, I find that high-speed two-qubit gates can be optimised for two-dimensional architectures, with fidelities well above thresholds required for fault tolerant error correction, around 99.99%. Furthermore, I find that fast gates in these architectures are robust to the presence of large numbers of surrounding ions. Following previous studies [1, 2] which have identified pulse imperfections as a dominant source of error in fast gates, I perform a worst-case error analysis. I find the fast gates presented in this thesis to require very small errors in single-qubit rotations, and I present recommendations for achieving those requirements. I also investigate other experimental considerations, and make recommendations for overcoming other technical challenges in realising fast gates.