Browsing by Author "Brown, Kenneth R"

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.

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.

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.

As trapped-ion quantum technologies advance, quantum simulation platforms and quantum computers scale in the number of qubits available and their possible operations. As the laser control systems and the micromotion from the trapping potential become harder to manage, the possibility of implementing atomic/molecular hybrid trapped ion systems has been investigated. Such systems require state preparation, manipulation, and detection of molecular ions, which have more complex energy-level structures and selection rules.

This thesis reports a preliminary study on Dipole-Phonon Quantum Logic(DPQL), which is the interaction between trapped molecular ions and atomic ions, and the possibility of realizing indirect laserless control of the electronic state of the molecular ion.

The experimental candidate is co-trapped calcium and calcium oxide ions. They are laser-cooled to the motional ground state to study the mapping from the molecule’s electronic state to the shared motion, which could then be detected on the atomic ion. A Monte-Carlo simulation is performed to predict the experimental observation of phonon number change events. The controlling program is organized and reordered with a scheduler program to increase the experiment’s efficiency.

The previous experimental control is migrated and upgraded to a new architecture. The Monte-Carlo simulation suggests that the signal should be observed in the lab environment at a timescale of tens of minutes. This study lays the groundwork for further investigations into DPQL and its potential applications.

In this dissertation we will discuss methods for creating error-robust logical qubits which have been optimized for trapped ion quantum computers. We will cover the basic building blocks of quantum information and develop an understanding of the standard techniques for building fault-tolerant quantum computers through the use of quantum error correcting codes. We will then focus on trapped ion systems, although many of the errors we consider also occur in other hardware implementations.

The majority of this dissertation is concerned with taking advantage of the structure found in experimental errors to maximize system performance. Using numerical simulation, we study the interplay of structured error models and quantum error correction. We then cover optimizations to the standard quantum error correction framework, both through gate compilation and code design, to correct coherent gate overrotation and dephasing errors. The latter section will also include experiments run on a quantum computer at the University of Maryland which verify the effectiveness of our ideas. We will end with a discussion of a method for quantum error detection in near-term systems by extending the flag gadget framework often used in quantum error correction.

Through this body of work we hope to provide evidence for the value, within the context of quantum error correction, of detailed understanding of our physical systems. Oftentimes, codes and protocols are designed without actual implementation in mind. While these studied often produce useful results, more effective methods can sometimes be found when the physics is kept in mind. Our hope is that this dissertation motivates further study of the physical error processes present in quantum computing architectures, as well as development of novel methods to correct them.

Trapped atomic ions are one of the leading candidates for scalable quantum computation and simulation. As the system scales up, both high-performance hardware and robust quantum control are essential for building a reliable large-scale quantum computer: high-performance hardware suppresses the external noise level and robust quantum control guarantees high-fidelity quantum gates under external noise. Moreover, for analog simulations and computations, using bosonic states for quantum information processing can be beneficial but characterizing complex bosonic states is challenging. In this thesis we report our progress on both hardware and software control of trapped ion systems. We design and construct a compact cryogenic trapped-ion platform that is easy to integrate and manufacture, and characterize the system behavior which shows several advantages over conventional trapped-ion systems in UHV chambers. We develop a robust modulated two-qubit gate scheme using pulse design to improve the robustness of two-qubit gates to mode frequency drift and verify its robustness on the compact cryogenic platform. We also report our work on characterizing complex motional states in a long ion chain by using Jaynes-Cummings-type interactions between bosonic states and two-level systems. We measured the Fock state population of various complex motional states and the density matrix of a motional Bell state. These works offer us new insights into building a high-performance, large-scale quantum computing platform as well as characterizing complex quantum states.

The advent of quantum computation foretells a new era in science and technology, but the fragility of quantum bits (qubits) and the unreliability of gates hinder the realization of functioning quantum computers. For ion trap quantum computers in particular, 2-qubit operations relying on the M\o lmer-S\o rensen interaction have the greatest error rates. This dissertation introduces frequency-modulated (FM) pulses as a measure to maximize 2-qubit gate fidelity and a way to calibrate gate errors through the measurement of circuit performance.

A key challenge of two-qubit gates in ion chains is unwanted residual entanglement between the ion spin and its motion. Frequency-modulated pulses are developed to achieve such goal. This theoretical advance has led to high-fidelity 2-qubit gates that are robust against small frequency drifts in a 5-ion experiment. Combining frequency and amplitude modulation, numerical calculations suggest that entanglement between an arbitrary pair of qubits are possible in a lattice with up to 50 ions. More recently, long-distance 2-qubit gates have been realized within a 17-ion chain.

Quantum circuit calibration is proposed to improve quantum circuits using feedback from measurement results. A relationship between the error parameters and measured observables can be established to identify systematic circuit errors. The calibration of a 6-qubit parity check circuit targeting 2-qubit overrotations has been implemented using measurement results from an experimental 15-ion trap. This improvement is conducive to quantum error correction protocols which involve high-weight stabilizers. A 4-bit Toffoli circuit with an error vector of length 6 is calibrated using a custom circuit simulator, reducing the average error size by a factor of 4. Using linear and quadratic approximation, a 6-bit Toffoli circuit with 12 error parameters is calibrated in the presence of 3 ancilla qubits.

Quantum computing is an emerging technology with the potential to provide computational power beyond the capabilities of current computers. The field of quantum computing is evolving rapidly, and small-scale quantum physics experiments have grown into commercial quantum systems with tens of qubits. While qubits are at the center of the quantum computer, complex classical control systems are required to operate them. Current state-of-the-art quantum systems already require tens to hundreds of devices to be controlled with high precision, and the complexity will further increase for larger quantum systems. Hence, building the next generation of quantum computers will not only be a physics challenge, but also a significant engineering challenge covering the fields of electrical engineering, computer engineering, and computer science. This thesis focuses on the computer engineering and computer science challenges faced when building the next generation of quantum computers. We show that well-designed software architectures for quantum control systems can yield significant improvements in software performance, modularity, and portability. Software testing and validation are essential to ensure quality, and we show that we can perform fast and accurate functional simulations of real-time quantum control software. Efficient calibration of quantum systems is also a challenge, and we introduce a graph-based approach to address the calibration challenge. Finally, we present a graph-based pulse representation to enable pulse-level access for quantum systems.

Quantum experiments often require finer control than offered by circuit-level abstractions. While such abstractions hide hardware-specific details, they also hide the details of control fields, which are crucial for quantum optimal control. Currently, the writing of pulse-level quantum experiments is a slow process producing code that is tightly coupled to hardware-specifics. In this thesis, I seek to solve this problem by introducing a software framework for the rapid design of ARTIQ experiments at the pulse-level. I describe the implementation of this framework, targeting direct digital synthesizers, and demonstrate its capabilities. A scheme for integration into Duke ARTIQ Extensions (DAX) is also discussed, enabling hybrid quantum experiments.

In this report we validate that Minimum Weight Perfect Matching (MWPM) decoding ofa surface code helps attain a higher code threshold than standard decoding by taking into account the correlations of errors that occur on the lattice. Correlated decoding cannot be directly performed using MWPM due to the presence of hyperedges in the graph. Decomposing correlated errors into simultaneous X and Z excitations, along with considering an asymmetric code for optimal performance of this scheme, yields a codecapacity threshold of 15% for standard depolarizing error by updating the weights of one decoding graph based on the corrections of another.