Basic circuit compilation techniques for an ion-trap quantum machine (1603.07678v4)

Abstract: We study the problem of compilation of quantum algorithms into optimized physical-level circuits executable in a quantum information processing (QIP) experiment based on trapped atomic ions. We report a complete strategy: starting with an algorithm in the form of a quantum computer program, we compile it into a high-level logical circuit that goes through multiple stages of decomposition into progressively lower-level circuits until we reach the physical execution-level specification. We skip the fault-tolerance layer, as it is not within the scope of this work. The different stages are structured so as to best assist with the overall optimization while taking into account numerous optimization criteria, including minimizing the number of expensive two-qubit gates, minimizing the number of less expensive single-qubit gates, optimizing the runtime, minimizing the overall circuit error, and optimizing classical control sequences. Our approach allows a trade-off between circuit runtime and quantum error, as well as to accommodate future changes in the optimization criteria that may likely arise as a result of the anticipated improvements in the physical-level control of the experiment.

• The paper outlines techniques to compile quantum algorithms into efficient circuits optimized for ion-trap systems, minimizing gates, runtime, and error for improved performance.
• The approach utilizes native ion-trap gates and shows optimized constructions for operations like the CNOT gate, significantly reducing gate count compared to canonical methods.
• Practically, these methods improve algorithm performance on current ion-trap hardware by reducing gate count and errors, enabling more complex experiments than previously feasible.

Quantum Circuit Compilation Techniques for Ion-Trap Quantum Computing

The paper explores methodologies for compiling quantum algorithms into optimized circuits suitable for execution on an ion-trap quantum information processing system. The focus is on transforming high-level quantum algorithms into efficient lower-level circuits that are compatible with the constraints and capabilities of ion-trap quantum machines, specifically avoiding the inclusion of fault-tolerant techniques.

Key Aspects of the Research

The research outlines a process that begins with a quantum algorithm and transitions through multiple decomposition stages. Each stage aims to lower the representation level of the circuit until it reaches a physically executable format optimized for a trapped-ion system. The core optimization criteria include the minimization of two-qubit gates, single-qubit gates, circuit runtime, and overall circuit error. Additionally, it emphasizes optimizing classical control sequences, facilitating trade-offs between runtime and quantum error, and adapting to future improvements in experimental control.

Trapped Ion System Overview

Trapped ion systems store qubits within atomic ions using laser-induced interactions. The system allows high-fidelity state initialization and measurement, with qubit states manipulated through laser-driven gates. In the context of this compilation strategy, the paper detailed two essential types of gates:

1. Single-Qubit Gates: Notably, the ion-trap system utilizes $R(\theta, \phi)$ rotations, which allow precise control over qubit states with variations in rotation angle and phase controlled via lasers.
2. Two-Qubit Gates: The $XX(\chi)$ gate, based on the M\o lmer-S\o rensen interaction, is fundamental to entangling qubits. This gate's fidelity is dependent on the specific ion pairs used, with variations in phase dictated by experimental parameters.

Optimizations and Gate Implementations

The paper presents several optimized implementations of critical quantum operations:

• CNOT Gate Construction: By leveraging the $XX$ interaction, the CNOT gate can be constructed with reduced single-qubit gate overhead compared to prior implementations.
• Controlled Gates: The authors demonstrate that controlled roots of Pauli gates require only one $XX$ interaction, significantly reducing complexity compared to canonical methods.
• Flexibility in Rotation Sequences: The ability to equivalently express $RX$, $RY$, and $RZ$ rotations optimizes circuit depth and fidelity by exploiting the native capabilities of the ion-trap platform.

Practical and Theoretical Implications

Practically, the proposed methodology significantly improves the performance of quantum algorithms on currently available hardware by reducing gate count and error rates, directly influencing the feasibility of executing more complex quantum algorithms experimentally. Theoretically, this work facilitates future research into adapting quantum algorithms for hardware-specific implementations, further bridging the gap between quantum theory and practical quantum computing.

Future Developments

The speculated improvements in physical-level control—such as parallel execution of gates and enhanced gate fidelities—are expected to further refine the balance between minimizing quantum errors and reducing execution time. This paper's methods are a foundational step towards automated, hardware-aware quantum algorithm compilation, essential for the progression to widespread implementation of quantum computing technology.

Ultimately, this research enhances the capability to automatically compile and optimize quantum circuits, enabling more sophisticated experiments on existing quantum hardware and paving the way for further advancements as technology and methods evolve.