Automated optimization of large quantum circuits with continuous parameters (1710.07345v2)

Abstract: We develop and implement automated methods for optimizing quantum circuits of the size and type expected in quantum computations that outperform classical computers. We show how to handle continuous gate parameters and report a collection of fast algorithms capable of optimizing large-scale quantum circuits. For the suite of benchmarks considered, we obtain substantial reductions in gate counts. In particular, we provide better optimization in significantly less time than previous approaches, while making minimal structural changes so as to preserve the basic layout of the underlying quantum algorithms. Our results help bridge the gap between the computations that can be run on existing hardware and those that are expected to outperform classical computers.

• The paper introduces automated optimization methods that significantly reduce gate counts in large quantum circuits with continuous parameters.
• It employs a suite of heuristics driven by phase polynomial representation to achieve up to a 5.2× reduction in T-gates for benchmark circuits like quantum Fourier transforms and integer adders.
• These results bridge the gap between current quantum hardware limitations and the execution of quantum algorithms, paving the way for scalable quantum computing.

Automated Optimization of Large Quantum Circuits with Continuous Parameters

This paper describes the development and implementation of automated methods for optimizing quantum circuits characterized by large size and continuous parameters, intended for computations surpassing the capabilities of classical computers. The primary focus is reducing gate counts through algorithmic improvements rather than manual intervention. This work situates itself in the context of bridging the existing gap between the current quantum computing hardware and its potential superiority over classical systems.

The paper categorizes its contributions primarily through software-based optimizations. The authors highlight that global optimization of arbitrary quantum circuits remains QMA-hard, necessitating alternative strategies. Here, a suite of heuristics has been carefully chosen to maximize efficiency, maintaining the essential structure of quantum algorithms while achieving significant reductions in resource requirements.

Strong Numerical Results

The results presented emphasize substantial gate reductions in benchmark circuits, such as those involving the quantum Fourier transform (QFT) and integer adders, crucial for algorithms like Shor's factoring algorithm. As an example, using the aforementioned strategies, the Quipper library adder achieves a reduction in the T-gate count by up to a factor of 5.2 in automated scenarios, demonstrating the algorithm's efficacy. These optimizations translate into notable performance improvements, especially in larger benchmarks, indicating promising scalability.

Technical Contributions and Implications

The optimizations leverage the specific properties of quantum circuits expressed in terms of $\{cnot, \}$ gates, and a novel utilization of the phase polynomial representation generalizes beyond prior studies focused on $\{cnot, t\}$ circuits alone. The paper takes into special consideration the practical limitations imposed by early quantum computing technologies, addressing the challenges through structural-agnostic optimization algorithms that do not impose additional interactions.

Moreover, this research remains unique by including continuous gate parameters within its optimization framework, relevant given quantum information processing technologies, such as superconducting qubits or trapped ions, that natively support these gates. Therefore, the presented work has significant ramifications for both near-term quantum computing applications, where fault-tolerant discrete Clifford+$t$ sets may be approximated through continuous forms before compilation, and for longer-term implementations preserving physical-level efficiency.

Speculation for Future AI Developments

Given the advancement outlined in this paper, future prospects could involve further refinement of the optimization routines, potentially incorporating template-based or peep-hole schemes for more exhaustive exploration of circuit space. Concurrently, adjusting the cost function to weigh diverse resources like qubits and distinct gates differently could yield optimizers making informed trade-offs, particularly pertinent in an era moving towards quantum volume as a metric.

In summary, the work performed showcases an effective integration of algorithmic principles tailored specifically for quantum computing's burgeoning needs. This paper's insights reflect a progressive stride towards harnessing quantum hardware capabilities at scale, promoting the realization of practical quantum advantage.