Speed-oriented quantum circuit backend

Abstract: We present a new software package for efficient quantum circuit generation, designed to achieve optimal runtime performance. Despite being in an early stage of development, our implementation demonstrates significant advantages over existing tools. Using the quantum Fourier transform (QFT) as a benchmark, we show that our backend can generate circuits for systems with up to 2000 qubits faster than widely used frameworks such as Qiskit and Q#. This improvement is particularly relevant for applications where classical preprocessing time, including circuit generation, must be minimized to not diminish any potential quantum advantage - for example, in combinatorial optimization tasks. Additionally, our software provides high-level primitives for bit- and integer-level manipulations, offering a simplified interface for integration with high-level quantum programming languages.

• The paper introduces a quantum circuit backend that leverages layered data structures for constant-time gate insertion and cancellation.
• It details an instruction-list abstraction that streamlines complex arithmetic operations in quantum algorithms for rapid circuit construction.
• Empirical benchmarks reveal dramatic performance gains, with speedups up to 1,748,000× and minimal memory overhead for circuits with thousands of qubits.

Speed-oriented Quantum Circuit Backend: A Technical Essay

Introduction

This paper presents a specialized quantum circuit backend (QCB) designed for optimal runtime performance and minimal resource consumption during quantum circuit generation. The motivation is rooted in an observable shift in quantum algorithm deployment: as the quantum hardware scales, the classical preprocessing time for circuit generation becomes non-negligible, especially for large circuits or workloads in combinatorial optimization and similar applications.

The proposed backend emphasizes efficiency over function integration—contrasting with mainstream quantum software, which typically couples circuit generation and execution. High-level primitives for bit- and integer-level quantum manipulations are also provided, facilitating seamless integration into modern quantum programming environments.

Data Structures and Circuit Representation

Central to the efficiency is the backend's representation of quantum circuits. The authors adopt a layered model, where each layer is a set of non-interacting gates executable in parallel. This model enables localized optimization, such as commuting and canceling gates (especially inverses and consecutive parametric gates), which are not generally feasible with strictly sequential gate lists. Gates and layers are represented via custom-defined C structs, further optimizing storage and lookup times by employing two-dimensional arrays and lookup tables to track last-occupied layers per qubit and gate indices.

(Figure 1)

Figure 1: Visualization of the layered data structure and lookup tables for efficient gate insertion and cancellation in a 5-qubit QFT circuit.

Several additional optimizations are integrated, including immediate cancellation of inverse gates, aggregation of consecutive parametric gates, and efficient layer assignment via constant-time array lookups. The backend achieves $\mathcal{O}(1)$ insertion and retrieval whenever possible, a notable departure from the $\mathcal{O}(N)$ or $\mathcal{O}(\log N)$ strategies of competing frameworks.

Quantum Instruction Lists

Recognizing the prevalence of modular, arithmetic-heavy routines in quantum algorithms (e.g., Grover or QFT-based arithmetic), the backend introduces an instruction-list abstraction. Here, composite operations—such as integer addition, multiplication, and division—are encoded as preconstructed circuits (or instructions), which can be sequentially appended to a program. This abstraction optimizes both expressiveness and efficiency, permitting rapid construction of complex routines without storing every intermediate gate individually. It also provides a natural interface for future high-level quantum languages.

Performance Benchmarking

The backend's performance is evaluated using the quantum Fourier transform (QFT) as a benchmark, comparing both a gate-by-gate generated variant and a QFT-instruction variant against 11 leading quantum software platforms, including Qiskit, Q#, Cirq, Quipper, PennyLane, TKET, Ket, ProjectQ, and others. The focus is on runtime for circuit generation and memory consumption.

(Figure 2)

Figure 2: Running times for generating QFT circuits across multiple frameworks, including the proposed backend (both general and QFT-instruction variants).

(Figure 3)

Figure 3: Memory consumption for QFT circuit generation as a function of problem size, comparing the backend to major quantum software frameworks.

The numerical findings are strong:

• The backend outpaces PyTKet by factors of up to $47\times$ (general) and $1209\times$ (QFT-instruction) for circuits of up to 2000 qubits.
• Compared to Q#, the speedup reaches $67,800\times$ for the general and $1,748,000\times$ for the QFT-instruction variant.
• Memory usage for a 2000-qubit QFT is contained within 100-300 MB, approaching the theoretical minimum.
• Only Ket approaches similar memory efficiency for large instances, but this advantage is projected to diminish with circuit scale, as the backend nears the information-theoretical lower limit.

Implications and Future Directions

The empirical results challenge the implicit assumption that classical circuit generation overhead is negligible for large-scale quantum workflows. As demonstrated, existing tools introduce substantial overheads that rapidly become prohibitive as circuit widths grow into the thousands of qubits—an expected regime for practical quantum advantage.

The QCB’s approach—decoupling efficient circuit construction from execution or simulation, emphasizing minimal memory footprint, and modular high-level quantum instructions—provides a toolkit well-suited for integration into scalable, cloud-based, or distributed quantum software stacks. It is especially impactful for applications where fast circuit turn-around is essential, such as variational algorithms, quantum combinatorial optimization, and large batch-processing pipelines.

Practically, the streamlined backend will allow algorithm designers to conduct realistic resource estimation, including classical resource costs for end-to-end workflows. This is critical, for instance, when evaluating the real-world quantum advantage in combinatorial optimization [Wilkening et al., 2025, 2026].

In terms of future development, the backend would benefit from:

• Integration of advanced circuit optimization passes (e.g., peephole optimization, architecture-aware mapping).
• Multi-threaded implementations for parallel circuit construction.
• Inclusion of error-correction logic and translation to physical hardware constraints (e.g., limited connectivity, native gate sets).
• Further lowering constant-factor overheads and generalized instruction support for arbitrary routines.

Conclusion

The speed-oriented quantum circuit backend establishes a new standard for efficient quantum circuit generation, both in time and memory, validating that classical preprocessing has nontrivial impact on quantum computational workflows. The architecture—layered data structures, optimized insertion, and instruction-list abstraction—enables rapid construction even at extreme scales, with improvements above three orders of magnitude relative to dominant frameworks in the field.

As quantum devices mature to accommodate more qubits and deeper algorithms, such backend innovations will be indispensable for both reducing the total computation wall time and unlocking realistic, large-scale quantum software engineering. This work thus forms a robust foundation for next-generation, scalable quantum software environments and high-level programming paradigms.

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References

"Speed-oriented quantum circuit backend" (2604.21656)