[논문 리뷰] Momentum-Driven Reversible Logic Accelerates Efficient Irreversible Universal Computation

Kuen Wai Tang, Kyle J. Ray외 1명|arXiv (Cornell University)|2026. 02. 07.

Quantum Computing Algorithms and Architecture인용 수 0

한 줄 요약

논문은 커플된 양자 플럭스 매개변기 회로에서 두 가지 저전력 NAND 구현을 비교합니다: Controlled Erasure (CE) protocol와 새로운 Erasure-Flip (EF) protocol을 제시하며, EF가 비슷한 저에너지 비용으로 더 높은 속도와 충실도를 달성함을 보입니다.

ABSTRACT

We present implementations of two physically-embedded computation-universal logical operations using a 2-bit logical unit composed of coupled quantum flux parametrons -- Josephson-junction superconducting circuits. To illustrate universality, we investigate NAND gates built from these two distinct elementary operations. On the one hand, Controlled Erasure (CE) is designed using fixed-point analysis and assumes that information must be stored in locally-metastable distributions. On the other, Erasure-Flip (EF) leverages momentum as a computational resource and significantly outperforms the metastable approach, simultaneously achieving higher fidelity and faster computational speed without incurring any additional energetic cost. Notably, the momentum degree of freedom allows the EF to achieve universality by using both nontrivial reversible and irreversible logic simultaneously in different logical subspaces. These results not only provide a practical, high-performance protocol ripe for experimental realization but also underscore the broader potential of momentum-based computing paradigms.

연구 동기 및 목표

• CMOS 스케일링 한계와 데이터 센터의 에너지 수요로 인한 열역학적 한계에서 에너지 효율적 계산을 동기화한다.
• Realize universal NAND logic using physically embedded two-bit CQFP units.
• Compare two low-power protocols (CE and EF) for NAND implementation within a CQFP device.
• Quantify work, fidelity, and speed trade-offs for these protocols.
• Highlight the potential of momentum-based computing paradigms in superconducting circuits.

제안 방법

• Model a two-bit logical unit formed by coupled quantum flux parametrons (CQFP) as an underdamped Langevin system.
• Derive the CQFP potential landscape and its manipulation via external flux controls to implement NAND operations.
• Define partial NAND mappings to address two output bits from a 2-bit memory state.
• Analyze the Controlled Erasure (CE) protocol using fixed-point, metastable-state storage and saddle-node bifurcation.
• Introduce and simulate the Erasure-Flip (EF) protocol that uses momentum dynamics and quasi-harmonic potential to flip and erase bits.
• Compute work costs, fidelity, and speed from simulations across parameter sets and protocol durations.

실험 결과

연구 질문

• RQ1 Can a momentum-based protocol achieve higher fidelity and faster operation for NAND logic in CQFPs without increasing energy cost?
• RQ2 How do CE and EF compare in terms of work cost, error rates, and operational speed across different circuit parameters (β, γ) and barrier heights?
• RQ3 Does momentum-enabled EF enable universality by combining reversible and irreversible subspaces within the same device?
• RQ4 What are the thermodynamic limits (Landauer bound) and practical trade-offs for these physically embedded NAND operations?
• RQ5 How robust are CE and EF to parameter variations and nonadiabatic transitions in real CQFP implementations?

주요 결과

• EF achieves higher speed and fidelity than CE for NAND without extra energetic cost in simulations.
• CE shows two-peak work distributions and fidelity limited by storage-pair barrier escapes, with average work around 53.6 kB T under tested conditions.
• EF yields average total work about 16 kB T, with storage and erasure pair costs around 9 kB T and 23 kB T respectively, indicating efficient energy expenditure.
• Momentum dynamics in EF allow a complete or partial NAND mapping by exploiting kinetic energy and controlled barrier modulation.
• CE fidelity is strongly sensitive to barrier heights and parameter choices, and its speed is constrained by storage-pair dynamics.
• EF demonstrates that momentum-based computing can store and manipulate information in momentum space, enabling universal, efficient computation in CQFPs.