Cryogenic quantum computers play a leading role in demonstrating quantum advantage. Given the severe constraints on the cooling capacity in cryogenic environments, thermal design is crucial for the scalability of these computers. The sources of heat dissipation include passive inflow via inter-temperature wires and the power consumption of components located in the cryostat, such as wire amplifiers and quantum-classical interfaces. Thus, a critical challenge is to reduce the number of wires by reducing the required inter-temperature bandwidth while maintaining minimal additional power consumption in the cryostat. One solution to address this challenge is near-data processing using ultra-low-power computational logic within the cryostat. Based on the workload analysis and domain-specific system design focused on Variational Quantum Algorithms (VQAs), we propose the Cryogenic Counter-based Co-processor for VQAs (C3-VQA) to enhance the design scalability of cryogenic quantum computers under the thermal constraint. The C3-VQA utilizes single-flux-quantum logic, which is an ultra-low-power superconducting digital circuit that operates at the 4 K environment. The C3-VQA precomputes a part of the expectation value calculations for VQAs and buffers intermediate values using simple bit operation units and counters in the cryostat, thereby reducing the required inter-temperature bandwidth with small additional power consumption. Consequently, the C3-VQA reduces the number of wires, leading to a reduction in the total heat dissipation in the cryostat. Our evaluation shows that the C3-VQA reduces the total heat dissipation at the 4 K stage by 30% and 81% under sequential-shot and parallel-shot execution scenarios, respectively. Furthermore, a case study in quantum chemistry shows that the C3-VQA reduces total heat dissipation by 87% with a 10,000-qubit system.

15 pages, 9 figures, 5 tables. This is an extention of arXiv:2403.00363 and arXiv:2310.01630