Designing minimalistic variational quantum ansatz inspired by algorithmic cooling

Abstract Variational quantum algorithms offer a practical route to low-energy state preparation on near-term hardware, but performance depends strongly on ansatz design. We introduce the Heat-Exchange (HE) ansatz, a compact circuit family inspired by heat-bath algorithmic cooling and built from a tunable exchange interaction between a system qubit and an auxiliary bath qubit. On superconducting processors the exchange evolution $$U_{\textrm{HE}}(\theta )=\exp [-i\theta (XX+YY)/2]$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>U</mml:mi> <mml:mtext>HE</mml:mtext> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>θ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mo>exp</mml:mo> <mml:mrow> <mml:mo>[</mml:mo> <mml:mo>-</mml:mo> <mml:mi>i</mml:mi> <mml:mi>θ</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>X</mml:mi> <mml:mi>X</mml:mi> <mml:mo>+</mml:mo> <mml:mi>Y</mml:mi> <mml:mi>Y</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> <mml:mo>]</mml:mo> </mml:mrow> </mml:mrow> </mml:math> is implemented digitally as a shallow compiled gate sequence, requiring no mid-circuit reset, measurement, or feedback. We benchmark HE on two complementary tasks: weighted MaxCut on random complete graphs (noise-free simulation and hardware runs on with readout error mitigation) and a one-dimensional Heisenberg chain with a pinned site within a dissipative-VQE-style workflow (noise-free simulation). HE increases the probability of sampling the best cut compared with a hardware-efficient baseline and QAOA under limited evaluation budgets and yields ground-state energies with sub-percent relative error for the impurity chain. These results highlight exchange-driven cooling blocks as compact, parameter-efficient, hardware-compatible primitives for near-term variational workflows.