Quantum cooling, a deterministic process that drives any state to the lowest eigenstate, has been widely used from studying ground state properties of chemistry and condensed matter quantum physics to general optimization problems. However, the cooling procedure is generally non-unitary, hence its realization on a quantum computer either requires deep circuits or assumes specific input states with variational circuits. Here, we propose universal quantum cooling algorithms that overcome these limitations. By utilizing a dual-phase representation of decaying functions, we show how to universally and deterministically realize a general cooling procedure with shallow quantum circuits. We demonstrate its applications in cooling an arbitrary input state with known ground state energy, corresponding to satisfactory, linear algebra tasks, and quantum state compiling tasks, and preparing unknown eigenvalues and eigenstates, corresponding to quantum many-body problems. Compared to quantum phase estimation, our method uses only one ancillary qubit and much shallower circuits, showing exponential improvement of the circuit complexity with respect to the final state infidelity. We numerically benchmark the algorithms for the $8$-qubit Heisenberg model and verify its feasibility for accurately finding eigenenergies and obtaining eigenstate measurements. Our work paves the way for efficient and universal quantum algorithmic cooling with near-term as well as universal fault-tolerant quantum devices.
Dr. You Zhou now is a Research Fellow at Centre for Quantum Technologies, National University of Singapore, after a Postdoc at Harvard University, He got his Ph.D. of quantum information from Tsinghua University, and Bachelor of EE from Zhejiang University. You Zhou is interested in multipartite entanglement, quantum benchmarking, and the application to quantum (many-body) physics.Pei Zeng is currently a Postdoc scholar at the University of Chicago. He formerly received his PhD in Institute for Interdisciplinary Information Sciences, Tsinghua University in 2020.