  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.
