Paper
Quantum Krylov algorithm using unitary decomposition for exact eigenstates of fermionic systems using quantum computers
Authors
Ayush Asthana
Abstract
Quantum Krylov algorithms have emerged as a useful framework for quantum simulations in quantum chemistry and many-body physics, offering a favorable trade-off between potential quantum speedups and practical resource demands. However, the current primary approach to building Krylov vectors in these algorithms is to use real or imaginary-time evolution, which is not exact, require an arbitrary time-step parameter (), and degrade the Krylov vectors quickly with increasing . In this paper, we develop a quantum Krylov algorithm without time evolution and with an exact formulation of the Krylov subspace, named ``Quantum Krylov using Unitary Decomposition'' (QKUD), along with implementation proposals for quantum computers. Not only is this algorithm exact in the limit of the error parameter , but it also produces more accurate Krylov vectors at than conventional time evolution due to more favorable error scaling (O() vs O()). Through simulations, we demonstrate that these theoretical benefits yield numerical advantages: (i) QKUD provides numerically exact results at small , (ii) it remains stable across a broad range of values, indicating low parameter sensitivity, and (iii) it can solve problems unreachable by conventional time evolution. This development resolves a central limitation of quantum Krylov algorithms, namely their inexactness and sensitivity to the time-step parameter, and paves the way for new and powerful quantum Krylov algorithms for quantum computers with a stronger promise of quantum advantage.