Real-time quantum Krylov subspace algorithms with stochastic compilation and double factorization

Real-time quantum Krylov diagonalization algorithms provide a low-cost alternative to standard quantum phase estimation algorithms for ground and excited-state energy estimation. While deterministic Trotter-Suzuki methods are typically used to compile the time evolution operator in such algorithms, the necessary gate depths are prohibitively large for the simulation of large-scale systems on near-term devices. In this talk, I will discuss our recent work which introduces a new class of randomized quantum Krylov diagonalization (rQKD) algorithms which uses a combination of stochastic compilations strategies inspired by qDRIFT as well as low-rank double factorized Hamiltonian encoding strategies resulting in circuit depths with modest quantum resource requirements. To demonstrate the potential of the proposed rQKD algorithms, we provide numerical benchmarks for a variety of molecular systems with circuit-based statevector simulators achieving ground state energy errors of less than 1 kcal/mol with circuit depths orders of magnitude shallower than those required for deterministic Trotter-Suzuki decompositions.