Quantum state preparation and nonunitary evolution with diagonal operators

Realizing non-unitary transformations on unitary-gate based quantum devices is critically important for simulating a variety of physical problems including open systems and subnormalized states. We present dilation algorithm to simulate operations using probabilistic computing with only one ancilla qubit. utilize the singular-value decomposition (SVD) decompose any general operator into product two unitary operators diagonal operator, which we show can be implemented by in 1-qubit dilated space. While techniques increase number qubits calculation, thus gate complexity, our limits required space has known circuit decompositions. use this prepare random sub-normalized two-level states device high fidelity. Furthermore, accurate dynamics dephasing channel an amplitude damping computed device. The presented will most useful implementing when SVD readily computed, case noisy intermediate-scale era.