Universal quantum simulation of single-qubit nonunitary operators using duality quantum algorithm

Quantum information processing enhances human’s power to simulate nature in quantum level and solve complex problem efficiently. During the process, a series of operators is performed to evolve the system or undertake a computing task. In recent year, research interest in non-Hermitian quantum systems, dissipative-quantum systems and new quantum algorithms has greatly increased, which nonunitary operators take an important role in. In this work, we utilize the linear combination of unitaries technique for nonunitary dynamics on a single qubit to give explicit decompositions of the necessary unitaries, and simulate arbitrary time-dependent single-qubit nonunitary operator F(t) using duality quantum algorithm. We find that the successful probability is not only decided by F(t) and the initial state, but also is inversely proportional to the dimensions of the used ancillary Hilbert subspace. In a general case, the simulation can be achieved in both eight- and six-dimensional Hilbert spaces. In phase matching conditions, F(t) can be simulated by only two qubits. We illustrate our method by simulating typical non-Hermitian systems and single-qubit measurements. Our method can be extended to high-dimensional case, such as Abrams–Lloyd’s two-qubit gate. By discussing the practicability, we expect applications and experimental implementations in the near future.