Year: 2022
Type: article
Abstract: Realizing nonunitary transformations on unitary-gate-based quantum devices is critically important for simulating a variety of physical problems, including open quantum systems and subnormalized quantum states. We present a dilation-based algorithm to simulate nonunitary operations using probabilistic quantum computing with only one ancilla qubit. We utilize the singular-value decomposition (SVD) to decompose any general quantum operator into a product of two unitary operators and a diagonal nonunitary operator, which we show can be implemented by a diagonal unitary operator in a one-qubit dilated space. While dilation techniques increase the number of qubits in the calculation, and thus the gate complexity, our algorithm limits the operations required in the dilated space to a diagonal unitary operator, which has known circuit decompositions. We use this algorithm to prepare random subnormalized two-level states on a quantum device with high fidelity. Furthermore, we present the accurate nonunitary dynamics of two-level open quantum systems in a dephasing channel and an amplitude-damping channel computed on a quantum device. The algorithm presented will be most useful for implementing general nonunitary operations when the SVD can be readily computed, which is the case for most operators in the noisy intermediate-scale quantum computing era.
Source: Physical Review A
Institutions: University of Chicago, Harvard University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G1673814530, QUANTUM COMPUTING ALGORITHMS AND APPLICATIONS FOR COHERENT AND STRONGLY CORRELATED CHEMICAL SYSTEMS, RAISE-QAC-QSA: Open Quantum Systems on Noisy Intermediate-Scale Quantum Devices, G518131803, EAGER‐QAC‐QSA: Quantum Chemistry with Mean-field Cost from Semidefinite Programming on Quantum Computing Devices
OpenAlex ID: W4229004460