2024/04/05 by Zachary Stier, Stier, Zachary
Economics, Econometrics and Finance · #FOS: Physical sciences #Quantum Physics (quant-ph) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2404.04198
openalex publication_date 2024/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the problem of state synthesis in the DQC1 (One Clean Qubit) model of quantum computation, which provides a single pure qubit and n maximally mixed qubits, and after applying any quantum circuit some subset of the qubits are measured or discarded. In the case of discarding, we show that it is impossible to prepare additional pure qubits, and that it is impossible to prepare very low-temperature Gibbs states on additional qubits. In the case of measurements, we show that the probability of synthesizing m additional qubits is bounded by 21-m, and that the probability of preparing low-temperature Gibbs states is bounded by 22-m. As a consequence, we give a lower-bound the runtime of a recently studied class of repeated interaction quantum algorithms. The techniques used study states and circuits at the level of entries of their respective density and unitary matrices.