General approaches in ensemble quantum computing

Bi Qiao, Harry E. Ruda

Jeongho Bang, Junghee Ryu, Chang‐Woo Lee +3 more

A model of quantum computation (QC) is compared with a generalized classical computation model, named stochastic ensemble computation (SEnC), in article number 1800037 by Jeongho Bang, Jinhyoung Lee, Wonmin Son and co-workers. SEnC runs in an ensemble consisting of finite copies of single probabilistic entities, and hence is a generalized probabilistic Turing machine. Impossibility of simulating a QC in the SEnC is proved, manifesting “QC is characterized beyond any classical probabilistic computation,” i.e., SEnC ⊆ QC.

Jeffrey A. George, Michael E. Colvin, Viswanathan V. Krishnan

Jeongho Bang, Junghee Ryu, Chang‐Woo Lee +3 more

Abstract In this study, a distinctive feature of quantum computation (QC) is characterized. To this end, a seemingly‐powerful classical computing model, called “stochastic ensemble machine (SEnM),” is considered. The SEnM runs with an ensemble consisting of finite copies of a single probabilistic machine, hence is as powerful as a probabilistic Turing machine (PTM). Then the hypothesis—that is, the SEnM can effectively simulate a general circuit model of QC—is tested by introducing an information‐theoretic inequality, named readout inequality. The inequality is satisfied by the SEnM and imposes a critical condition: if the hypothesis holds, the inequality should be satisfied by the probing model of QC. However, it is shown that the above hypothesis is not generally accepted with the inequality violation; namely, such a simulation necessarily fails, implying that PTM ⊆ QC.

Viswanathan V. Krishnan

Yasushi Yoneta

Preparing thermal equilibrium states is an essential task for finite-temperature quantum simulations. In statistical mechanics, microstates in thermal equilibrium can be obtained from statistical ensembles. To date, numerous ensembles have been devised, ranging from Gibbs ensembles such as the canonical and microcanonical ensembles to a variety of generalized ensembles. Since these ensembles yield equivalent thermodynamic predictions, one can freely choose an ensemble for computational convenience. In this paper, we exploit this flexibility to develop an efficient quantum algorithm for preparing thermal equilibrium states. We first present a quantum algorithm for implementing generalized ensembles within the framework of quantum singular value transformation. We then perform a detailed analysis of the computational cost and elucidate its dependence on the choice of the ensemble. Our analysis shows that employing an appropriate ensemble can significantly mitigate ensemble-dependent overhead and yield improved scaling of the computational cost with system size compared to existing methods based on the canonical ensemble. We also numerically demonstrate that our approach achieves a significant reduction in the computational cost even for small finite-size systems. Our algorithm applies to arbitrary thermodynamic systems at any temperature and is thus expected to offer a practical and versatile method for computing finite-temperature properties of quantum many-body systems. These results highlight the potential of ensemble design as a powerful tool for enhancing the efficiency of a broad class of quantum algorithms.