Transforming unitary operations via quantum circuits: Universal unitary inversion, transposition, and complex conjugation

Zapraszamy w piatek 10.12.2021r. o godz. 12:15

Seminarium hybrid form  pt.: Transforming unitary operations via quantum circuits: Universal unitary inversion, transposition, and complex conjugation. Speaker: dr Marco Túlio Quintino, Affiliation: Austrian Academy of Sciences

Place:https://zoom.us/j/91729944437?pwd=TkJpNUVROUxjQ2NwZDZ0RlA1Mk8rZz09

Abstract:Given a general d-dimensional unitary operation U for which, apart from the dimension, its description is unknown, is it possible to design a quantum circuit to implement its inverse? How does the situation change when k uses of unitary operation U are allowed? And what about transforming U into another operation described by f(U), where f is a general function from unitary operators to unitary operators? Do these circuits require a long depth, or can they be parallelised?

Using the unitary inversion problem as common tread, we will carefully address these questions by means of quantum circuits and quantum processes, also referred to as quantum combs. For instance, we construct a probabilistic universal quantum circuit that can invert k uses of an arbitrary unitary operation in which the success probability approaches 1 exponentially in the number of uses k. Also, we present a deterministic non-exact one in which the average fidelity approaches 1 exponentially in k. This exponential performance is contrasted with parallel circuits, which do not allow such exponential performance. We finish the talk by discussing the potential use of quantum processes which do not respect a definite causal order.