Randomness is a central ingredient in classical computing and information processing: It is used in probabilistic algorithms, in cryptography, and in complexity theory. It should thus come not as a surprise that quantum randomness also finds plenty of applications in the quantum world, which however stretch beyond the quantum counterparts of the classical usecases. It even seems that nature itself is a nearly perfect quantum scrambler: chaotic quantum systems have properties that are best describe through random quantum models and even black holes scramble information in a way that is best described by quantum randomness.
We are developing efficient ways of generating quantum randomness using random quantum circuits. We exploit these constructions to build scalable methods for quantum information protocols, such as noise characterization in quantum devices and property learning in quantum many-body systems.
We study constructive ways of generating quantum randomness in terms of random quantum circuits. These are quantum circuits composed of randomly chosen local gates. With increasing circuit depth, these randomize more and more effectively. It was only recently established that already very short circuits randomize surprisingly well, which opens the possibility of constructing extremely efficient applications. Our research focuses on the question of how well short random quantum circuits randomize and how their efficiency depends on the circuit geometry, the used gate set, and other parameters. In this way, we lay the foundations of efficient and robust applications.
Quantum experiments are getting better and better in coherently manipulating many-body quantum systems. We can use this to study interesting many-body phenomena or manipulate quantum information in quantum computers. However, even with perfect quantum control, we are left with the highly non-trivial problem of extracting information from the prepared quantum states. An example for this would be the expectation value of a given Hamiltonian, because we are trying to find its ground state through a variational quantum algorithm.
Shadow estimation is a popular approach which utilizes randomized measurements to estimate expectation values of a quantum state using relatively few samples. For certain expectation values, such as state fidelities, a relativity high degree of randomization is necessary, typically involving deep circuits. We have worked on the performance of constant-depth random circuits in this context.