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Linear Growth of Complexity in Brownian Circuits

Generating randomness efficiently is a key capability in both classical and quantum information processing applications. For example, Haar-random quantum states serve as primitives for applications including quantum cryptography, quantum process tomography, and randomized benchmarking. How quickly can these random states be generated? And how much randomness is really necessary for any given application? In this talk, I will address these questions in Brownian quantum circuit models, which admit a large-$N$ limit that can be solved exactly.

Statistical mechanics models for hybrid quantum circuits

The central philosophy of statistical mechanics and random-matrix theory of complex systems is that while individual instances are essentially intractable to simulate, the statistical properties of random ensembles obey simple universal “laws”. This same philosophy promises powerful methods for studying the dynamics of quantum information in ideal and noisy quantum circuits – for which classical description of individual circuits is expected to be generically intractable.

Efficient experimental verification of quantum computers and quantum simulators via randomized analog verification

Near-term quantum information processors will not be capable of quantum error correction, but instead will implement algorithms using the physical native interactions of the device. These interactions can be used to implement quantum gates that are often continuously-parameterized (e.g., by rotation angles), as well as to implement analog quantum simulations that seek to explore the dynamics of a particular Hamiltonian of interest.