The complexity of quantum states has become a key quantity of interest across various
subfields of physics, from quantum computing to the theory of black holes. The evolution of …

We prove that random quantum circuits on any geometry, including a 1D line, can form
approximate unitary designs over $ n $ qubits in $\log n $ depth. In a similar manner, we …

The applications of random quantum circuits range from quantum computing and quantum
many-body systems to the physics of black holes. Many of these applications are related to …

The concept of quantum complexity has far-reaching implications spanning theoretical
computer science, quantum many-body physics, and high-energy physics. The quantum …

The generation of k-designs (pseudorandom distributions that emulate the Haar measure up
to k moments) with local quantum circuit ensembles is a problem of fundamental importance …

Abstract Quantum Neural Networks (QNN) are considered a candidate for achieving
quantum advantage in the Noisy Intermediate Scale Quantum computer (NISQ) era. Several …

In this work, we show that learning the output distributions of brickwork random quantum
circuits is average-case hard in the statistical query model. This learning model is widely …

We propose and investigate a new method of quantum process tomography (QPT) which we
call projected least squares (PLS). In short, PLS consists of first computing the least-squares …

We study random quantum circuits and their rate of producing bipartite entanglement,
specifically with respect to the choice of 2-qubit gates and the order (protocol) in which these …

Random unitaries are useful in quantum information and related fields but hard to generate
with limited resources. An approximate unitary $ k $-design is an ensemble of unitaries and …