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 …

We present a classical algorithm for estimating expectation values of arbitrary observables
on most quantum circuits across all circuit architectures and depths, including those with all …

Quantum pseudorandomness has found applications in many areas of quantum information,
ranging from entanglement theory, to models of scrambling phenomena in chaotic quantum …

Unitary t-designs are distributions on the unitary group whose first t moments appear
maximally random. Previous work has established several upper bounds on the depths at …

In the accompanying paper of arxiv: 2408.13472, we have established the method of
characterizing the maximal order of approximate unitary designs generated by symmetric …

A unitary state $ t $-design is an ensemble of pure quantum states whose moments match
up to the $ t $-th order those of states uniformly sampled from a $ d $-dimensional Hilbert …

The spectral gap of local random quantum circuits is a fundamental property that determines
how close the moments of the circuit's unitaries match those of a Haar random distribution …

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 …

Understanding thermalisation in quantum many-body systems is among the most enduring
problems in modern physics. A particularly interesting question concerns the role played by …

The Clifford hierarchy is a fundamental structure in quantum computation, classifying unitary
operators based on their commutation relations with the Pauli group. Despite its …