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 …

We introduce a framework for simulating, on an $(n+ 1) $-qubit quantum computer, the
action of a Gaussian Bosonic (GB) circuit on a state over $2^ n $ modes. Specifically, we …

Classical neural networks with random initialization famously behave as Gaussian
processes in the limit of many neurons, which allows one to completely characterize their …

Lie algebraic techniques are powerful and widely used tools for studying dynamics and
metrology in quantum optics. When the Hamiltonian generates a Lie algebra with finite …

We introduce a framework for simulating, on an $(n+ 1) $-qubit quantum computer, the
action of a Gaussian Bosonic (GB) circuit on a state over $2^ n $ modes. Specifically, we …