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Learning quantum states and unitaries of bounded gate complexity
While quantum state tomography is notoriously hard, most states hold little interest to
practically minded tomographers. Given that states and unitaries appearing in nature are of …
practically minded tomographers. Given that states and unitaries appearing in nature are of …
Incompressibility and spectral gaps of random circuits
Random reversible and quantum circuits form random walks on the alternating group
$\mathrm {Alt}(2^ n) $ and unitary group $\mathrm {SU}(2^ n) $, respectively. Known bounds …
$\mathrm {Alt}(2^ n) $ and unitary group $\mathrm {SU}(2^ n) $, respectively. Known bounds …
Efficient approximate unitary designs from random Pauli rotations
We construct random walks on simple Lie groups that quickly converge to the Haar measure
for all moments up to order t. Specifically, a step of the walk on the unitary or orthogonal …
for all moments up to order t. Specifically, a step of the walk on the unitary or orthogonal …
Quantum complexity phase transitions in monitored random circuits
Recently, the dynamics of quantum systems that involve both unitary evolution and quantum
measurements have attracted attention due to the exotic phenomenon of measurement …
measurements have attracted attention due to the exotic phenomenon of measurement …
Efficient quantum pseudorandomness from hamiltonian phase states
Quantum pseudorandomness has found applications in many areas of quantum information,
ranging from entanglement theory, to models of scrambling phenomena in chaotic quantum …
ranging from entanglement theory, to models of scrambling phenomena in chaotic quantum …
Lower bound for simulation cost of open quantum systems: Lipschitz continuity approach
Simulating quantum dynamics is one of the most promising applications of quantum
computers. While the upper bound of the simulation cost has been extensively studied …
computers. While the upper bound of the simulation cost has been extensively studied …
Resource-dependent complexity of quantum channels
Quantum complexity theory is concerned with the amount of elementary quantum resources
needed to build a quantum system or a quantum operation. The fundamental question in …
needed to build a quantum system or a quantum operation. The fundamental question in …
Projective toric designs, quantum state designs, and mutually unbiased bases
Abstract Toric $ t $-designs, or equivalently $ t $-designs on the diagonal subgroup of the
unitary group, are sets of points on the torus over which sums reproduce integrals of degree …
unitary group, are sets of points on the torus over which sums reproduce integrals of degree …