Learning quantum states and unitaries of bounded gate complexity

H Zhao, L Lewis, I Kannan, Y Quek, HY Huang… - PRX Quantum, 2024 - APS
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 …

Incompressibility and spectral gaps of random circuits

CF Chen, J Haah, J Haferkamp, Y Liu, T Metger… - arxiv preprint arxiv …, 2024 - arxiv.org
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 …

Efficient approximate unitary designs from random Pauli rotations

J Haah, Y Liu, X Tan - 2024 IEEE 65th Annual Symposium on …, 2024 - ieeexplore.ieee.org
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 …

Quantum complexity phase transitions in monitored random circuits

R Suzuki, J Haferkamp, J Eisert, P Faist - Quantum, 2025 - quantum-journal.org
Recently, the dynamics of quantum systems that involve both unitary evolution and quantum
measurements have attracted attention due to the exotic phenomenon of measurement …

Efficient quantum pseudorandomness from hamiltonian phase states

J Bostanci, J Haferkamp, D Hangleiter… - arxiv preprint arxiv …, 2024 - arxiv.org
Quantum pseudorandomness has found applications in many areas of quantum information,
ranging from entanglement theory, to models of scrambling phenomena in chaotic quantum …

Lower bound for simulation cost of open quantum systems: Lipschitz continuity approach

Z Ding, M Junge, P Schleich, P Wu - Communications in Mathematical …, 2025 - Springer
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 …

Resource-dependent complexity of quantum channels

R Araiza, Y Chen, M Junge, P Wu - arxiv preprint arxiv:2303.11304, 2023 - arxiv.org
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 …

Projective toric designs, quantum state designs, and mutually unbiased bases

JT Iosue, TC Mooney, A Ehrenberg, AV Gorshkov - Quantum, 2024 - quantum-journal.org
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 …