Quantum Codes from Twisted Unitary -Groups
E Kubischta, I Teixeira - Physical Review Letters, 2024 - APS
We introduce twisted unitary t-groups, a generalization of unitary t-groups under a twisting
by an irreducible representation. We then apply representation theoretic methods to the Knill …
by an irreducible representation. We then apply representation theoretic methods to the Knill …
Quantum Circuits for Exact Unitary -Designs and Applications to Higher-Order Randomized Benchmarking
A unitary t-design is a powerful tool in quantum information science and fundamental
physics. Despite its usefulness, only approximate implementations were known for general t …
physics. Despite its usefulness, only approximate implementations were known for general t …
On stabiliser techniques and their application to simulation and certification of quantum devices
M Heinrich - 2021 - kups.ub.uni-koeln.de
The stabiliser formalism is a widely used and successful subtheory of quantum mechanics
consisting of stabiliser states, Clifford unitaries and Pauli measurements. The power of the …
consisting of stabiliser states, Clifford unitaries and Pauli measurements. The power of the …
Efficient construction of quantum physical unclonable functions with unitary t-designs
Quantum physical unclonable functions, or QPUFs, are rapidly emerging as theoretical
hardware solutions to provide secure cryptographic functionalities such as key-exchange …
hardware solutions to provide secure cryptographic functionalities such as key-exchange …
Quantum private broadcasting
A Broadbent, CE González-Guillén, C Schuknecht - Physical Review A, 2022 - APS
In private broadcasting, a single plaintext is broadcast to multiple recipients in an encrypted
form, such that each recipient can decrypt locally. When the message is classical, a …
form, such that each recipient can decrypt locally. When the message is classical, a …
The complex conjugate invariants of Clifford groups
E Bannai, M Oura, D Zhao - Designs, Codes and Cryptography, 2021 - Springer
Abstract Nebe, Rains and Sloane studied the polynomial invariants for real and complex
Clifford groups and they give a new conceptual proof that these invariants are spanned by …
Clifford groups and they give a new conceptual proof that these invariants are spanned by …
On computational complexity of unitary and state design properties
We study unitary and state $ t $-designs from a computational complexity theory perspective.
First, we address the problems of computing frame potentials that characterize …
First, we address the problems of computing frame potentials that characterize …
Optimal Designs for Regression on Lie Groups
S Chakraborty, H Dette, M Kroll - arXiv preprint arXiv:2410.00429, 2024 - arxiv.org
We consider a linear regression model with complex-valued response and predictors from a
compact and connected Lie group. The regression model is formulated in terms of …
compact and connected Lie group. The regression model is formulated in terms of …
Generalized group designs: overcoming the 4-design-barrier and constructing novel unitary 2-designs in arbitrary dimensions
Unitary designs are essential tools in several quantum information protocols. Similarly to
other design concepts, unitary designs are mainly used to facilitate averaging over a …
other design concepts, unitary designs are mainly used to facilitate averaging over a …
Randomness and complexity in random complex quantum systems
J Haferkamp - 2022 - refubium.fu-berlin.de
Die Schnittstelle von Komplexitätstheorie und Quantenphysik umfasst Quantentechnologien
bis hin zu fundamentalen Fragen über die Physik schwarzer Löcher. Während die Methoden …
bis hin zu fundamentalen Fragen über die Physik schwarzer Löcher. Während die Methoden …