Quantum computation and quantum information
Quantum computation and quantum information
Quantum expanders from any classical Cayley graph expander
Quantum Information & Computation
Efficient Quantum Tensor Product Expanders and k-Designs
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Classical and quantum tensor product expanders
Quantum Information & Computation
Quantum expanders from any classical Cayley graph expander
Quantum Information & Computation
A linearized stabilizer formalism for systems of finite dimension
Quantum Information & Computation
Exponential quantum speed-ups are generic
Quantum Information & Computation
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We present a simple way to quantize the well-known Margulis expander map. The result is a quantum expander which acts on discrete Wigner functions in the same way the classical Margulis expander acts on probability distributions. The quantum version shares all essential properties of the classical counterpart, e.g., it has the same degree and spectrum. Unlike previous constructions of quantum expanders, our method does not rely on non-Abelian harmonic analysis. Analogues for continuous variable systems are mentioned. Indeed, the construction seems one of the few instances where applications based on discrete and continuous phase space methods can be developed in complete analogy.