Abstract
Complexity can be defined for states, but in many ways it is more natural to start with the complexity of operations that you can do to a system. That means the complexity of unitary operators.
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Notes
- 1.
We continue to work with systems of K qubits. The space of states is \(2^K\) dimensional.
- 2.
The bar in \(\bar{j}\) indicates time reversal or in relativistic quantum field theory the CPT operation.
- 3.
In the case of maximally entangled systems I mean a restricted form of complexity in which gates are only permitted to act on each side of the entangled system separately, thus preserving the maximal entanglement.
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Susskind, L. (2020). Dual Role of Unitaries. In: Three Lectures on Complexity and Black Holes. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-45109-7_5
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DOI: https://doi.org/10.1007/978-3-030-45109-7_5
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