8 votes

What is quantum t-design (intuitive understanding)?

The $t$ in $t$-design is essentially a measure of how good a job the set of gates does in terms of randomising a state (the larger t, the more random, with properly random requiring the infinite limit)...
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4 votes

At what depth and for what architecture are random quantum circuits $1$-designs?

To study unitary $t$-designs, we define the moment operator with respect to a probability measure $\nu$ as $$ M_t(\nu) := \int_{U(d)} U^{\otimes t} (\cdot) (U^{\otimes t})^\dagger d\nu(U) \simeq \int_{...
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3 votes

Aproximating unitaries with elements from a t-design

It’s straightforward to see that a random element $U$ drawn from a design is, with very high probability, far away from any fixed unitary $V$, i.e. you can show that the distance between $U$ and $V$ (...
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