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Multiple choice
A classical random walk on a line spreads diffusively with standard deviation
σ
∼
t
\sigma \sim \sqrt{t}
σ
∼
t
. For the Hadamard discrete-time quantum walk, how does the position spread with the number of steps
t
t
t
?
Diffusively,
σ
∼
t
\sigma \sim \sqrt{t}
σ
∼
t
, the same as the classical walk
Logarithmically,
σ
∼
log
(
t
)
\sigma \sim \log(t)
σ
∼
lo
g
(
t
)
It does not spread at all; the walker stays at the origin
Ballistically,
σ
∼
t
\sigma \sim t
σ
∼
t
(linear in
t
t
t
)
Check answer