At qubits, with the gate set used in the counting argument, each gate position has…

PHYSICS · Subjective · Fermi University Physics · Quantum Information & Technology · The quantum circuit model and quantum algorithms · The quantum circuit model and quantum algorithms

Quantum Information and Technology, Ch The quantum circuit model

Problem

n=20

qubits, with the gate set

\{H,T,\mathrm{CNOT}\}

used in the counting argument, each gate position has

n(n+1)

choices (an

H

or a

T

on any of the

n

wires, or a

\mathrm{CNOT}

on any ordered pair of the

n

wires). Using the same reasoning as the

n=10

estimate already worked, estimate the smallest circuit size

G

such that circuits of size

G

could possibly reach even one per cent of the states of the

20

-qubit sphere to accuracy

0.1

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