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feat: add quantum logic gates & circuits

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Kristofers Solo 2025-06-05 17:46:24 +03:00
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@ -11,6 +11,10 @@
#let distance = $space.quad space.quad$ #let distance = $space.quad space.quad$
#let tensor = $lr(times.circle)$ #let tensor = $lr(times.circle)$
#let CNOT = $lr(C N O T)$
#let CCNOT = $lr(C C N O T)$
#let SWAP = $lr(S W A P)$
#let CU = $lr(C-U)$
= Bre-Ket Notation = Bre-Ket Notation
== Ket $ket(psi)$ == Ket $ket(psi)$
@ -319,3 +323,28 @@ $
ket(0) ket(0)
$ $
= Quantum Logic Gates & Circuits
== Common Multi-Qubit Gates
=== $CNOT$ (Controlled-NOT)
$ CNOT ket(c) ket(t)=ket(c)ket(t tensor c) $
#figure(quantum-circuit(..tq.build(tq.cx(0, 1))))
=== $SWAP$ Gate
Swaps two qubits.
#figure(quantum-circuit(..tq.build(tq.swap(0, 1))))
=== Toffoli Gate ($CCNOT$)
$ CCNOT ket(c_1 c_2 t)=ket(c_1 c_2 t tensor (c_1 dot c_2)) $
#figure(quantum-circuit(..tq.build(tq.ccx(0, 1, 2))))
=== Universality (Universalitāte)
Jebkurai unitārai $U$: $U=U_m U_(m-1) ... U_1$, katra $U_i$ maina tikai 2 bāzes
stāvokļus
$
U_i ket(x_1 ... x_n)=a ket(x_1 ... x_n) + b ket(y_1 ... y_n) \
U_i ket(y_1 ... y_n)=c ket(x_1 ... x_n) + d ket(y_1 ... y_n) \
U_i ket(z_1 ... z_n)=ket(z_1 ... z_n)
$
ja $z_1 ... z_n != x_1 ...x_n$, $z_1 ... z_n != y_1 .. y_n$.