add a small conclusion

presentations/tf-qas.typ

@@ -4,6 +4,8 @@
 #import "@preview/cetz:0.3.4"
 #import "@preview/typsium:0.2.0": ce
 #import "@preview/numbly:0.1.0": numbly
+#import "@preview/quill:0.7.2": *
+#import "@preview/quill:0.7.2": tequila as tq
 #import "./theme.typ": *
 
 #set heading(numbering: numbly("{1}.", default: "1.1"))
@@ -41,12 +43,6 @@
 )
 
 
-#slide[
-- #text(fill: purple)[Purple text is a question I have]
-- #text(fill: red)[Red text is something I think they did not do well]
-- #text(fill: orange)[Orange text is something I would have preferred a reference for]
-]
-
 #title-slide()
 
 #outline(depth: 1, title: text(fill: rgb("#00a6d6"))[Content])
@@ -54,21 +50,27 @@
 = Introduction
 
 == Variational Quantum Algorithms
+
+- NISQ era
  
 - Classical optimisation
 
 - Parametrized Quantum Circuit
 
-- Very structure dependent
+#pause
+- Performance is circuit dependent
 
 == Quantum Architecture Search
 
-- Automated Design
+- Automated Parametrized Quantum Ciruit finding
+  - Solution to circuit dependency
 
+#pause
 - New Problems
   - Exponential search space
   - Ranking circuits during search
 
+#pause
 - Parallels with Neural Architecture Search
   - Differentiable QAS
   - Reinforcement-learning QAS
@@ -84,17 +86,21 @@
   - Possibility for easier transfer
 
 - Need to prove correlation with ground-truth
-  #text(fill: red)[- not done in paper]
+  #text(fill: red)[- not done in paper@training-free]
 
 = Method
 
 == Overview
 
 #align(horizon)[
+The Steps of the protocol:
+#pause
 1. Sample circuits from search space
 
+#pause
 2. Filter using Path proxy
 
+#pause
 3. Rank on Expressibility
 ]
 
@@ -102,11 +108,21 @@
 
 Following Neural Predictor based QAS@npqas
 - Native gate set ($cal(A) = {R_x, R_y, R_z, X X, Y Y, Z Z}$)
-- Layer based sampling
-  - Layers of $n/2$ gates
-- Gate based sampling
-  - placing 1 gate at a time
-
+#grid(
+  columns: (auto, auto),
+  rows: (auto, auto),
+  gutter: 1em,
+  [- Layer based sampling
+    - Layers of $n/2$ gates
+  ], grid.cell(rowspan:2)[
+    #quantum-circuit(equal-row-heights: true, row-spacing: 0.8em, wires: 6, 1, $R_l$, 1,[\ ],[\ ],1,$R_l$, 1,[\ ],[\ ],1,$R_l$)
+    #quantum-circuit(equal-row-heights: true, row-spacing: 0.8em, wires: 6, 3, [\ ], 1, $R_l$, 1,[\ ],[\ ],1,$R_l$, 1,[\ ],[\ ],1,$R_l$)
+    #quantum-circuit(equal-row-heights: true, row-spacing: 1.35em, wires: 6, 1, ctrl(1), 1, [\ ], 1, targ(), 1,[\ ], 1, ctrl(1),[\ ],1,targ(), 1,[\ ], 1, ctrl(1),[\ ],1,targ())
+  ],
+  [- Gate based sampling
+    - placing 1 gate at a time
+  ], []
+)
 - Why not fully random circuits?
   - Mitigating barren plateaus
   - Mitigating high circuit depth
@@ -115,25 +131,28 @@ Following Neural Predictor based QAS@npqas
 == Path Proxy
 
 #slide(composer: (auto, auto))[
-- 'zero-cost'
-  #text(fill:orange)[- best case: $O("Operations" times "Qubits"^2)$] 
-  // I think it'd scale like this, but am uncertain since they didn't explain it anywhere
+- *'zero-cost'*
   - below $7.8 times 10^(-4)$s
+  #text(fill:orange)[- $O("Operations" times "Qubits"^2)$] 
 
+#pause
 1. Represent as Directed acyclic graph
-
+#pause
 2. Count distinct paths from input-to-output
-
+#pause
 3. Top-R highest path count circuits
 ][
+  #meanwhile
   #image("tf-qas/circuit.png", height: 40%)
+  #pause
   #image("tf-qas/dag.png")
   #text(size: 0.6em)[#align(right)[from Training-Free QAS@training-free]]
 ]
 
 == Expressibility Proxy
 
-#text(fill: red)[- Performance hinges on Expressibility]
+Assumption: Expressibility $|->$ Performance
+#pause
 - Particularly valueable without prior knowledge
 
 #block(fill: blue.lighten(85%), inset: 12pt, radius: 6pt, stroke: 2pt + blue)[
@@ -155,25 +174,28 @@ Following Neural Predictor based QAS@npqas
   - Heisenberg model
   - $"Be"space.hair"H"_2$ molecule
 
+#pause
 - Compared to
   - Network-Predictive QAS@npqas
-  #text(fill: red)[- Hardware-efficient ansatz@hea-kandala] // but like, which one
-  - Random sampling
+  - Hardware-efficient ansatz@hea-kandala // but like, which one
+  - Their random sampling
 
+#pause
 - Implementation details
   - TensorCircuit python package@tensorcircuit
-  #text(fill: red)[- No code included anywhere]
+  #pause
+  #text(fill: red)[- No code so one cannot reproduce]
 
 == Proxy combinations
 
 #slide(composer: (auto, auto))[
   - Only Path
     - Fast proxy (each $~ 2 times 10^(-4) "s"$)
-    - Many queries (each $~ 10 "s"$)
+    - Many ADAM queries
   
   - Only Expressibility
     - Slower proxy (each $~ 0.21 "s"$)
-    - Fewer queries
+    - Fewer queries (each $~ 10 "s"$)
 
   - Combined
     - Fast proxy filtering
@@ -186,13 +208,15 @@ Following Neural Predictor based QAS@npqas
 == Comparison with State of the Art
 
 #slide(composer: (1fr, auto))[
-#text(fill: purple)[- Where do these come from?]
+- Where do these come from?
 
 - A lot fewer queries
 
 - Shorter search times
 
-#text(fill: red)[- No ways to reproduce given]
+#pause
+However:
+- No way to reproduce and check
 ][
   #image("tf-qas/outcomes.png", height: 85%)
   #text(size: 0.6em)[#align(right)[from Training-Free QAS@training-free]]
@@ -200,14 +224,28 @@ Following Neural Predictor based QAS@npqas
 
 = Conclusion
 
-==
+== Takeaways
 
-- Combining proxies // can work better than seperately
+- Combining proxies
 
-- Training-Free methods are promising
+- Training-Free methods can work better than HEA
 
-#text(fill:red)[- Not reproducible]
+== What will I do (differently)
 
+Sampling: 
+- Evolutionary Algorithm instead of random sampling
+  - With hardware constraints
+  - Can build on parts of "Genetic optimization of ansatz 
+    expressibility for enhanced variational quantum algorithm 
+    performance."@genetic-expressibility
+
+#pause
+Filtering:
+- Noise proxy
+- Better entanglement proxy
+
+#pause
+And of course: Share my code
 
 #slide[
   == References <touying:unoutlined>