254 lines
5.8 KiB
Typst
254 lines
5.8 KiB
Typst
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#import "@preview/touying:0.6.1": *
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#import "@preview/physica:0.9.5": *
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#import "@preview/cetz:0.3.4"
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#import "@preview/typsium:0.2.0": ce
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#import "@preview/numbly:0.1.0": numbly
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#import "@preview/quill:0.7.2": *
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#import "@preview/quill:0.7.2": tequila as tq
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#import "./theme.typ": *
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#set heading(numbering: numbly("{1}.", default: "1.1"))
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#show ref: set text(size:0.5em, baseline: -0.75em)
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#let cetz-canvas = touying-reducer.with(reduce: cetz.canvas, cover: cetz.draw.hide.with(bounds: true))
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#show: university-theme.with(
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config-info(
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title: "Training-Free QAS", // Required
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date: datetime.today().display(),
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authors: ("Noa Aarts"),
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// Optional Styling (for more / explanation see in the typst universe)
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// ignore how bad the images look i'll adjust it until Monday
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title-color: blue.darken(10%),
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),
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config-common(
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// handout: true, // enable this for a version without animations
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),
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aspect-ratio: "16-9",
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config-colors(
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primary: rgb("#00a6d6"),
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secondary: rgb("#00b3dc"),
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tertiary: rgb("#b8cbde"),
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neutral-lightest: rgb("#ffffff"),
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neutral-darkest: rgb("#000000"),
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),
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)
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#show outline.entry: it => link(
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it.element.location(),
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text(fill: rgb("#00b3dc"), size: 1.3em)[#it.indented(it.prefix(), it.body())],
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)
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#title-slide()
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#outline(depth: 1, title: text(fill: rgb("#00a6d6"))[Content])
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= Introduction
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== Variational Quantum Algorithms
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- NISQ era
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- Classical optimisation
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- Parametrized Quantum Circuit
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#pause
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- Performance is circuit dependent
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== Quantum Architecture Search
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- Automated Parametrized Quantum Ciruit finding
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- Solution to circuit dependency
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#pause
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- New Problems
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- Exponential search space
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- Ranking circuits during search
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#pause
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- Parallels with Neural Architecture Search
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- Differentiable QAS
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- Reinforcement-learning QAS
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- Predictor-based QAS
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- Weight-sharing QAS
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== Training Free Proxies
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- No need to train parametrized quantum circuit
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\ $->$ Faster searching
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- No objective functions
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- Possibility for easier transfer
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- Need to prove correlation with ground-truth
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#text(fill: red)[- not done in paper@training-free]
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= Method
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== Overview
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#align(horizon)[
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The Steps of the protocol:
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#pause
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1. Sample circuits from search space
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#pause
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2. Filter using Path proxy
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#pause
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3. Rank on Expressibility
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]
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== Search Space
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Following Neural Predictor based QAS@npqas
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- Native gate set ($cal(A) = {R_x, R_y, R_z, X X, Y Y, Z Z}$)
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#grid(
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columns: (auto, auto),
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rows: (auto, auto),
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gutter: 1em,
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[- Layer based sampling
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- Layers of $n/2$ gates
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], grid.cell(rowspan:2)[
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#quantum-circuit(equal-row-heights: true, row-spacing: 0.8em, wires: 6, 1, $R_l$, 1,[\ ],[\ ],1,$R_l$, 1,[\ ],[\ ],1,$R_l$)
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#quantum-circuit(equal-row-heights: true, row-spacing: 0.8em, wires: 6, 3, [\ ], 1, $R_l$, 1,[\ ],[\ ],1,$R_l$, 1,[\ ],[\ ],1,$R_l$)
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#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())
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],
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[- Gate based sampling
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- placing 1 gate at a time
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], []
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)
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- Why not fully random circuits?
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- Mitigating barren plateaus
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- Mitigating high circuit depth
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#text(fill:purple)[- What is the difference with gate-based?]
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== Path Proxy
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#slide(composer: (auto, auto))[
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- *'zero-cost'*
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- below $7.8 times 10^(-4)$s
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#text(fill:orange)[- $O("Operations" times "Qubits"^2)$]
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#pause
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1. Represent as Directed acyclic graph
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#pause
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2. Count distinct paths from input-to-output
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#pause
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3. Top-R highest path count circuits
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][
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#meanwhile
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#image("tf-qas/circuit.png", height: 40%)
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#pause
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#image("tf-qas/dag.png")
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#text(size: 0.6em)[#align(right)[from Training-Free QAS@training-free]]
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]
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== Expressibility Proxy
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Assumption: Expressibility $|->$ Performance
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#pause
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- Particularly valueable without prior knowledge
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#block(fill: blue.lighten(85%), inset: 12pt, radius: 6pt, stroke: 2pt + blue)[
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*Expressibility:* \
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The capability to uniformly reach the entire Hilbert space.
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]
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1. Calculate expressibility:
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#align(center)[$cal(E)(cal(C)) = -D_"KL" (P(cal(C),F) || P_"Haar" (F)$]
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2. Top expressibility circuits
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= Results
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== Evaluation
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- Three variational quantum eigensolver tasks
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- Transverse field Ising model
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- Heisenberg model
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- $"Be"space.hair"H"_2$ molecule
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#pause
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- Compared to
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- Network-Predictive QAS@npqas
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- Hardware-efficient ansatz@hea-kandala // but like, which one
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- Their random sampling
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#pause
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- Implementation details
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- TensorCircuit python package@tensorcircuit
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#pause
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#text(fill: red)[- No code so one cannot reproduce]
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== Proxy combinations
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#slide(composer: (auto, auto))[
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- Only Path
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- Fast proxy (each $~ 2 times 10^(-4) "s"$)
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- Many ADAM queries
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- Only Expressibility
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- Slower proxy (each $~ 0.21 "s"$)
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- Fewer queries (each $~ 10 "s"$)
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- Combined
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- Fast proxy filtering
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- Even fewer queries
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][
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#image("tf-qas/table.png")
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#text(size: 0.6em)[#align(right)[from Training-Free QAS@training-free]]
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]
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== Comparison with State of the Art
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#slide(composer: (1fr, auto))[
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- Where do these come from?
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- A lot fewer queries
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- Shorter search times
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#pause
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However:
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- No way to reproduce and check
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][
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#image("tf-qas/outcomes.png", height: 85%)
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#text(size: 0.6em)[#align(right)[from Training-Free QAS@training-free]]
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]
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= Conclusion
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== Takeaways
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- Combining proxies
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- Training-Free methods can work better than HEA
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== What will I do (differently)
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Sampling:
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- Evolutionary Algorithm instead of random sampling
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- With hardware constraints
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- Can build on parts of "Genetic optimization of ansatz
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expressibility for enhanced variational quantum algorithm
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performance."@genetic-expressibility
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#pause
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Filtering:
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- Noise proxy
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- Better entanglement proxy
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#pause
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And of course: Share my code
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#slide[
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== References <touying:unoutlined>
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#bibliography("references.bib", title: [])
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]
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