Solve a linear ODE du/dt = A(t)u + b(t)Linear multistep method, all-at-once encoding · 2 parts inside · the Atlas has a full record of thisLinear multistep method, all-at-once encoding · 2 parts inside · the Atlas has a full record of this — click the line to open it hereTaylor propagator, all-at-once encoding · 2 parts insideTaylor propagator, all-at-once encoding · 2 parts inside — click the line to open it hereChebyshev spectral method, global collocation · 2 parts insideChebyshev spectral method, global collocation · 2 parts inside — click the line to open it hereDyson propagator, all-at-once encoding · 2 parts insideDyson propagator, all-at-once encoding · 2 parts inside — click the line to open it hereTime-marching with uniform singular value amplification · 2 parts insideTime-marching with uniform singular value amplification · 2 parts inside — click the line to open it hereLCHS — linear combination of Hamiltonian simulation · 3 parts inside, open · the Atlas has a full record of thisLCHS — linear combination of Hamiltonian simulation · 3 parts inside, open · the Atlas has a full record of thisLCHS — linear combination of Hamiltonian simulation · 3 parts inside, open · the Atlas has a full record of this — click the line to close itKernel-weighted combination of unitary propagatorsKernel-weighted combination of unitary propagators — click the line to read about it hereSimulate Hamiltonian evolution · 3 ways through · the Atlas has a full record of thisSimulate Hamiltonian evolution · 3 ways through · the Atlas has a full record of this — click the line to open it hereLCHS — linear combination of Hamiltonian simulationthe method itself — click the name to read about it hereSchrödingerisation (linear PDEs as Schrödinger equations) · 3 parts insideSchrödingerisation (linear PDEs as Schrödinger equations) · 3 parts inside — click the line to open it hereLinear multistep method, all-at-once encoding · 2 parts inside · the Atlas has a full record of this — click the name to read about it hereMultistep, all-at-onceTaylor propagator, all-at-once encoding · 2 parts inside — click the name to read about it hereTaylor, all-at-onceChebyshev spectral method, global collocation · 2 parts inside — click the name to read about it hereSpectral methodDyson propagator, all-at-once encoding · 2 parts inside — click the name to read about it hereDyson, all-at-onceTime-marching with uniform singular value amplification · 2 parts inside — click the name to read about it hereTime-marchingLCHS — linear combination of Hamiltonian simulation · 3 parts inside, open · the Atlas has a full record of this — click the name to close itLCHSKernel-weighted combination of unitary propagators — click the name to read about it hereLCHS identitySimulate Hamiltonian evolution · 3 ways through · the Atlas has a full record of this — click the name to read about it hereSimulate Hamiltonian evolutionLCHS — linear combination of Hamiltonian simulation — click the name to read about it herecombine by LCU, keep the flagged branchSchrödingerisation (linear PDEs as Schrödinger equations) · 3 parts inside — click the name to read about it hereSchrödingerisationLinear ODE system — you start hereAnswer about the solution — you finish hereHamiltonian surrogate, with the map back — what one part hands to the nextCircuit for e^{-iHt} — what one part hands to the next

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Where the routes meet

Every circle is drawn once. This step has no smaller object recorded inside it, so the strands between its two circles are the recorded ways of taking it — one strand per method.

All the starting points

9 recorded ways of doing Solve a linear ODE du/dt = A(t)u + b(t); 7 are drawn — the other 2 are refinements with the same internals, folded into their parents' cards. Nothing smaller is recorded inside it, so there is no object in the middle to draw.

7 lines have something recorded inside that you have not opened.

Of the routes that have been taken apart, 15 are built entirely from named slots, 15 hand off part of the work and finish the rest themselves, and 20 are one undivided act. None of the three is a defect; they are different things to reuse.

Every line on this figure, in words

The lines on this figure

  1. Linear multistep method, all-at-once encoding — opens into 2 · a way across — click it to open it here
  2. Taylor propagator, all-at-once encoding — opens into 2 · a way across — click it to open it here
  3. Chebyshev spectral method, global collocation — opens into 2 · a way across — click it to open it here
  4. Dyson propagator, all-at-once encoding — opens into 2 · a way across — click it to open it here
  5. Time-marching with uniform singular value amplification — opens into 2 · a way across — click it to open it here
  6. LCHS — linear combination of Hamiltonian simulation — open · opened: what was inside is drawn in its place
  7. Kernel-weighted combination of unitary propagators
  8. Simulate Hamiltonian evolution — opens into 3 · a way across — click it to open it here
  9. Schrödingerisation (linear PDEs as Schrödinger equations) — opens into 3 · a way across — click it to open it here
  • Every line on this figure is one a recorded source takes.

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Where you are

Path

  1. Solve a nonlinear ODE dy/dt = F(y)
  2. Solve a linear ODE du/dt = A(t)u + b(t)

Ways through: 9

Routes that skip it

No recorded route avoids this step.

Narrower kinds

Read the full write-up

Every step you can open

1 of these have an object recorded in the middle; the rest open into the methods that fill them.

What is on this map, counted

What is here, counted

147 nodes — 31 slots and 116 methods.

76 of the 147 link to a record in the Atlas, between them naming 89 records. The rest name papers and nothing else: this graph describes work the catalogue has not got yet, and the nodes with no record are the list of what a corpus pass has to go and read.

0 slots have no method recorded, and 32 methods have not been taken apart. Both are shown as what they are rather than left blank.

Every claim here rests on a source. This graph cites 140 papers; they and the 172 the Atlas cites alone are registered in one place, with what each reports and everywhere it is cited from. Papers