Solve a nonlinear ODE dy/dt = F(y)Embed a nonlinear system into a linear one · 6 ways throughEmbed a nonlinear system into a linear one · 6 ways through — click the line to open it hereSolve a linear ODE du/dt = A(t)u + b(t) · 9 ways through · the Atlas has a full record of thisSolve a linear ODE du/dt = A(t)u + b(t) · 9 ways through · the Atlas has a full record of this — click the line to open it hereChoose a time discretization or propagator approximation → Quantum linear solve · 2 parts inside, openChoose a time discretization or propagator approximation · 6 ways throughChoose a time discretization or propagator approximation · 6 ways through — click the line to open it hereQuantum linear solve · 5 ways throughQuantum linear solve · 5 ways through — click the line to open it hereSimulate Hamiltonian evolution → Estimate an observable · 2 parts inside, openSimulate 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 hereEstimate an observable · 4 ways throughEstimate an observable · 4 ways through — click the line to open it hereEmbed a nonlinear system into a linear one · 6 ways through — click the name to read about it hereEmbed nonlinear as linearSolve a linear ODE du/dt = A(t)u + b(t) · 9 ways through · the Atlas has a full record of this — click the name to read about it hereSolve a linear ODE du/dt = A(t)u + b(t)Choose a time discretization or propagator approximation · 6 ways through — click the name to read about it hereDiscretize time or the propagatorQuantum linear solve · 5 ways through — click the name to read about it hereQuantum linear solveSimulate Hamiltonian evolution · 3 ways through · the Atlas has a full record of this — click the name to read about it hereSimulate Hamiltonian evolutionEstimate an observable · 4 ways through — click the name to read about it hereEstimate an observableNonlinear initial-value problem — you start hereLinear ODE system — 1 way arrive here, 3 lead onAnswer about the solution — you finish hereLinear system Ax = b — what one part hands to the nextEvolution circuit, input in hand — what one part hands to the nextReplace a spatial domain with a finite gridGraph-Laplacian finite differencesGraph-Laplacian finite differences — click the line to read about it hereCentral differences, space onlyCentral differences, space only — click the line to read about it hereGraph-Laplacian finite differences — click the name to read about it hereGraph-Laplacian finite differencesCentral differences, space only — click the name to read about it hereCentral differences, space onlyPartial differential equation — you start hereLinear ODE system — you finish hereDiscretize a PDE into one linear systemForward-time, centre-space (FTCS)Forward-time, centre-space (FTCS) — click the line to read about it herePhase-space grid for a boundary-value problemPhase-space grid for a boundary-value problem — click the line to read about it hereForward-time, centre-space (FTCS) — click the name to read about it hereForward-time, centre-space (FTCS)Phase-space grid for a boundary-value problem — click the name to read about it herePhase-space grid for a boundary-value problemPartial differential equation — you start hereLinear system Ax = b — you finish hereCompile a circuit to a specific deviceNISQ transpilation (retargetable pass pipeline) · 2 parts insideNISQ transpilation (retargetable pass pipeline) · 2 parts inside — click the line to open it hereFault-tolerant compilation (Clifford+T pipeline) · 2 parts insideFault-tolerant compilation (Clifford+T pipeline) · 2 parts inside — click the line to open it hereNISQ transpilation (retargetable pass pipeline) · 2 parts inside — click the name to read about it hereNISQ transpilationFault-tolerant compilation (Clifford+T pipeline) · 2 parts inside — click the name to read about it hereFault-tolerant compilationAbstract circuit — you start hereDevice circuit — you finish hereRecover a noiseless expectation value by post-processingZero-noise extrapolation (ZNE)Zero-noise extrapolation (ZNE) — click the line to read about it hereProbabilistic error cancellation (PEC)Probabilistic error cancellation (PEC) — click the line to read about it hereReadout (measurement) error mitigationReadout (measurement) error mitigation — click the line to read about it hereCheck the symmetries the answer must haveCheck the symmetries the answer must have — click the line to read about it hereZero-noise extrapolation (ZNE) — click the name to read about it hereZero-noise extrapolation (ZNE)Probabilistic error cancellation (PEC) — click the name to read about it hereProbabilistic error cancellation (PEC)Readout (measurement) error mitigation — click the name to read about it hereReadout (measurement) error mitigationCheck the symmetries the answer must have — click the name to read about it hereSymmetry verificationNoisy expectation value — you start hereBias-reduced expectation value — you finish hereEstimate an excited-state energyVariational quantum deflation · 3 parts inside · the Atlas has a full record of thisVariational quantum deflation · 3 parts inside · the Atlas has a full record of this — click the line to open it hereSubspace-search variational eigensolver · 3 parts inside · the Atlas has a full record of thisSubspace-search variational eigensolver · 3 parts inside · the Atlas has a full record of this — click the line to open it hereQuantum subspace expansionQuantum subspace expansion — click the line to read about it hereQuantum equation of motionQuantum equation of motion — click the line to read about it hereFolded-spectrum variational eigensolver · 3 parts inside · the Atlas has a full record of thisFolded-spectrum variational eigensolver · 3 parts inside · the Atlas has a full record of this — click the line to open it herePenalty-constrained variational eigensolver · 3 parts inside · the Atlas has a full record of thisPenalty-constrained variational eigensolver · 3 parts inside · the Atlas has a full record of this — click the line to open it hereMultistate contracted variational eigensolver · 3 parts inside · the Atlas has a full record of thisMultistate contracted variational eigensolver · 3 parts inside · the Atlas has a full record of this — click the line to open it hereVariational quantum deflation · 3 parts inside · the Atlas has a full record of this — click the name to read about it hereVQDSubspace-search variational eigensolver · 3 parts inside · the Atlas has a full record of this — click the name to read about it hereSSVQEQuantum subspace expansion — click the name to read about it hereSubspace expansionQuantum equation of motion — click the name to read about it hereqEOMFolded-spectrum variational eigensolver · 3 parts inside · the Atlas has a full record of this — click the name to read about it hereFolded spectrumPenalty-constrained variational eigensolver · 3 parts inside · the Atlas has a full record of this — click the name to read about it herePenalty termsMultistate contracted variational eigensolver · 3 parts inside · the Atlas has a full record of this — click the name to read about it hereMC-VQEHamiltonian whose excited state is wanted — you start hereNumber with an error bar — you finish hereMeasure what the machine can actually doQuantum volume from random square circuitsQuantum volume from random square circuits — click the line to read about it hereRandomized benchmarking over Clifford sequencesRandomized benchmarking over Clifford sequences — click the line to read about it hereQuantum volume from random square circuits — click the name to read about it hereQuantum volumeRandomized benchmarking over Clifford sequences — click the name to read about it hereRBPhysical qubits — you start hereNumber about the machine — you finish hereRecover the period of a periodic functionPeriod finding in a finite cyclic groupPeriod finding in a finite cyclic group — click the line to read about it herePeriod finding over the realsPeriod finding over the reals — click the line to read about it hereFinding a lattice of periodsFinding a lattice of periods — click the line to read about it herePeriod finding in a finite cyclic group — click the name to read about it hereOrder findingPeriod finding over the reals — click the name to read about it hereIrrational periodFinding a lattice of periods — click the name to read about it herePeriod latticeFunction promised to be periodic — you start hereThe period, recovered — you finish hereFind the item a check acceptsFixed-iteration amplitude rotationFixed-iteration amplitude rotation — click the line to read about it hereSearch by state discriminationSearch by state discrimination — click the line to read about it hereFixed-iteration amplitude rotation — click the name to read about it hereGrover searchSearch by state discrimination — click the name to read about it hereSearch by state discriminationMarking oracle over a domain — you start hereA marked item, with its query bill — you finish hereWalk a graph to the vertex you wantWalk over subsets that remember their queriesWalk over subsets that remember their queries — click the line to read about it hereWalk the backtracking tree itselfWalk the backtracking tree itself — click the line to read about it hereWalk over subsets that remember their queries — click the name to read about it hereWalk over subsets that remember their queriesWalk the backtracking tree itself — click the name to read about it hereWalk the backtracking tree itselfSearch graph with a marked set — you start hereA marked item, with its query bill — you finish hereSearch a cost Hamiltonian for the assignment it minimisesAlternate a cost unitary with a mixer, p timesAlternate a cost unitary with a mixer, p times — click the line to read about it hereInterpolate slowly to the problem HamiltonianInterpolate slowly to the problem Hamiltonian — click the line to read about it hereAlternate a cost unitary with a mixer, p times — click the name to read about it hereAlternate a cost unitary with a mixer, p timesInterpolate slowly to the problem Hamiltonian — click the name to read about it hereInterpolate slowly to the problem HamiltonianCost Hamiltonian, diagonal in the computational basis — you start hereAssignment, with the objective value it achieves — you finish here

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Where the routes meet

11 problems nothing else needs — the places a reader arrives. Open a line to see what is recorded inside it, or click its name to go there.

13 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

Solve a nonlinear ODE dy/dt = F(y)

  1. Embed a nonlinear system into a linear one — opens into 6 · a way across — click it to open it here
  2. Solve a linear ODE du/dt = A(t)u + b(t) — opens into 9 · a way across — click it to open it here
  3. Choose a time discretization or propagator approximation → Quantum linear solve — open
  4. Choose a time discretization or propagator approximation — opens into 6 · a way across — click it to open it here
  5. Quantum linear solve — opens into 5 · a way across — click it to open it here
  6. Simulate Hamiltonian evolution → Estimate an observable — open
  7. Simulate Hamiltonian evolution — opens into 3 · a way across — click it to open it here
  8. Estimate an observable — opens into 4 · a way across — click it to open it here

Replace a spatial domain with a finite grid

  1. Graph-Laplacian finite differences
  2. Central differences, space only

Discretize a PDE into one linear system

  1. Forward-time, centre-space (FTCS)
  2. Phase-space grid for a boundary-value problem

Compile a circuit to a specific device

  1. NISQ transpilation (retargetable pass pipeline) — opens into 2 · a way across — click it to open it here
  2. Fault-tolerant compilation (Clifford+T pipeline) — opens into 2 · a way across — click it to open it here

Recover a noiseless expectation value by post-processing

  1. Zero-noise extrapolation (ZNE)
  2. Probabilistic error cancellation (PEC)
  3. Readout (measurement) error mitigation
  4. Check the symmetries the answer must have

Estimate an excited-state energy

  1. Variational quantum deflation — opens into 3 · a way across — click it to open it here
  2. Subspace-search variational eigensolver — opens into 3 · a way across — click it to open it here
  3. Quantum subspace expansion
  4. Quantum equation of motion
  5. Folded-spectrum variational eigensolver — opens into 3 · a way across — click it to open it here
  6. Penalty-constrained variational eigensolver — opens into 3 · a way across — click it to open it here
  7. Multistate contracted variational eigensolver — opens into 3 · a way across — click it to open it here

Measure what the machine can actually do

  1. Quantum volume from random square circuits
  2. Randomized benchmarking over Clifford sequences

Recover the period of a periodic function

  1. Period finding in a finite cyclic group
  2. Period finding over the reals
  3. Finding a lattice of periods

Find the item a check accepts

  1. Fixed-iteration amplitude rotation
  2. Search by state discrimination

Walk a graph to the vertex you want

  1. Walk over subsets that remember their queries
  2. Walk the backtracking tree itself

Search a cost Hamiltonian for the assignment it minimises

  1. Alternate a cost unitary with a mixer, p times
  2. Interpolate slowly to the problem Hamiltonian

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