Quantum Gates (4) 

QuantumToMultiwaySystem supports any quantum gate with an integer matrix representation. Examples of Pauli-X, Pauli-Y, Pauli-Z, root-NOT and Hadamard were shown previously. Other examples include the SWAP gate:

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The root-SWAP gate:

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The CNOT gate:

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The Toffoli gate:

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The Fredkin gate:

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Quantum Bases (2) 

By default, QuantumToMultiwaySystem assumes that all states and operators are expressed in the computational basis:

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However, QuantumToMultiwaySystem supports any quantum basis with an integer matrix representation. For instance, here is the same gate (root-SWAP) compiled instead using the Bell basis:

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Rules and Initial Conditions (2) 

QuantumToMultiwaySystem accepts both full (association) and partial (matrix) specifications of quantum operators:

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QuantumToMultiwaySystem accepts both individual initial conditions and lists of initial conditions:

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Event Selection Functions (2) 

Apply only the first possible event at each step (effectively converting a quantum Turing machine into a classical Turing machine):

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Apply the first and last possible events at each step:

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State Node Rendering (5) 

By default, states are labeled by their contents:

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Use no labeling for states:

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"StatesGraphStructure" yields the same result:

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Use raw state names as node labels:

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Use a named shape as each state label:

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Event Node Rendering (4) 

By default, both states and events are labeled by their contents:

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Use no labels for states or events:

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"EvolutionEventsGraphStructure" yields an equivalent result:

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Use raw event expressions as their labels:

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Initialization Events (2) 

By default, "AllEventsList" does not include initialization events:

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The option "IncludeInitializationEvents" allows one to override this default:

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Initialization events have special default rendering:

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Graph Layout Options (2) 

Places arrows in the middle of edges:

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Generate an example of multiway quantum evolution:

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Force the initial state node to be at the top:

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Step Numbers and State IDs (2) 

By default, equivalent states are merged across all time steps:

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Merging of equivalent states across different time steps can be prevented by including step numbers:

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List the states:

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Merging of equivalent states at the same time step can be prevented by also including state IDs:

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List the states:

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Step numbers and IDs also apply to events:

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See the events:

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Event Instances (2) 

By default, multiple instances of equivalent updating events are merged in the states graph:

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Merging of equivalent events can be prevented by including event instances:

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State (Path) Weights (2) 

Vertices of a states graph can be weighted by their relative rate of occurrence at each time step:

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Vertices can also be weighted by the number of distinct evolution paths that lead to them:

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MaxItems (2) 

By default, "CausalGraphInstances" returns all possible causal graphs:

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The number of causal graphs returned can be limited using MaxItems:

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Predecessors and Resolvents (2) 

By default, "BranchPairsList" returns only a list of branch pairs:

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Common predecessor states can be shown using "GivePredecessors":

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Similarly, "BranchPairResolutionsList" by default lists only resolved and unresolved branch pairs:

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Common resolvents of resolved branch pairs can be shown using "GiveResolvents":

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Show both common predecessors and common resolvents, where appropriate:

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Full Branchial Space (2) 

By default, non-branch pair states are not shown as part of the branchial graph:

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They can be shown using "IncludeFullBranchialSpace":

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