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Quantum Operation Counts
Quantum Operation Counts
E.g. quantum Fourier transforms
Operation count is affected by size n of the transform, and the precision p (measured by the maximum denominator):
classical ops: 2^n * 4 * p quantum: 1 (or p)
Operation count is affected by size n of the transform, and the precision p (measured by the maximum denominator):
classical ops: 2^n * 4 * p quantum: 1 (or p)
Two Approaches to Experiments
Two Approaches to Experiments
1. You explicitly (conceptually) set up a state [imagine the experimenter has free will]
1. You explicitly (conceptually) set up a state [imagine the experimenter has free will]
Analogous to generational multiway system where you insist on having done all the updates necessary to reach a classical state
2. You wait for the universe to deliver the state you want to study
2. You wait for the universe to deliver the state you want to study
You wait for causal invariance to deliver you the classical state
By inserting completions, you are going to case #1
By inserting completions, you are going to case #1
Analogous to adding completions in theorem proving
(i.e. adding lemmas; but adding lemmas is an exponential speedup)
(i.e. adding lemmas; but adding lemmas is an exponential speedup)
Visualizing Branchial Space
Visualizing Branchial Space
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GridGraph[{2,2,2},VertexLabelsAutomatic]
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HighlightGraph[GridGraph[{2,2,2}],Subgraph[GridGraph[{2,2,2}],{1,3,5}]]
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HighlightGraph[GridGraph[{2,2,2,2}],Subgraph[GridGraph[{2,2,2,2}],{1,3,5}]]
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GridGraph[Table[2,7]]
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Graph3D[%]
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ResourceFunction["MultiwaySystem"][{"A""AB"},"AA",3,"StatesGraph"]
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GridGraph[{2,2,2},VertexLabels->Automatic]
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Take the ancestry distance, and the further back they branch, the further apart they should be.
Ancestry distance k between nodes; 1 - k/(total history)
Enumerate SSs
Enumerate SSs
[[[ Of possible substitution systems, how many correspond to named quantum operators? ]]]
[[[ Of possible substitution systems, how many correspond to named quantum operators? ]]]
Analog of Event Horizons in Branchial / Multiway Space
Analog of Event Horizons in Branchial / Multiway Space
Simple event horizon: superselection rule
Disconnection in branchial graph
Superselection sector
Superselection sector
Validation for a quantum circuit
Geometrization of correctness proofs
Geometrization of correctness proofs
Computability is topology of branchial space; computational complexity of rulial space
Systematic Measurement
Systematic Measurement