├── zh ├── axioms │ ├── noop.qrule │ ├── z-id.qrule │ ├── x-id.qrule │ ├── h-id.qrule │ ├── z-spider.qrule │ ├── x-spider.qrule │ ├── z-pi-commute.qrule │ ├── h-bialg.qrule │ ├── h-spider.qrule │ └── disconnect.qrule ├── .DS_Store ├── theorems │ ├── .DS_Store │ ├── x-id-may.qrule │ ├── x-id-many.qrule │ ├── x-spider-many.qrule │ ├── z-spider-many-to-one.qrule │ ├── z-pi-commute-many.qrule │ ├── z-sp-many-2.qrule │ ├── h-bialg-many.qrule │ ├── n-disconnect.qrule │ ├── z-sp-many-2p.qrule │ ├── n-disconnect1.qrule │ ├── gen-n-disconnect.qrule │ ├── disconnect-4p.qrule │ ├── sp-lem1.qrule │ ├── disconnect-4.qrule │ ├── split.qrule │ ├── gen-split.qrule │ ├── lem.qrule │ └── lem1.qrule ├── main.qproject ├── graphs │ ├── split1.qgraph │ ├── example.qgraph │ ├── lem1-graph.qgraph │ ├── example1.qgraph │ ├── 3-tensor-contract.qgraph │ └── 3-tensor.qgraph └── derivations │ └── n-disconnect1.qderive ├── spekkens.zip ├── bialgebra.zip ├── zx-cliffordt.zip ├── zx-stabilizer.zip ├── zx-stabilizer ├── axioms │ ├── green_scalar.qrule │ ├── red_scalar.qrule │ ├── green_id.qrule │ ├── red_id.qrule │ ├── green_copy.qrule │ ├── red_copy.qrule │ ├── green_to_red.qrule │ ├── red_to_green.qrule │ ├── green_elim.qrule │ ├── green_loop.qrule │ ├── red_loop.qrule │ ├── red_elim.qrule │ ├── euler.qrule │ ├── euler2.qrule │ ├── hopf.qrule │ ├── gen_bialg_simp.qrule │ ├── red_pi.qrule │ ├── green_pi.qrule │ ├── green_sp.qrule │ ├── red_sp.qrule │ └── gen_bialg.qrule ├── README.md ├── simprocs │ ├── basic-simp.py │ └── rotate-simp.py ├── theorems │ ├── bb_green_to_red.qrule │ ├── green_elim.qrule │ ├── green_id_on_red.qrule │ ├── green_sp_simp.qrule │ ├── red_sp_simp.qrule │ ├── bb_green_sp_simp.qrule │ ├── bb_green_sp.qrule │ ├── rotate_lem.qrule │ ├── rotate.qrule │ └── rotate_targeted.qrule ├── derivations │ ├── green_id_on_red.qderive │ ├── green_elim.qderive │ ├── green_sp_simp.qderive │ ├── red_sp_simp.qderive │ └── bb_green_sp_simp.qderive ├── graphs │ ├── threegates.qgraph │ ├── gss_cc(n,n).qgraph │ ├── sample.qgraph │ └── cnot-circuit.qgraph └── main.qproject ├── README.md ├── bialgebra ├── README.md ├── simprocs │ └── basic_simp.ML ├── axioms │ ├── green-id.qrule │ ├── red-id.qrule │ ├── distribute.qrule │ ├── green-merge.qrule │ └── red-merge.qrule ├── graphs │ └── test.qgraph ├── main.qproject └── theorems │ └── example.qrule ├── zx-cliffordt ├── axioms │ ├── E.qrule │ ├── S2.qrule │ ├── B1.qrule │ ├── EU.qrule │ ├── H.qrule │ ├── S1.qrule │ ├── K2.qrule │ ├── B2.qrule │ ├── SUP.qrule │ ├── C1.qrule │ ├── C2.qrule │ └── C3.qrule ├── graphs │ ├── DoubleEdge.qgraph │ ├── K1.qgraph │ └── scalar1.qgraph ├── theorems │ ├── HadamardAnn.qrule │ ├── ScalarRemove.qrule │ └── Hopf.qrule ├── derivations │ └── HadamardAnn.qderive └── main.qproject ├── spekkens ├── graphs │ ├── S2ForGreenNodes.qgraph │ ├── TwoHadamard.qgraph │ ├── S1ForGreenNodes.qgraph │ └── ExampleWeb.qgraph ├── axioms │ ├── S2-green.qrule │ ├── S2.qrule │ ├── B1.qrule │ ├── 11-commutation.qrule │ ├── Euler.qrule │ ├── 11-copy.qrule │ ├── Hadamard.qrule │ ├── S1.qrule │ └── B2.qrule ├── theorems │ ├── HadamardAnn.qrule │ └── S1-green.qrule ├── main.qproject └── derivations │ └── S1-green.qderive └── zx-qutrit-stabilizer ├── S2.qrule ├── axioms ├── H1a.qrule ├── H1b.qrule ├── B1.qrule ├── P1a.qrule ├── P1b.qrule ├── P1c.qrule ├── EU.qrule ├── K2a.qrule ├── K2b.qrule ├── K1a.qrule ├── K1b.qrule ├── B2.qrule ├── S1.qrule ├── H2a.qrule └── H2b.qrule ├── graphs ├── Lemma4.1.start.qgraph └── S1-red.qgraph ├── main.qproject └── derivations └── Lemma4.1.qderive /zh/axioms/noop.qrule: -------------------------------------------------------------------------------- 1 | {"lhs":{},"rhs":{}} -------------------------------------------------------------------------------- /spekkens.zip: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/zxcalc/sample-projects/HEAD/spekkens.zip -------------------------------------------------------------------------------- /zh/.DS_Store: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/zxcalc/sample-projects/HEAD/zh/.DS_Store -------------------------------------------------------------------------------- /bialgebra.zip: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/zxcalc/sample-projects/HEAD/bialgebra.zip -------------------------------------------------------------------------------- /zx-cliffordt.zip: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/zxcalc/sample-projects/HEAD/zx-cliffordt.zip -------------------------------------------------------------------------------- /zx-stabilizer.zip: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/zxcalc/sample-projects/HEAD/zx-stabilizer.zip -------------------------------------------------------------------------------- /zh/theorems/.DS_Store: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/zxcalc/sample-projects/HEAD/zh/theorems/.DS_Store -------------------------------------------------------------------------------- /zx-stabilizer/axioms/green_scalar.qrule: -------------------------------------------------------------------------------- 1 | {"lhs":{"node_vertices":{"v0":{"annotation":{"coord":[0.0,0.0]}}}},"rhs":{}} -------------------------------------------------------------------------------- /zx-stabilizer/axioms/red_scalar.qrule: -------------------------------------------------------------------------------- 1 | {"lhs":{"node_vertices":{"v1":{"data":{"type":"X","value":""},"annotation":{"coord":[0.0,1.0]}}}},"rhs":{}} -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # sample-projects 2 | 3 | this repository is for storing the sample projects that demonstrate the capabilities of Quantomatic, 4 | as well as allowing consistency between researchers for the more popular theories. 5 | -------------------------------------------------------------------------------- /bialgebra/README.md: -------------------------------------------------------------------------------- 1 | # bialgebra-project 2 | 3 | This is a Quantomatic project on bialgebras. It includes the necessary axioms, a simplification procedures which always produces unique normal forms and a sample graph with a derivation. 4 | -------------------------------------------------------------------------------- /zx-stabilizer/README.md: -------------------------------------------------------------------------------- 1 | zx-project 2 | ========== 3 | 4 | This is a Quantomatic project which contains all of the ZX-calculus axioms and 5 | some useful theorems and simplification procedures. It also includes sample 6 | graphs and derivations. 7 | -------------------------------------------------------------------------------- /zx-cliffordt/axioms/E.qrule: -------------------------------------------------------------------------------- 1 | {"lhs":{"node_vertices":{"v0":{"data":{"type":"X","value":"- \\pi / 4"},"annotation":{"coord":[0.0,0.0]}},"v1":{"data":{"type":"Z","value":"\\pi / 4"},"annotation":{"coord":[0.0,2.0]}}},"undir_edges":{"e0":{"src":"v1","tgt":"v0"}}},"rhs":{}} -------------------------------------------------------------------------------- /spekkens/graphs/S2ForGreenNodes.qgraph: -------------------------------------------------------------------------------- 1 | {"wire_vertices":{"b0":{"annotation":{"boundary":true,"coord":[-6.0,4.0]}},"b1":{"annotation":{"boundary":true,"coord":[-6.0,2.0]}}},"node_vertices":{"v0":{"annotation":{"coord":[-6.0,3.0]}}},"undir_edges":{"e0":{"src":"b0","tgt":"v0"},"e1":{"src":"v0","tgt":"b1"}}} -------------------------------------------------------------------------------- /bialgebra/simprocs/basic_simp.ML: -------------------------------------------------------------------------------- 1 | open RG_SimpUtil 2 | 3 | 4 | val simps = load_ruleset [ 5 | "axioms/red-merge", "axioms/red-id", 6 | "axioms/green-merge", "axioms/green-id", 7 | "axioms/distribute" 8 | ]; 9 | 10 | val simproc = REDUCE_ALL simps; 11 | 12 | register_simproc ("basic_simp", simproc); 13 | 14 | 15 | 16 | 17 | -------------------------------------------------------------------------------- /zx-stabilizer/simprocs/basic-simp.py: -------------------------------------------------------------------------------- 1 | from quanto.util.Scripting import * 2 | 3 | simps = load_rules([ 4 | "axioms/red_copy", "axioms/red_sp", "axioms/green_sp", "axioms/hopf", 5 | "axioms/red_scalar", "axioms/green_scalar", "axioms/green_id", 6 | "axioms/red_id", "axioms/red_loop", "axioms/green_loop"]) 7 | 8 | register_simproc("basic-simp", REDUCE(simps)) 9 | 10 | 11 | -------------------------------------------------------------------------------- /zh/axioms/z-id.qrule: -------------------------------------------------------------------------------- 1 | {"lhs":{"wire_vertices":{"b0":{"annotation":{"boundary":true,"coord":[0.0,-1.5]}},"b1":{"annotation":{"boundary":true,"coord":[0.0,1.5]}}},"node_vertices":{"v0":{"annotation":{"coord":[0.0,0.0]}}},"undir_edges":{"e0":{"src":"b0","tgt":"v0"},"e1":{"src":"v0","tgt":"b1"}}},"rhs":{"wire_vertices":{"b0":{"annotation":{"boundary":true,"coord":[0.0,-1.0]}},"b1":{"annotation":{"boundary":true,"coord":[0.0,1.0]}}},"undir_edges":{"e0":{"src":"b0","tgt":"b1"}}}} -------------------------------------------------------------------------------- /spekkens/graphs/TwoHadamard.qgraph: -------------------------------------------------------------------------------- 1 | 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-------------------------------------------------------------------------------- /zx-stabilizer/simprocs/rotate-simp.py: -------------------------------------------------------------------------------- 1 | from quanto.util.Scripting import * 2 | 3 | simps0 = load_rules([ 4 | "axioms/red_copy", "axioms/green_copy", 5 | "axioms/red_sp", "axioms/green_sp", 6 | "axioms/hopf", 7 | "axioms/red_scalar", "axioms/green_scalar", 8 | "axioms/red_loop", "axioms/green_loop"]) 9 | 10 | simps = simps0 + load_rules(["axioms/green_id", "axioms/red_id"]) 11 | 12 | green_id_inv = load_rule("axioms/green_id").inverse() 13 | red_id_inv = load_rule("axioms/red_id").inverse() 14 | rotate = load_rule("theorems/rotate_targeted") 15 | 16 | 17 | def num_boundary_X(g): 18 | return len([v for v in verts(g) 19 | if g.isBoundary(v) and g.isAdjacentToType(v, 'X')]) 20 | 21 | def next_rotation_Z(g): 22 | vs = [(g.arity(v),v) for v in verts(g) 23 | if g.typeOf(v) == 'Z' and 24 | vertex_angle_is(g, v, '0') and 25 | not 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