{"id":13693772,"url":"https://github.com/itsubaki/q","last_synced_at":"2025-04-08T03:09:29.784Z","repository":{"id":26575140,"uuid":"115798843","full_name":"itsubaki/q","owner":"itsubaki","description":"Quantum Computation Simulator for 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source library","Go","Quantum simulators"],"sub_categories":["数学计算","Mathematical Calculations"],"readme":"# q\n\n[![PkgGoDev](https://pkg.go.dev/badge/github.com/itsubaki/q)](https://pkg.go.dev/github.com/itsubaki/q)\n[![Go Report Card](https://goreportcard.com/badge/github.com/itsubaki/q?style=flat-square)](https://goreportcard.com/report/github.com/itsubaki/q)\n[![tests](https://github.com/itsubaki/q/workflows/tests/badge.svg)](https://github.com/itsubaki/q/actions)\n[![codecov](https://codecov.io/gh/itsubaki/q/branch/main/graph/badge.svg?token=iNccCs1Tez)](https://codecov.io/gh/itsubaki/q)\n\n- quantum computation simulator\n- pure Go implementation\n- using only the standard library\n\n## Example\n\n### Bell state\n\n```go\nqsim := q.New()\n\n// generate qubits of |0\u003e|0\u003e\nq0 := qsim.Zero()\nq1 := qsim.Zero()\n\n// apply quantum circuit\nqsim.H(q0).CNOT(q0, q1)\n\nfor _, s := range qsim.State() {\n  fmt.Println(s)\n}\n// [00][  0]( 0.7071 0.0000i): 0.5000\n// [11][  3]( 0.7071 0.0000i): 0.5000\n\nm0 := qsim.Measure(q0)\nm1 := qsim.Measure(q1)\nfmt.Println(m0.Equals(m1)) // always true\n\nfor _, s := range qsim.State() {\n  fmt.Println(s)\n}\n// [00][  0]( 1.0000 0.0000i): 1.0000\n// or\n// [11][  3]( 1.0000 0.0000i): 1.0000\n```\n\n### Quantum teleportation\n\n```go\nqsim := q.New()\n\n// generate qubits of |phi\u003e|0\u003e|0\u003e\nphi := qsim.New(1, 2)\nq0 := qsim.Zero()\nq1 := qsim.Zero()\n\n// |phi\u003e is normalized. |phi\u003e = a|0\u003e + b|1\u003e, |a|^2 = 0.2, |b|^2 = 0.8\nfor _, s := range qsim.State(phi) {\n  fmt.Println(s)\n}\n// [0][  0]( 0.4472 0.0000i): 0.2000\n// [1][  1]( 0.8944 0.0000i): 0.8000\n\nqsim.H(q0).CNOT(q0, q1)\nqsim.CNOT(phi, q0).H(phi)\n\n// Alice send mz, mx to Bob\nmz := qsim.Measure(phi)\nmx := qsim.Measure(q0)\n\n// Bob Apply X and Z\nqsim.CondX(mx.IsOne(), q1)\nqsim.CondZ(mz.IsOne(), q1)\n\n// Bob got |phi\u003e state with q1\nfor _, s := range qsim.State(q1) {\n  fmt.Println(s)\n}\n// [0][  0]( 0.4472 0.0000i): 0.2000\n// [1][  1]( 0.8944 0.0000i): 0.8000\n```\n\n### Error correction\n\n```go\nqsim := q.New()\n\nq0 := qsim.New(1, 2) // (0.2, 0.8)\n\n// encoding\nq1 := qsim.Zero()\nq2 := qsim.Zero()\nqsim.CNOT(q0, q1).CNOT(q0, q2)\n\n// error: first qubit is flipped\nqsim.X(q0)\n\n// add ancilla qubit\nq3 := qsim.Zero()\nq4 := qsim.Zero()\n\n// error correction\nqsim.CNOT(q0, q3).CNOT(q1, q3)\nqsim.CNOT(q1, q4).CNOT(q2, q4)\n\nm3 := qsim.Measure(q3)\nm4 := qsim.Measure(q4)\n\nqsim.CondX(m3.IsOne() \u0026\u0026 m4.IsZero(), q0)\nqsim.CondX(m3.IsOne() \u0026\u0026 m4.IsOne(), q1)\nqsim.CondX(m3.IsZero() \u0026\u0026 m4.IsOne(), q2)\n\n// decoding\nqsim.CNOT(q0, q2).CNOT(q0, q1)\n\nfor _, s := range qsim.State(q0) {\n  fmt.Println(s)\n}\n// [0][  0]( 0.4472 0.0000i): 0.2000\n// [1][  1]( 0.8944 0.0000i): 0.8000\n```\n\n### Grover's search algorithm\n\n```go\nqsim := q.New()\n\n// initial state\nq0 := qsim.Zero()\nq1 := qsim.Zero()\nq2 := qsim.Zero()\nq3 := qsim.Zero()\n\n// superposition\nqsim.H(q0, q1, q2, q3)\n\n// iteration\nN := number.Pow(2, qsim.NumQubits())\nr := math.Floor(math.Pi / 4 * math.Sqrt(float64(N)))\nfor i := 0; i \u003c int(r); i++ {\n  // oracle for |110\u003e|x\u003e\n  qsim.X(q2, q3)\n  qsim.H(q3).CCCNOT(q0, q1, q2, q3).H(q3)\n  qsim.X(q2, q3)\n\n  // amplification\n  qsim.H(q0, q1, q2, q3)\n  qsim.X(q0, q1, q2, q3)\n  qsim.H(q3).CCCNOT(q0, q1, q2, q3).H(q3)\n  qsim.X(q0, q1, q2, q3)\n  qsim.H(q0, q1, q2, q3)\n}\n\nfor _, s := range qsim.State() {\n  fmt.Println(s)\n}\n// [0000][  0]( 0.0508 0.0000i): 0.0026\n// [0001][  1]( 0.0508 0.0000i): 0.0026\n// [0010][  2]( 0.0508 0.0000i): 0.0026\n// [0011][  3]( 0.0508 0.0000i): 0.0026\n// [0100][  4]( 0.0508 0.0000i): 0.0026\n// [0101][  5]( 0.0508 0.0000i): 0.0026\n// [0110][  6]( 0.0508 0.0000i): 0.0026\n// [0111][  7]( 0.0508 0.0000i): 0.0026\n// [1000][  8]( 0.0508 0.0000i): 0.0026\n// [1001][  9]( 0.0508 0.0000i): 0.0026\n// [1010][ 10]( 0.0508 0.0000i): 0.0026\n// [1011][ 11]( 0.0508 0.0000i): 0.0026\n// [1100][ 12](-0.9805 0.0000i): 0.9613 -\u003e answer!\n// [1101][ 13]( 0.0508 0.0000i): 0.0026\n// [1110][ 14]( 0.0508 0.0000i): 0.0026\n// [1111][ 15]( 0.0508 0.0000i): 0.0026\n```\n\n### Shor's factoring algorithm\n\n```go\nN := 15\na := 7 // co-prime\n\nfor i := range 10 {\n  qsim := q.New()\n\n  // initial state\n  q0 := qsim.Zero()\n  q1 := qsim.Zero()\n  q2 := qsim.Zero()\n\n  q3 := qsim.Zero()\n  q4 := qsim.Zero()\n  q5 := qsim.Zero()\n  q6 := qsim.One()\n\n  // superposition\n  qsim.H(q0, q1, q2)\n\n  // Controlled-U\n  qsim.CNOT(q2, q4)\n  qsim.CNOT(q2, q5)\n\n  // Controlled-U^2\n  qsim.CNOT(q3, q5).CCNOT(q1, q5, q3).CNOT(q3, q5)\n  qsim.CNOT(q6, q4).CCNOT(q1, q4, q6).CNOT(q6, q4)\n\n  // inverse QFT\n  qsim.Swap(q0, q2)\n  qsim.InvQFT(q0, q1, q2)\n\n  // measure q0, q1, q2\n  m := qsim.Measure(q0, q1, q2).BinaryString()\n\n  // find s/r. 0.010 -\u003e 0.25 -\u003e 1/4, 0.110 -\u003e 0.75 -\u003e 3/4, ...\n  s, r, d, ok := number.FindOrder(a, N, fmt.Sprintf(\"0.%s\", m))\n  if !ok || number.IsOdd(r) {\n    continue\n  }\n\n  // gcd(a^(r/2)-1, N), gcd(a^(r/2)+1, N)\n  p0 := number.GCD(number.Pow(a, r/2)-1, N)\n  p1 := number.GCD(number.Pow(a, r/2)+1, N)\n  if number.IsTrivial(N, p0, p1) {\n    continue\n  }\n\n  // result\n  fmt.Printf(\"i=%d: N=%d, a=%d. p=%v, q=%v. s/r=%d/%d ([0.%v]~%.3f)\\n\", i, N, a, p0, p1, s, r, m, d)\n}\n\n// i=2: N=15, a=7. p=3, q=5. s/r=1/4 ([0.010]~0.250)\n```\n\n- In general, See [`cmd/shor`](./cmd/shor/main.go)\n\n### Any 1-qubit quantum gate and its controlled gate\n\n```go\nh := gate.U(math.Pi/2, 0, math.Pi)\nx := gate.U(math.Pi, 0, math.Pi)\n\nqsim := q.New()\nq0 := qsim.Zero()\nq1 := qsim.Zero()\n\nqsim.Apply(h, q0)\nqsim.C(x, q0, q1)\n\nfor _, s := range qsim.State() {\n  fmt.Println(s)\n}\n// [00][  0]( 0.7071 0.0000i): 0.5000\n// [11][  3]( 0.7071 0.0000i): 0.5000\n```\n\n## References\n\n[1] M. A. Nielsen and I. L. Chuang, *Quantum Computation and Quantum Information*, 10th anniv. ed. Cambridge, U.K.: Cambridge Univ. Press, 2010.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fitsubaki%2Fq","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fitsubaki%2Fq","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fitsubaki%2Fq/lists"}