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q

package module

v1.1.10 Latest Latest Go to latest Published: Oct 9, 2022 License: MIT Imports: 5 Imported by: 14

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Repository

github.com/itsubaki/q

README ¶

q

quantum computation simulator
pure golang implementation
using only the standard library

Example

Bell state

qsim := q.New()

// generate qubits of |0>|0>
q0 := qsim.Zero()
q1 := qsim.Zero()

// apply quantum circuit
qsim.H(q0).CNOT(q0, q1)

for _, s := range qsim.State() {
  fmt.Println(s)
}
// [00][  0]( 0.7071 0.0000i): 0.5000
// [11][  3]( 0.7071 0.0000i): 0.5000

m0 := qsim.Measure(q0)
m1 := qsim.Measure(q1)
fmt.Printf("%v %v\n", m0.IsZero(), m1.IsZero())
// if m0.IsZero() is true, m1.IsZero() is also true
// if m0.IsOne()  is true, m1.IsOne()  is also true

for _, s := range qsim.State() {
  fmt.Println(s)
}
// [00][  0]( 1.0000 0.0000i): 1.0000
// or
// [11][  3]( 1.0000 0.0000i): 1.0000

Quantum teleportation

qsim := q.New()

// generate qubits of |phi>|0>|0>
phi := qsim.New(1, 2)
q0 := qsim.Zero()
q1 := qsim.Zero()

// |phi> is normalized. |phi> = a|0> + b|1>, |a|^2 = 0.2, |b|^2 = 0.8
for _, s := range qsim.State(phi) {
  fmt.Println(s)
}
// [0][  0]( 0.4472 0.0000i): 0.2000
// [1][  1]( 0.8944 0.0000i): 0.8000

qsim.H(q0).CNOT(q0, q1)
qsim.CNOT(phi, q0).H(phi)

// Alice send mz, mx to Bob
mz := qsim.Measure(phi)
mx := qsim.Measure(q0)

// Bob Apply X and Z
qsim.ConditionX(mx.IsOne(), q1)
qsim.ConditionZ(mz.IsOne(), q1)

// Bob got |phi> state with q1
for _, s := range qsim.State(q1) {
  fmt.Println(s)
}
// [0][  0]( 0.4472 0.0000i): 0.2000
// [1][  1]( 0.8944 0.0000i): 0.8000

Error correction

qsim := q.New()

q0 := qsim.New(1, 2) // (0.2, 0.8)

// encoding
q1 := qsim.Zero()
q2 := qsim.Zero()
qsim.CNOT(q0, q1).CNOT(q0, q2)

// error: first qubit is flipped
qsim.X(q0)

// add ancilla qubit
q3 := qsim.Zero()
q4 := qsim.Zero()

// error correction
qsim.CNOT(q0, q3).CNOT(q1, q3)
qsim.CNOT(q1, q4).CNOT(q2, q4)

m3 := qsim.Measure(q3)
m4 := qsim.Measure(q4)

qsim.ConditionX(m3.IsOne() && m4.IsZero(), q0)
qsim.ConditionX(m3.IsOne() && m4.IsOne(), q1)
qsim.ConditionX(m3.IsZero() && m4.IsOne(), q2)

// decoding
qsim.CNOT(q0, q2).CNOT(q0, q1)

for _, s := range qsim.State(q0) {
  fmt.Println(s)
}
// [0][  0]( 0.4472 0.0000i): 0.2000
// [1][  1]( 0.8944 0.0000i): 0.8000

Grover's search algorithm

qsim := q.New()

// initial state
q0 := qsim.Zero()
q1 := qsim.Zero()
q2 := qsim.Zero()
q3 := qsim.Zero()

// superposition
qsim.H(q0, q1, q2, q3)

// iteration
N := number.Pow(2, qsim.NumberOfBit())
r := math.Floor(math.Pi / 4 * math.Sqrt(float64(N)))
for i := 0; i < int(r); i++ {
  // oracle for |110>|x>
  qsim.X(q2, q3)
  qsim.H(q3).CCCNOT(q0, q1, q2, q3).H(q3)
  qsim.X(q2, q3)

  // amplification
  qsim.H(q0, q1, q2, q3)
  qsim.X(q0, q1, q2, q3)
  qsim.H(q3).CCCNOT(q0, q1, q2, q3).H(q3)
  qsim.X(q0, q1, q2, q3)
  qsim.H(q0, q1, q2, q3)
}

for _, s := range qsim.State() {
  fmt.Println(s)
}

// [0000][  0]( 0.0508 0.0000i): 0.0026
// [0001][  1]( 0.0508 0.0000i): 0.0026
// [0010][  2]( 0.0508 0.0000i): 0.0026
// [0011][  3]( 0.0508 0.0000i): 0.0026
// [0100][  4]( 0.0508 0.0000i): 0.0026
// [0101][  5]( 0.0508 0.0000i): 0.0026
// [0110][  6]( 0.0508 0.0000i): 0.0026
// [0111][  7]( 0.0508 0.0000i): 0.0026
// [1000][  8]( 0.0508 0.0000i): 0.0026
// [1001][  9]( 0.0508 0.0000i): 0.0026
// [1010][ 10]( 0.0508 0.0000i): 0.0026
// [1011][ 11]( 0.0508 0.0000i): 0.0026
// [1100][ 12](-0.9805 0.0000i): 0.9613 -> answer!
// [1101][ 13]( 0.0508 0.0000i): 0.0026
// [1110][ 14]( 0.0508 0.0000i): 0.0026
// [1111][ 15]( 0.0508 0.0000i): 0.0026

Shor's factoring algorithm

N := 15
a := 7 // co-prime

for i := 0; i < 10; i++{
  qsim := q.New()

  // initial state
  q0 := qsim.Zero()
  q1 := qsim.Zero()
  q2 := qsim.Zero()

  q3 := qsim.Zero()
  q4 := qsim.Zero()
  q5 := qsim.Zero()
  q6 := qsim.One()

  // superposition
  qsim.H(q0, q1, q2)

  // Controlled-U
  qsim.CNOT(q2, q4)
  qsim.CNOT(q2, q5)

  // Controlled-U^2
  qsim.CNOT(q3, q5).CCNOT(q1, q5, q3).CNOT(q3, q5)
  qsim.CNOT(q6, q4).CCNOT(q1, q4, q6).CNOT(q6, q4)

  // inverse QFT
  qsim.Swap(q0, q2)
  qsim.InvQFT(q0, q1, q2)

  // measure q0, q1, q2
  m := qsim.Measure(q0, q1, q2).BinaryString()

  // find s/r. 0.010 -> 0.25 -> 1/4, 0.110 -> 0.75 -> 3/4, ...
  s, r, d, ok := number.FindOrder(a, N, fmt.Sprintf("0.%s", m))
  if !ok || number.IsOdd(r) {
    continue
  }

  // gcd(a^(r/2)-1, N), gcd(a^(r/2)+1, N)
  p0 := number.GCD(number.Pow(a, r/2)-1, N)
  p1 := number.GCD(number.Pow(a, r/2)+1, N)
  if number.IsTrivial(N, p0, p1) {
    continue
  }

  // result
  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)
}

// i=2: N=15, a=7. p=3, q=5. s/r=1/4 ([0.010]~0.250)

In general, See cmd/shor

Reference

Michael A. Nielsen, Issac L. Chuang. Quantum Computation and Quantum Information.

Documentation ¶

Overview ¶

Example (BellState) ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	q0 := qsim.Zero()
	q1 := qsim.Zero()

	qsim.H(q0).CNOT(q0, q1)

	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[00][  0]( 0.7071 0.0000i): 0.5000
[11][  3]( 0.7071 0.0000i): 0.5000

Example (BellState2) ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
	"github.com/itsubaki/q/math/rand"
)

func main() {
	qsim := q.New()
	qsim.Seed = []int{1}
	qsim.Rand = rand.Math

	r := qsim.ZeroWith(2)

	qsim.H(r[0])
	qsim.CNOT(r[0], r[1])

	c0 := qsim.Measure(r[0]).Int()
	c1 := qsim.Measure(r[1]).Int()

	fmt.Printf("%v%v\n", c0, c1)

}

Output:

11

Example (ErrorCorrection) ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	q0 := qsim.New(1, 2)

	fmt.Println("q0:")
	for _, s := range qsim.State(q0) {
		fmt.Println(s)
	}

	// encoding
	q1 := qsim.Zero()
	q2 := qsim.Zero()
	qsim.CNOT(q0, q1).CNOT(q0, q2)

	// error: first qubit is flipped
	qsim.X(q0)

	fmt.Println("q0(flipped):")
	for _, s := range qsim.State(q0) {
		fmt.Println(s)
	}

	// add ancilla qubit
	q3 := qsim.Zero()
	q4 := qsim.Zero()

	// error correction
	qsim.CNOT(q0, q3).CNOT(q1, q3)
	qsim.CNOT(q1, q4).CNOT(q2, q4)

	m3 := qsim.Measure(q3)
	m4 := qsim.Measure(q4)

	qsim.ConditionX(m3.IsOne() && m4.IsZero(), q0)
	qsim.ConditionX(m3.IsOne() && m4.IsOne(), q1)
	qsim.ConditionX(m3.IsZero() && m4.IsOne(), q2)

	// decoding
	qsim.CNOT(q0, q2).CNOT(q0, q1)

	fmt.Println("q0(corrected):")
	for _, s := range qsim.State(q0) {
		fmt.Println(s)
	}

}

Output:

q0:
[0][  0]( 0.4472 0.0000i): 0.2000
[1][  1]( 0.8944 0.0000i): 0.8000
q0(flipped):
[0][  0]( 0.8944 0.0000i): 0.8000
[1][  1]( 0.4472 0.0000i): 0.2000
q0(corrected):
[0][  0]( 0.4472 0.0000i): 0.2000
[1][  1]( 0.8944 0.0000i): 0.8000

Example (Grover3qubit) ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	// NOTE: C. Figgatt, D. Maslov, K. A. Landsman, N. M. Linke, S. Debnath, and C. Monroe. Complete 3-Qubit Grover Search on a Programmable Quantum Computer.
	qsim := q.New()

	// initial state
	r := qsim.ZeroWith(3)
	a := qsim.One()

	// superposition
	qsim.H(r...).H(a)

	// oracle for |011>|1>
	qsim.X(r[0]).CCCNOT(r[0], r[1], r[2], a).X(r[0])

	// amplification
	qsim.H(r...).H(a)
	qsim.X(r...).CCZ(r[0], r[1], r[2]).X(r...)
	qsim.H(r...)

	for _, s := range qsim.State(r, a) {
		fmt.Println(s)
	}

}

Output:

[000 1][  0   1](-0.1768 0.0000i): 0.0313
[001 1][  1   1](-0.1768 0.0000i): 0.0313
[010 1][  2   1](-0.1768 0.0000i): 0.0313
[011 1][  3   1](-0.8839 0.0000i): 0.7813
[100 1][  4   1](-0.1768 0.0000i): 0.0313
[101 1][  5   1](-0.1768 0.0000i): 0.0313
[110 1][  6   1](-0.1768 0.0000i): 0.0313
[111 1][  7   1](-0.1768 0.0000i): 0.0313

Example (Grover4qubit) ¶

package main

import (
	"fmt"
	"math"

	"github.com/itsubaki/q"
	"github.com/itsubaki/q/math/number"
)

func main() {
	// NOTE: Eric R. Johnson, Nic Harrigan, and Merecedes Gimeno-Segovia. Programming Quantum Computers. O'Reilly.
	qsim := q.New()

	// initial state
	q0 := qsim.Zero()
	q1 := qsim.Zero()
	q2 := qsim.Zero()
	q3 := qsim.Zero()

	// superposition
	qsim.H(q0, q1, q2, q3)

	// iteration
	N := number.Pow(2, qsim.NumberOfBit())
	r := math.Floor(math.Pi / 4 * math.Sqrt(float64(N)))
	for i := 0; i < int(r); i++ {
		// oracle for |110>|x>
		qsim.X(q2, q3)
		qsim.H(q3).CCCNOT(q0, q1, q2, q3).H(q3)
		qsim.X(q2, q3)

		// amplification
		qsim.H(q0, q1, q2, q3)
		qsim.X(q0, q1, q2, q3)
		qsim.H(q3).CCCNOT(q0, q1, q2, q3).H(q3)
		qsim.X(q0, q1, q2, q3)
		qsim.H(q0, q1, q2, q3)
	}

	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[0000][  0]( 0.0508 0.0000i): 0.0026
[0001][  1]( 0.0508 0.0000i): 0.0026
[0010][  2]( 0.0508 0.0000i): 0.0026
[0011][  3]( 0.0508 0.0000i): 0.0026
[0100][  4]( 0.0508 0.0000i): 0.0026
[0101][  5]( 0.0508 0.0000i): 0.0026
[0110][  6]( 0.0508 0.0000i): 0.0026
[0111][  7]( 0.0508 0.0000i): 0.0026
[1000][  8]( 0.0508 0.0000i): 0.0026
[1001][  9]( 0.0508 0.0000i): 0.0026
[1010][ 10]( 0.0508 0.0000i): 0.0026
[1011][ 11]( 0.0508 0.0000i): 0.0026
[1100][ 12](-0.9805 0.0000i): 0.9613
[1101][ 13]( 0.0508 0.0000i): 0.0026
[1110][ 14]( 0.0508 0.0000i): 0.0026
[1111][ 15]( 0.0508 0.0000i): 0.0026

Example (QFT) ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
	"github.com/itsubaki/q/quantum/gate"
)

func main() {
	qsim := q.New()

	q0 := qsim.Zero()
	q1 := qsim.One()
	q2 := qsim.Zero()

	qsim.H(q0)
	qsim.CR(gate.Theta(2), q1, q0)
	qsim.CR(gate.Theta(3), q2, q0)
	qsim.H(q1)
	qsim.CR(gate.Theta(2), q2, q1)
	qsim.H(q2)
	qsim.Swap(q0, q2)

	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[000][  0]( 0.3536 0.0000i): 0.1250
[001][  1]( 0.0000 0.3536i): 0.1250
[010][  2](-0.3536 0.0000i): 0.1250
[011][  3]( 0.0000-0.3536i): 0.1250
[100][  4]( 0.3536 0.0000i): 0.1250
[101][  5]( 0.0000 0.3536i): 0.1250
[110][  6](-0.3536 0.0000i): 0.1250
[111][  7]( 0.0000-0.3536i): 0.1250

Example (QuantumTeleportation) ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	phi := qsim.New(1, 2)
	q0 := qsim.Zero()
	q1 := qsim.Zero()

	fmt.Println("phi:")
	for _, s := range qsim.State(phi) {
		fmt.Println(s)
	}

	qsim.H(q0).CNOT(q0, q1)
	qsim.CNOT(phi, q0).H(phi)

	qsim.CNOT(q0, q1)
	qsim.CZ(phi, q1)

	qsim.Measure(phi, q0)

	fmt.Println("q1:")
	for _, s := range qsim.State(q1) {
		fmt.Println(s)
	}

}

Output:

phi:
[0][  0]( 0.4472 0.0000i): 0.2000
[1][  1]( 0.8944 0.0000i): 0.8000
q1:
[0][  0]( 0.4472 0.0000i): 0.2000
[1][  1]( 0.8944 0.0000i): 0.8000

Example (QuantumTeleportation2) ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	phi := qsim.New(1, 2)
	q0 := qsim.Zero()
	q1 := qsim.Zero()

	fmt.Println("phi:")
	for _, s := range qsim.State(phi) {
		fmt.Println(s)
	}

	qsim.H(q0).CNOT(q0, q1)
	qsim.CNOT(phi, q0).H(phi)

	mz := qsim.Measure(phi)
	mx := qsim.Measure(q0)

	qsim.ConditionX(mx.IsOne(), q1)
	qsim.ConditionZ(mz.IsOne(), q1)

	fmt.Println("q1:")
	for _, s := range qsim.State(q1) {
		fmt.Println(s)
	}

}

Output:

phi:
[0][  0]( 0.4472 0.0000i): 0.2000
[1][  1]( 0.8944 0.0000i): 0.8000
q1:
[0][  0]( 0.4472 0.0000i): 0.2000
[1][  1]( 0.8944 0.0000i): 0.8000

Example (ShorFactoring15) ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
	"github.com/itsubaki/q/math/number"
	"github.com/itsubaki/q/math/rand"
)

func main() {
	// NOTE: Zhengjun Cao, Zhenfu Cao, Lihua Liu. Remarks on Quantum Modular Exponentiation and Some Experimental Demonstrations of Shor’s Algorithm.
	N := 15
	a := 7

	qsim := q.New()
	qsim.Seed = []int{1}
	qsim.Rand = rand.Math

	// initial state
	q0 := qsim.Zero()
	q1 := qsim.Zero()
	q2 := qsim.Zero()

	q3 := qsim.Zero()
	q4 := qsim.Zero()
	q5 := qsim.Zero()
	q6 := qsim.One()

	// superposition
	qsim.H(q0, q1, q2)

	// Controlled-U^(2^0)
	qsim.CNOT(q2, q4)
	qsim.CNOT(q2, q5)

	// Controlled-U^(2^1)
	qsim.CNOT(q3, q5).CCNOT(q1, q5, q3).CNOT(q3, q5)
	qsim.CNOT(q6, q4).CCNOT(q1, q4, q6).CNOT(q6, q4)

	// inverse QFT
	qsim.Swap(q0, q2)
	qsim.InvQFT(q0, q1, q2)

	// measure q0, q1, q2
	m := qsim.Measure(q0, q1, q2).BinaryString()

	// find s/r. 0.010 -> 0.25 -> 1/4, 0.110 -> 0.75 -> 3/4, ...
	s, r, d, ok := number.FindOrder(a, N, fmt.Sprintf("0.%s", m))
	if !ok || number.IsOdd(r) {
		return
	}

	// gcd(a^(r/2)-1, N), gcd(a^(r/2)+1, N)
	p0 := number.GCD(number.Pow(a, r/2)-1, N)
	p1 := number.GCD(number.Pow(a, r/2)+1, N)

	// check non-trivial factor
	if number.IsTrivial(N, p0, p1) {
		return
	}

	fmt.Printf("N=%d, a=%d. p=%v, q=%v. s/r=%d/%d ([0.%v]~%.3f)\n", N, a, p0, p1, s, r, m, d)

}

Output:

N=15, a=7. p=3, q=5. s/r=3/4 ([0.110]~0.750)

Example (ShorFactoring21) ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
	"github.com/itsubaki/q/math/number"
	"github.com/itsubaki/q/math/rand"
)

func main() {
	N := 21
	a := 8

	qsim := q.New()
	qsim.Seed = []int{1}
	qsim.Rand = rand.Math

	r0 := qsim.ZeroWith(4)
	r1 := qsim.ZeroLog2(N)

	qsim.X(r1[len(r1)-1])
	qsim.H(r0...)
	qsim.CModExp2(a, N, r0, r1)
	qsim.InvQFT(r0...)

	m := qsim.Measure(r0...).BinaryString()
	s, r, d, ok := number.FindOrder(a, N, fmt.Sprintf("0.%s", m))
	if !ok || number.IsOdd(r) {
		return
	}

	p0 := number.GCD(number.Pow(a, r/2)-1, N)
	p1 := number.GCD(number.Pow(a, r/2)+1, N)
	if number.IsTrivial(N, p0, p1) {
		return
	}

	fmt.Printf("N=%d, a=%d. p=%v, q=%v. s/r=%d/%d ([0.%v]~%.3f)\n", N, a, p0, p1, s, r, m, d)

}

Output:

N=21, a=8. p=7, q=3. s/r=1/2 ([0.1000]~0.500)

Example (ShorFactoring51) ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
	"github.com/itsubaki/q/math/number"
	"github.com/itsubaki/q/math/rand"
	"github.com/itsubaki/q/quantum/gate"
)

func main() {
	// NOTE: Michael R. Geller, Zhongyuan Zhou. Factoring 51 and 85 with 8 qubits.
	N := 51
	a := 5 // 5, 7, 10, 11, 14, 20, 22, 23, 28, 29, 31, 37, 40, 41, 44, 46

	qsim := q.New()
	qsim.Seed = []int{1}
	qsim.Rand = rand.Math

	q0 := qsim.Zero()
	q1 := qsim.Zero()
	q2 := qsim.Zero()
	q3 := qsim.Zero()

	q4 := qsim.Zero()
	q5 := qsim.Zero()
	q6 := qsim.Zero()
	q7 := qsim.Zero()

	qsim.H(q0, q1, q2, q3)

	qsim.CNOT(q0, q4)
	qsim.CNOT(q1, q5)
	qsim.CNOT(q2, q6)
	qsim.CNOT(q3, q7)

	// inverse QFT
	qsim.Swap(q0, q1, q2, q3)
	qsim.H(q3)
	qsim.CR(-1*gate.Theta(2), q3, q2)
	qsim.H(q2)
	qsim.CR(-1*gate.Theta(3), q3, q1)
	qsim.CR(-1*gate.Theta(2), q2, q1)
	qsim.H(q1)
	qsim.CR(-1*gate.Theta(4), q3, q0)
	qsim.CR(-1*gate.Theta(3), q2, q0)
	qsim.CR(-1*gate.Theta(2), q1, q0)
	qsim.H(q0)

	m := qsim.Measure(q0, q1, q2, q3).BinaryString()
	s, r, d, ok := number.FindOrder(a, N, fmt.Sprintf("0.%s", m))
	if !ok || number.IsOdd(r) {
		return
	}

	p0 := number.GCD(number.Pow(a, r/2)-1, N)
	p1 := number.GCD(number.Pow(a, r/2)+1, N)
	if number.IsTrivial(N, p0, p1) {
		return
	}

	fmt.Printf("N=%d, a=%d. p=%v, q=%v. s/r=%d/%d ([0.%v]~%.3f)\n", N, a, p0, p1, s, r, m, d)

}

Output:

N=51, a=5. p=3, q=17. s/r=15/16 ([0.1111]~0.938)

Example (ShorFactoring85) ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
	"github.com/itsubaki/q/math/number"
	"github.com/itsubaki/q/math/rand"
	"github.com/itsubaki/q/quantum/gate"
)

func main() {
	// NOTE: Michael R. Geller, Zhongyuan Zhou. Factoring 51 and 85 with 8 qubits.
	N := 85
	a := 14

	qsim := q.New()
	qsim.Seed = []int{1}
	qsim.Rand = rand.Math

	q0 := qsim.Zero()
	q1 := qsim.Zero()
	q2 := qsim.Zero()
	q3 := qsim.Zero()

	q4 := qsim.Zero()
	q5 := qsim.Zero()
	q6 := qsim.Zero()
	q7 := qsim.Zero()

	qsim.H(q0, q1, q2, q3)

	qsim.CNOT(q0, q4)
	qsim.CNOT(q1, q5)
	qsim.CNOT(q2, q6)
	qsim.CNOT(q3, q7)

	// inverse QFT
	qsim.Swap(q0, q1, q2, q3)
	qsim.H(q3)
	qsim.CR(-1*gate.Theta(2), q3, q2).H(q2)
	qsim.CR(-1*gate.Theta(3), q3, q1).CR(-1*gate.Theta(2), q2, q1).H(q1)
	qsim.CR(-1*gate.Theta(4), q3, q0).CR(-1*gate.Theta(3), q2, q0).CR(-1*gate.Theta(2), q1, q0).H(q0)

	m := qsim.Measure(q0, q1, q2, q3).BinaryString()
	s, r, d, ok := number.FindOrder(a, N, fmt.Sprintf("0.%s", m))
	if !ok || number.IsOdd(r) {
		return
	}

	p0 := number.GCD(number.Pow(a, r/2)-1, N)
	p1 := number.GCD(number.Pow(a, r/2)+1, N)
	if number.IsTrivial(N, p0, p1) {
		return
	}

	fmt.Printf("N=%d, a=%d. p=%v, q=%v. s/r=%d/%d ([0.%v]~%.3f)\n", N, a, p0, p1, s, r, m, d)

}

Output:

N=85, a=14. p=5, q=17. s/r=15/16 ([0.1111]~0.938)

Example (Top) ¶

package main

import (
	"fmt"
	"sort"

	"github.com/itsubaki/q"
	"github.com/itsubaki/q/math/rand"
	"github.com/itsubaki/q/quantum/qubit"
)

func main() {
	N := 21
	a := 11

	qsim := q.New()
	qsim.Seed = []int{1}
	qsim.Rand = rand.Math

	r0 := qsim.ZeroWith(4)
	r1 := qsim.ZeroLog2(N)

	qsim.X(r1[len(r1)-1])
	qsim.H(r0...)
	qsim.CModExp2(a, N, r0, r1)
	qsim.IQFT(r0...)
	qsim.M(r1...)

	top := func(n int, s []qubit.State) []qubit.State {
		sort.Slice(s, func(i, j int) bool { return s[i].Probability > s[j].Probability })
		if len(s) < n {
			return s
		}

		return s[:n]
	}

	for _, s := range top(10, qsim.State(r0)) {
		fmt.Println(s)
	}

}

Output:

[1000][  8](-0.4330 0.0000i): 0.1875
[0000][  0]( 0.4330 0.0000i): 0.1875
[1101][ 13](-0.1334 0.3219i): 0.1214
[0101][  5]( 0.1334-0.3219i): 0.1214
[1011][ 11]( 0.1334 0.3219i): 0.1214
[0011][  3](-0.1334-0.3219i): 0.1214
[0100][  4]( 0.0000-0.1443i): 0.0208
[0110][  6](-0.1021 0.1021i): 0.0208
[1010][ 10](-0.1021-0.1021i): 0.0208
[0010][  2]( 0.1021 0.1021i): 0.0208

Constants ¶

This section is empty.

Variables ¶

This section is empty.

Functions ¶

func Index ¶

func Index(qb ...Qubit) []int

Types ¶

type Q ¶

type Q struct {
	Seed []int
	Rand func(seed ...int) float64
	// contains filtered or unexported fields
}

func New ¶

func New() *Q

func (*Q) Amplitude ¶

func (q *Q) Amplitude() []complex128

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	q0 := qsim.Zero()
	q1 := qsim.Zero()

	qsim.H(q0)
	qsim.CNOT(q0, q1)

	for _, a := range qsim.Amplitude() {
		fmt.Println(a)
	}

}

Output:

(0.7071067811865476+0i)
(0+0i)
(0+0i)
(0.7071067811865476+0i)

func (*Q) Apply ¶

func (q *Q) Apply(m matrix.Matrix, qb ...Qubit) *Q

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
	"github.com/itsubaki/q/quantum/gate"
)

func main() {
	qsim := q.New()

	q0 := qsim.Zero()
	q1 := qsim.Zero()
	n := qsim.NumberOfBit()

	qsim.Apply(gate.H(), q0)
	qsim.Apply(gate.CNOT(n, q0.Index(), q1.Index()))

	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[00][  0]( 0.7071 0.0000i): 0.5000
[11][  3]( 0.7071 0.0000i): 0.5000

func (*Q) C ¶

func (q *Q) C(m matrix.Matrix, control, target Qubit) *Q

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
	"github.com/itsubaki/q/quantum/gate"
)

func main() {
	qsim := q.New()

	q0 := qsim.Zero()
	q1 := qsim.Zero()

	qsim.H(q0)
	qsim.C(gate.X(), q0, q1) // qsim.CNOT(q0, q1)

	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[00][  0]( 0.7071 0.0000i): 0.5000
[11][  3]( 0.7071 0.0000i): 0.5000

func (*Q) CCCNOT ¶

func (q *Q) CCCNOT(control0, control1, control2, target Qubit) *Q

func (*Q) CCNOT ¶

func (q *Q) CCNOT(control0, control1, target Qubit) *Q

func (*Q) CCZ ¶

func (q *Q) CCZ(control0, control1, target Qubit) *Q

func (*Q) CModExp2 ¶

func (q *Q) CModExp2(a, N int, control []Qubit, target []Qubit) *Q

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	c := qsim.ZeroWith(3)
	t := qsim.ZeroLog2(15)

	qsim.X(c...)
	qsim.X(t[len(t)-1])
	for _, s := range qsim.State(c, t) {
		fmt.Println(s)
	}

	// qsim.ControlledModExp2(7, 0, 15, c[0], t)
	// qsim.ControlledModExp2(7, 1, 15, c[1], t)
	// qsim.ControlledModExp2(7, 2, 15, c[2], t)
	// equals to
	qsim.CModExp2(7, 15, c, t)
	for _, s := range qsim.State(c, t) {
		fmt.Println(s)
	}

}

Output:

[111 0001][  7   1]( 1.0000 0.0000i): 1.0000
[111 1101][  7  13]( 1.0000 0.0000i): 1.0000

func (*Q) CNOT ¶

func (q *Q) CNOT(control, target Qubit) *Q

func (*Q) CR ¶

func (q *Q) CR(theta float64, control, target Qubit) *Q

func (*Q) CZ ¶

func (q *Q) CZ(control, target Qubit) *Q

func (*Q) Clone ¶

func (q *Q) Clone() *Q

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	clone := qsim.Clone()
	clone.Zero()
	clone.Zero()

	q0 := qsim.Zero()
	q1 := qsim.Zero()
	qsim.X(q0, q1)

	fmt.Println(clone)
	fmt.Println(qsim)
	fmt.Println(qsim.Clone())

}

Output:

[(1+0i) (0+0i) (0+0i) (0+0i)]
[(0+0i) (0+0i) (0+0i) (1+0i)]
[(0+0i) (0+0i) (0+0i) (1+0i)]

func (*Q) Condition ¶

func (q *Q) Condition(condition bool, m matrix.Matrix, qb ...Qubit) *Q

func (*Q) ConditionX ¶

func (q *Q) ConditionX(condition bool, qb ...Qubit) *Q

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	q0 := qsim.Zero()

	qsim.ConditionX(false, q0)
	for _, s := range qsim.State() {
		fmt.Println(s)
	}

	qsim.ConditionX(true, q0)
	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[0][  0]( 1.0000 0.0000i): 1.0000
[1][  1]( 1.0000 0.0000i): 1.0000

func (*Q) ConditionZ ¶

func (q *Q) ConditionZ(condition bool, qb ...Qubit) *Q

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	q0 := qsim.One()

	qsim.ConditionZ(false, q0)
	for _, s := range qsim.State() {
		fmt.Println(s)
	}

	qsim.ConditionZ(true, q0)
	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[1][  1]( 1.0000 0.0000i): 1.0000
[1][  1](-1.0000 0.0000i): 1.0000

func (*Q) Controlled ¶

func (q *Q) Controlled(m matrix.Matrix, control []Qubit, target Qubit) *Q

func (*Q) ControlledModExp2 ¶

func (q *Q) ControlledModExp2(a, j, N int, control Qubit, target []Qubit) *Q

Example (Mod15) ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	c := qsim.Zero()
	t := qsim.ZeroLog2(15)

	qsim.X(c)
	qsim.X(t[len(t)-1])
	for _, s := range qsim.State(c, t) {
		fmt.Println(s)
	}

	// 7^2^0 * 1 mod 15 = 7
	qsim.ControlledModExp2(7, 0, 15, c, t)
	for _, s := range qsim.State(c, t) {
		fmt.Println(s)
	}

	// 7^2^1 * 7 mod 15 = 13
	qsim.ControlledModExp2(7, 1, 15, c, t)
	for _, s := range qsim.State(c, t) {
		fmt.Println(s)
	}

	// 7^2^2 * 13 mod 15 = 13
	qsim.ControlledModExp2(7, 2, 15, c, t)
	for _, s := range qsim.State(c, t) {
		fmt.Println(s)
	}

}

Output:

[1 0001][  1   1]( 1.0000 0.0000i): 1.0000
[1 0111][  1   7]( 1.0000 0.0000i): 1.0000
[1 1101][  1  13]( 1.0000 0.0000i): 1.0000
[1 1101][  1  13]( 1.0000 0.0000i): 1.0000

Example (Mod21) ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	c := qsim.Zero()
	t := qsim.ZeroLog2(21)

	qsim.X(c)
	qsim.X(t[len(t)-1])
	for _, s := range qsim.State(c, t) {
		fmt.Println(s)
	}

	// 2^2^0 * 1 mod 21 = 2
	qsim.ControlledModExp2(2, 0, 21, c, t)
	for _, s := range qsim.State(c, t) {
		fmt.Println(s)
	}

	// 2^2^1 * 2 mod 21 = 8
	qsim.ControlledModExp2(2, 1, 21, c, t)
	for _, s := range qsim.State(c, t) {
		fmt.Println(s)
	}

	// 2^2^2 * 8 mod 21 = 2
	qsim.ControlledModExp2(2, 2, 21, c, t)
	for _, s := range qsim.State(c, t) {
		fmt.Println(s)
	}

	// 2^2^3 * 2 mod 21 = 8
	qsim.ControlledModExp2(2, 3, 21, c, t)
	for _, s := range qsim.State(c, t) {
		fmt.Println(s)
	}

}

Output:

[1 00001][  1   1]( 1.0000 0.0000i): 1.0000
[1 00010][  1   2]( 1.0000 0.0000i): 1.0000
[1 01000][  1   8]( 1.0000 0.0000i): 1.0000
[1 00010][  1   2]( 1.0000 0.0000i): 1.0000
[1 01000][  1   8]( 1.0000 0.0000i): 1.0000

func (*Q) ControlledNot ¶

func (q *Q) ControlledNot(control []Qubit, target Qubit) *Q

func (*Q) ControlledR ¶

func (q *Q) ControlledR(theta float64, control []Qubit, target Qubit) *Q

func (*Q) ControlledZ ¶

func (q *Q) ControlledZ(control []Qubit, target Qubit) *Q

func (*Q) H ¶

func (q *Q) H(qb ...Qubit) *Q

func (*Q) I ¶

func (q *Q) I(qb ...Qubit) *Q

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	q0 := qsim.Zero()
	qsim.I(q0)

	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[0][  0]( 1.0000 0.0000i): 1.0000

func (*Q) IQFT ¶

func (q *Q) IQFT(qb ...Qubit) *Q

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	q0 := qsim.Zero()
	q1 := qsim.One()
	q2 := qsim.Zero()

	qsim.QFT(q0, q1, q2)
	qsim.IQFT(q0, q1, q2)
	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[010][  2]( 1.0000 0.0000i): 1.0000

func (*Q) InvQFT ¶

func (q *Q) InvQFT(qb ...Qubit) *Q

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	q0 := qsim.Zero()
	q1 := qsim.One()
	q2 := qsim.Zero()

	qsim.QFT(q0, q1, q2)
	qsim.InvQFT(q0, q1, q2)
	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[010][  2]( 1.0000 0.0000i): 1.0000

func (*Q) InverseQFT ¶

func (q *Q) InverseQFT(qb ...Qubit) *Q

func (*Q) M ¶

func (q *Q) M(qb ...Qubit) *qubit.Qubit

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
	"github.com/itsubaki/q/math/rand"
)

func main() {
	qsim := q.New()
	qsim.Seed = []int{1}
	qsim.Rand = rand.Math

	q0 := qsim.Zero()
	q1 := qsim.Zero()
	q2 := qsim.Zero()
	qsim.X(q0)

	fmt.Println(qsim.M(q0))
	fmt.Println(qsim.M(q0, q1, q2))
	fmt.Println(qsim.M())

}

Output:

[(0+0i) (1+0i)]
[(0+0i) (0+0i) (0+0i) (0+0i) (1+0i) (0+0i) (0+0i) (0+0i)]
[(0+0i) (0+0i) (0+0i) (0+0i) (1+0i) (0+0i) (0+0i) (0+0i)]

func (*Q) Measure ¶

func (q *Q) Measure(qb ...Qubit) *qubit.Qubit

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
	"github.com/itsubaki/q/math/rand"
)

func main() {
	qsim := q.New()
	qsim.Seed = []int{1}
	qsim.Rand = rand.Math

	q0 := qsim.Zero()
	q1 := qsim.Zero()
	q2 := qsim.Zero()
	qsim.X(q0)

	fmt.Println(qsim.Measure(q0))
	fmt.Println(qsim.Measure(q0, q1, q2))
	fmt.Println(qsim.Measure())

}

Output:

[(0+0i) (1+0i)]
[(0+0i) (0+0i) (0+0i) (0+0i) (1+0i) (0+0i) (0+0i) (0+0i)]
[(0+0i) (0+0i) (0+0i) (0+0i) (1+0i) (0+0i) (0+0i) (0+0i)]

func (*Q) New ¶

func (q *Q) New(v ...complex128) Qubit

func (*Q) NewOf ¶

func (q *Q) NewOf(binary string) []Qubit

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	qb := qsim.NewOf("0101")
	m0 := qsim.Measure(qb[0]) // 0
	m1 := qsim.Measure(qb[1]) // 1
	m2 := qsim.Measure(qb[2]) // 0
	m3 := qsim.Measure(qb[3]) // 1

	fmt.Println(m0)
	fmt.Println(m1)
	fmt.Println(m2)
	fmt.Println(m3)

}

Output:

[(1+0i) (0+0i)]
[(0+0i) (1+0i)]
[(1+0i) (0+0i)]
[(0+0i) (1+0i)]

func (*Q) NumberOfBit ¶

func (q *Q) NumberOfBit() int

func (*Q) One ¶

func (q *Q) One() Qubit

func (*Q) OneWith ¶

func (q *Q) OneWith(n int) []Qubit

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	r := qsim.OneWith(2)
	qsim.H(r...)

	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[00][  0]( 0.5000 0.0000i): 0.2500
[01][  1](-0.5000 0.0000i): 0.2500
[10][  2](-0.5000 0.0000i): 0.2500
[11][  3]( 0.5000 0.0000i): 0.2500

func (*Q) Probability ¶

func (q *Q) Probability() []float64

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	q0 := qsim.Zero()
	q1 := qsim.Zero()

	qsim.H(q0)
	qsim.CNOT(q0, q1)

	for _, p := range qsim.Probability() {
		fmt.Printf("%.4f\n", p)
	}

}

Output:

0.5000
0.0000
0.0000
0.5000

func (*Q) QFT ¶

func (q *Q) QFT(qb ...Qubit) *Q

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	q0 := qsim.Zero()
	q1 := qsim.One()
	q2 := qsim.Zero()

	qsim.QFT(q0, q1, q2)
	qsim.Swap(q0, q2)

	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[000][  0]( 0.3536 0.0000i): 0.1250
[001][  1]( 0.0000 0.3536i): 0.1250
[010][  2](-0.3536 0.0000i): 0.1250
[011][  3]( 0.0000-0.3536i): 0.1250
[100][  4]( 0.3536 0.0000i): 0.1250
[101][  5]( 0.0000 0.3536i): 0.1250
[110][  6](-0.3536 0.0000i): 0.1250
[111][  7]( 0.0000-0.3536i): 0.1250

func (*Q) R ¶

func (q *Q) R(theta float64, qb ...Qubit) *Q

Example ¶

package main

import (
	"fmt"
	"math"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	q0 := qsim.One()
	qsim.R(2*math.Pi/4, q0)

	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[1][  1]( 0.0000 1.0000i): 1.0000

func (*Q) RX ¶

func (q *Q) RX(theta float64, qb ...Qubit) *Q

Example ¶

package main

import (
	"fmt"
	"math"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	q0 := qsim.Zero()
	qsim.RX(math.Pi, q0)

	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[1][  1]( 0.0000-1.0000i): 1.0000

func (*Q) RY ¶

func (q *Q) RY(theta float64, qb ...Qubit) *Q

Example ¶

package main

import (
	"fmt"
	"math"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	q0 := qsim.Zero()
	qsim.RY(math.Pi, q0)

	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[1][  1]( 1.0000 0.0000i): 1.0000

func (*Q) RZ ¶

func (q *Q) RZ(theta float64, qb ...Qubit) *Q

Example ¶

package main

import (
	"fmt"
	"math"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	q0 := qsim.Zero()
	qsim.RZ(math.Pi, q0)

	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[0][  0]( 0.0000-1.0000i): 1.0000

func (*Q) Raw ¶

func (q *Q) Raw() *qubit.Qubit

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()
	qsim.Zero()

	qb := qsim.Raw()

	d := qb.TraceDistance(qb)
	fmt.Println(d)

	f := qb.Fidelity(qb)
	fmt.Println(f)

}

Output:

0
1

func (*Q) Reset ¶

func (q *Q) Reset(qb ...Qubit)

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	r := qsim.ZeroWith(2)
	qsim.Reset(r...)

	for _, s := range qsim.State() {
		fmt.Println(s)
	}

	qsim.X(r...)
	qsim.Reset(r...)

	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[00][  0]( 1.0000 0.0000i): 1.0000
[00][  0]( 1.0000 0.0000i): 1.0000

func (*Q) S ¶

func (q *Q) S(qb ...Qubit) *Q

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	q0 := qsim.One()
	qsim.S(q0)

	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[1][  1]( 0.0000 1.0000i): 1.0000

func (*Q) State ¶

func (q *Q) State(reg ...any) []qubit.State

func (*Q) String ¶

func (q *Q) String() string

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	q0 := qsim.Zero()
	q1 := qsim.One()
	qsim.X(q0, q1)

	fmt.Println(qsim)

}

Output:

[(0+0i) (0+0i) (1+0i) (0+0i)]

func (*Q) Swap ¶

func (q *Q) Swap(qb ...Qubit) *Q

func (*Q) T ¶

func (q *Q) T(qb ...Qubit) *Q

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	q0 := qsim.One()
	qsim.T(q0)

	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[1][  1]( 0.7071 0.7071i): 1.0000

func (*Q) Toffoli ¶

func (q *Q) Toffoli(control0, control1, target Qubit) *Q

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	q0 := qsim.One()
	q1 := qsim.One()
	q2 := qsim.Zero()
	qsim.Toffoli(q0, q1, q2)

	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[111][  7]( 1.0000 0.0000i): 1.0000

func (*Q) U ¶

func (q *Q) U(theta, phi, lambda float64, qb ...Qubit) *Q

Example ¶

package main

import (
	"fmt"
	"math"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	q0 := qsim.Zero()
	qsim.U(math.Pi, 0, math.Pi, q0)

	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[1][  1]( 1.0000 0.0000i): 1.0000

func (*Q) X ¶

func (q *Q) X(qb ...Qubit) *Q

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	q0 := qsim.Zero()
	qsim.X(q0)

	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[1][  1]( 1.0000 0.0000i): 1.0000

func (*Q) Y ¶

func (q *Q) Y(qb ...Qubit) *Q

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	q0 := qsim.One()
	qsim.Y(q0)

	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[0][  0]( 0.0000-1.0000i): 1.0000

func (*Q) Z ¶

func (q *Q) Z(qb ...Qubit) *Q

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	q0 := qsim.One()
	qsim.Z(q0)

	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[1][  1](-1.0000 0.0000i): 1.0000

func (*Q) Zero ¶

func (q *Q) Zero() Qubit

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	q0 := qsim.Zero()
	q1 := qsim.Zero()
	qsim.H(q0, q1)

	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[00][  0]( 0.5000 0.0000i): 0.2500
[01][  1]( 0.5000 0.0000i): 0.2500
[10][  2]( 0.5000 0.0000i): 0.2500
[11][  3]( 0.5000 0.0000i): 0.2500

func (*Q) ZeroLog2 ¶

func (q *Q) ZeroLog2(N int) []Qubit

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	r := qsim.ZeroLog2(3)
	qsim.H(r...)

	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[00][  0]( 0.5000 0.0000i): 0.2500
[01][  1]( 0.5000 0.0000i): 0.2500
[10][  2]( 0.5000 0.0000i): 0.2500
[11][  3]( 0.5000 0.0000i): 0.2500

func (*Q) ZeroWith ¶

func (q *Q) ZeroWith(n int) []Qubit

Example ¶

package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

func main() {
	qsim := q.New()

	r := qsim.ZeroWith(2)
	qsim.H(r...)

	for _, s := range qsim.State() {
		fmt.Println(s)
	}

}

Output:

[00][  0]( 0.5000 0.0000i): 0.2500
[01][  1]( 0.5000 0.0000i): 0.2500
[10][  2]( 0.5000 0.0000i): 0.2500
[11][  3]( 0.5000 0.0000i): 0.2500

type Qubit ¶

type Qubit int

func (Qubit) Index ¶

func (q Qubit) Index() int

Source Files ¶

View all Source files

q.go

Directories ¶

Path	Synopsis
cmd
shor
math
epsilon
matrix
number
rand
vector
quantum
density
gate
qubit

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README ¶

q

Example

Bell state

Quantum teleportation

Error correction

Grover's search algorithm

Shor's factoring algorithm

Reference

Documentation ¶

Overview ¶

Index ¶

Examples ¶

Constants ¶

Variables ¶

Functions ¶

func Index ¶

Types ¶

type Q ¶

func New ¶

func (*Q) Amplitude ¶

func (*Q) Apply ¶

func (*Q) C ¶

func (*Q) CCCNOT ¶

func (*Q) CCNOT ¶

func (*Q) CCZ ¶

func (*Q) CModExp2 ¶

func (*Q) CNOT ¶

func (*Q) CR ¶

func (*Q) CZ ¶

func (*Q) Clone ¶

func (*Q) Condition ¶

func (*Q) ConditionX ¶

func (*Q) ConditionZ ¶

func (*Q) Controlled ¶

func (*Q) ControlledModExp2 ¶

func (*Q) ControlledNot ¶

func (*Q) ControlledR ¶

func (*Q) ControlledZ ¶

func (*Q) H ¶

func (*Q) I ¶

func (*Q) IQFT ¶

func (*Q) InvQFT ¶

func (*Q) InverseQFT ¶

func (*Q) M ¶

func (*Q) Measure ¶

func (*Q) New ¶

func (*Q) NewOf ¶

func (*Q) NumberOfBit ¶

func (*Q) One ¶

func (*Q) OneWith ¶

func (*Q) Probability ¶

func (*Q) QFT ¶

func (*Q) R ¶

func (*Q) RX ¶

func (*Q) RY ¶

func (*Q) RZ ¶

func (*Q) Raw ¶

func (*Q) Reset ¶

func (*Q) S ¶

func (*Q) State ¶

func (*Q) String ¶

func (*Q) Swap ¶

func (*Q) T ¶

func (*Q) Toffoli ¶

func (*Q) U ¶

func (*Q) X ¶

func (*Q) Y ¶

func (*Q) Z ¶

func (*Q) Zero ¶

func (*Q) ZeroLog2 ¶

func (*Q) ZeroWith ¶

type Qubit ¶

func (Qubit) Index ¶

Source Files ¶

Directories ¶