q

package module
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 Go to latest Published: Sep 9, 2023 License: MIT Imports: 5 Imported by: 13

README

q

PkgGoDev Go Report Card tests codecov

  • quantum computation simulator
  • pure Go 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.Println(m0.IsZero() == m1.IsZero()) // always 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.CondX(mx.IsOne(), q1)
qsim.CondZ(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.CondX(m3.IsOne() && m4.IsZero(), q0)
qsim.CondX(m3.IsOne() && m4.IsOne(), q1)
qsim.CondX(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)

References

  • 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"

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

func main() {
	qsim := q.New()
	qsim.Rand = rnd.Const()

	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 (DeutschJozsa) 
package main

import (
	"fmt"
	"math/rand"
	"time"

	"github.com/itsubaki/q"
)

func main() {
	type FuncType int
	const (
		Constant FuncType = iota
		Balanced
	)

	oracle := func(qsim *q.Q, q0, q1 q.Qubit) FuncType {
		r := rand.New(rand.NewSource(time.Now().UnixNano()))
		if r.Float64() > 0.5 {
			return Constant
		}

		qsim.CNOT(q0, q1)
		return Balanced
	}

	qsim := q.New()
	q0 := qsim.Zero()
	q1 := qsim.One()

	qsim.H(q0, q1)
	ans := oracle(qsim, q0, q1)
	qsim.H(q0)
	m0 := qsim.M(q0)

	if m0.IsZero() && ans == Constant {
		fmt.Println("Correct!")
	}

	if m0.IsOne() && ans == Balanced {
		fmt.Println("Correct!")
	}

}

Output:

Correct!
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.CondX(m3.IsOne() && m4.IsZero(), q0)
	qsim.CondX(m3.IsOne() && m4.IsOne(), q1)
	qsim.CondX(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"
)

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

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

	qsim.H(q0)
	qsim.CR(q.Theta(2), q1, q0)
	qsim.CR(q.Theta(3), q2, q0)
	qsim.H(q1)
	qsim.CR(q.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.CondX(mx.IsOne(), q1)
	qsim.CondZ(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"

	rnd "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.Rand = rnd.Const()

	// 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"

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

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

	qsim := q.New()
	qsim.Rand = rnd.Const()

	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"

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

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
	rng := rnd.Const()

	for {
		qsim := q.New()
		qsim.Rand = rng

		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*q.Theta(2), q3, q2)
		qsim.H(q2)
		qsim.CR(-1*q.Theta(3), q3, q1)
		qsim.CR(-1*q.Theta(2), q2, q1)
		qsim.H(q1)
		qsim.CR(-1*q.Theta(4), q3, q0)
		qsim.CR(-1*q.Theta(3), q2, q0)
		qsim.CR(-1*q.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) {
			continue
		}

		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
		}

		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)
		break
	}

}

Output:

N=51, a=5. p=3, q=17. s/r=3/16 ([0.0011]~0.188)
Example (ShorFactoring85) 
package main

import (
	"fmt"

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

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

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

	for {
		qsim := q.New()
		qsim.Rand = rng

		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*q.Theta(2), q3, q2).H(q2)
		qsim.CR(-1*q.Theta(3), q3, q1).CR(-1*q.Theta(2), q2, q1).H(q1)
		qsim.CR(-1*q.Theta(4), q3, q0).CR(-1*q.Theta(3), q2, q0).CR(-1*q.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) {
			continue
		}

		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
		}

		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)
		break
	}

}

Output:

N=85, a=14. p=5, q=17. s/r=3/16 ([0.0011]~0.188)
Example (SuperDenseCoding) 
package main

import (
	"fmt"

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

func main() {
	sdc := func(g matrix.Matrix) string {
		qsim := q.New()

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

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

		// encode
		qsim.Apply(g, q0)

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

		// measure
		return qsim.M(q0, q1).BinaryString()
	}

	fmt.Printf("I : %v\n", sdc(gate.I()))
	fmt.Printf("X : %v\n", sdc(gate.X()))
	fmt.Printf("Z : %v\n", sdc(gate.Z()))
	fmt.Printf("ZX: %v\n", sdc(gate.Z().Apply(gate.X())))

}

Output:

I : 00
X : 01
Z : 10
ZX: 11
Example (Top) 
package main

import (
	"fmt"
	"sort"

	"github.com/itsubaki/q"

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

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

	qsim := q.New()
	qsim.Rand = rnd.Const()

	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(s []qubit.State, n int) []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(qsim.State(r0), 10) {
		fmt.Println(s)
	}

}

Output:

[1000][  8](-0.4330 0.0000i): 0.1875
[0000][  0]( 0.4330 0.0000i): 0.1875
[1011][ 11]( 0.1334-0.3219i): 0.1214
[0011][  3](-0.1334 0.3219i): 0.1214
[1101][ 13](-0.1334-0.3219i): 0.1214
[0101][  5]( 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

Index

Examples

Constants

This section is empty.

Variables

This section is empty.

Functions

func Index 

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

Index returns the index list of qubits.

func Theta added in v0.0.3 

func Theta(k int) float64

Theta returns 2 * pi / 2**k

Types

type Q 

type Q struct {
	Rand func() float64
	// contains filtered or unexported fields
}

Q is a quantum computation simulator.

func New 

func New() *Q

New returns a new quantum computation simulator.

func (*Q) Amplitude 

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

Amplitude returns the amplitude of qubits.

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

Apply applies matrix to qubits.

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

CCCNOT applies CCCNOT gate.

func (*Q) CCNOT 

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

CCNOT applies CCNOT gate.

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

CModExp2 applies Controlled-ModExp2 gate.

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

CNOT applies CNOT gate.

func (*Q) CR 

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

CR applies Controlled-R gate.

func (*Q) CZ 

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

func (*Q) Clone 

func (q *Q) Clone() *Q

Clone returns a clone of a quantum computation simulator.

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) Cond added in v0.0.3 

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

Cond applies m if condition is true.

func (*Q) CondX added in v0.0.3 

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

CondX applies X gate if condition is true.

Example 
package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

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

	q0 := qsim.Zero()

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

	qsim.CondX(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) CondZ added in v0.0.3 

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

CondZ applies Z gate if condition is true.

Example 
package main

import (
	"fmt"

	"github.com/itsubaki/q"
)

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

	q0 := qsim.One()

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

	qsim.CondZ(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

ControlledModExp2 applies Controlled-ModExp2 gate.

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

ControlledNot applies CNOT gate.

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

ControlledZ applies Controlled-Z gate.

func (*Q) H 

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

H applies H gate.

func (*Q) I 

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

I applies I gate.

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

IQFT applies Inverse Quantum Fourier Transform.

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

InvQFT applies Inverse Quantum Fourier Transform.

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

InverseQFT applies Inverse Quantum Fourier Transform.

func (*Q) M 

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

M returns the measured state of qubits.

Example 
package main

import (
	"fmt"

	"github.com/itsubaki/q"

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

func main() {
	qsim := q.New()
	qsim.Rand = rnd.Const()

	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

Measure returns the measured state of qubits.

Example 
package main

import (
	"fmt"

	"github.com/itsubaki/q"

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

func main() {
	qsim := q.New()
	qsim.Rand = rnd.Const()

	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

New returns a new qubit.

func (*Q) NewOf 

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

NewOf returns a new qubit from binary string.

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

NumberOfBit returns the number of qubits.

func (*Q) One 

func (q *Q) One() Qubit

One returns a qubit in the one state.

func (*Q) OneWith 

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

One returns a qubit in the one state with n qubits.

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

Probability returns the probability of qubits.

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

QFT applies Quantum Fourier Transform.

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

R applies R gate with theta.

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

RX applies RX gate with theta.

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

RY applies RY gate with theta.

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

RZ applies RZ gate with theta.

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

Raw returns the internal 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)

Reset sets qubits to the zero state.

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

S applies S gate.

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

State returns the state of qubits.

func (*Q) String 

func (q *Q) String() string

String returns the string representation of a quantum computation simulator.

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

Swap applies Swap gate.

func (*Q) T 

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

T applies T gate.

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

Toffoli applies Toffoli gate.

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

U applies U gate.

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

X applies X gate.

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

Y applies Y gate.

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

Z applies Z gate.

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

Zero returns a qubit in the zero state.

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

ZeroLog2 returns a qubit in the zero state with log2(N) qubits.

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

ZeroWith returns a qubit in the zero state with n qubits.

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

Qubit is a quantum bit.

func (Qubit) Index 

func (q Qubit) Index() int

Index returns the index of qubit.

Source Files

View all Source files

Directories

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

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