qubit

package
v0.0.4 Latest Latest
Warning

This package is not in the latest version of its module.

 Go to latest Published: Jun 5, 2024 License: MIT Imports: 10 Imported by: 1

Documentation

Overview

Example (BellState) 
package main

import (
	"fmt"

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

func main() {
	q := qubit.Zero(2).Apply(
		gate.H().TensorProduct(gate.I()),
		gate.CNOT(2, 0, 1),
	)

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

}

Output:

[00][  0]( 0.7071 0.0000i): 0.5000
[11][  3]( 0.7071 0.0000i): 0.5000
Example (ErrorCorrectionBitFlip) 
package main

import (
	"fmt"

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

func main() {
	phi := qubit.New(1, 2)

	// encoding
	phi.TensorProduct(qubit.Zero(2))
	phi.Apply(
		gate.CNOT(3, 0, 1),
		gate.CNOT(3, 0, 2),
	)

	// error: first qubit is flipped
	phi.Apply(matrix.TensorProduct(gate.X(), gate.I(2)))

	// add ancilla qubit
	phi.TensorProduct(qubit.Zero(2))

	// z1z2
	phi.Apply(
		gate.CNOT(5, 0, 3),
		gate.CNOT(5, 1, 3),
	)

	// z2z3
	phi.Apply(
		gate.CNOT(5, 1, 4),
		gate.CNOT(5, 2, 4),
	)

	// measure
	m3 := phi.Measure(3)
	m4 := phi.Measure(4)

	// recover
	if m3.IsOne() && m4.IsZero() {
		phi.Apply(matrix.TensorProduct(gate.X(), gate.I(4)))
	}

	if m3.IsOne() && m4.IsOne() {
		phi.Apply(matrix.TensorProduct(gate.I(), gate.X(), gate.I(3)))
	}

	if m3.IsZero() && m4.IsOne() {
		phi.Apply(matrix.TensorProduct(gate.I(2), gate.X(), gate.I(2)))
	}

	// decoding
	phi.Apply(
		gate.CNOT(5, 0, 2),
		gate.CNOT(5, 0, 1),
	)

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

}

Output:

[00010][  2]( 0.4472 0.0000i): 0.2000
[10010][ 18]( 0.8944 0.0000i): 0.8000
Example (ErrorCorrectionPhaseFlip) 
package main

import (
	"fmt"

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

func main() {
	phi := qubit.New(1, 2)

	// encoding
	phi.TensorProduct(qubit.Zero(2))
	phi.Apply(
		gate.CNOT(3, 0, 1),
		gate.CNOT(3, 0, 2),
		gate.H(3),
	)

	// error: first qubit is flipped
	phi.Apply(matrix.TensorProduct(gate.Z(), gate.I(2)))

	// H
	phi.Apply(gate.H(3))

	// add ancilla qubit
	phi.TensorProduct(qubit.Zero(2))

	// x1x2
	phi.Apply(
		gate.CNOT(5, 0, 3),
		gate.CNOT(5, 1, 3),
	)

	// x2x3
	phi.Apply(
		gate.CNOT(5, 1, 4),
		gate.CNOT(5, 2, 4),
	)

	// H
	phi.Apply(matrix.TensorProduct(gate.H(3), gate.I(2)))

	// measure
	m3 := phi.Measure(3)
	m4 := phi.Measure(4)

	// recover
	if m3.IsOne() && m4.IsZero() {
		phi.Apply(matrix.TensorProduct(gate.Z(), gate.I(4)))
	}

	if m3.IsOne() && m4.IsOne() {
		phi.Apply(matrix.TensorProduct(gate.I(), gate.Z(), gate.I(3)))
	}

	if m3.IsZero() && m4.IsOne() {
		phi.Apply(matrix.TensorProduct(gate.I(2), gate.Z(), gate.I(2)))
	}

	// decoding
	phi.Apply(
		matrix.TensorProduct(gate.H(3), gate.I(2)),
		gate.CNOT(5, 0, 2),
		gate.CNOT(5, 0, 1),
	)

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

}

Output:

[00010][  2]( 0.4472 0.0000i): 0.2000
[10010][ 18]( 0.8944 0.0000i): 0.8000
Example (Grover2qubit) 
package main

import (
	"fmt"

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

func main() {
	oracle := gate.CZ(2, 0, 1)
	amp := matrix.Apply(
		gate.H(2),
		gate.X(2),
		gate.CZ(2, 0, 1),
		gate.X(2),
		gate.H(2),
	)

	q := qubit.Zero(2).Apply(
		gate.H(2),
		oracle,
		amp,
	)

	q.Measure(0)
	q.Measure(1)

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

}

Output:

[11][  3](-1.0000 0.0000i): 1.0000
Example (Grover3qubit) 
package main

import (
	"fmt"

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

func main() {
	oracle := matrix.Apply(
		matrix.TensorProduct(gate.X(), gate.I(3)),
		gate.ControlledNot(4, []int{0, 1, 2}, 3),
		matrix.TensorProduct(gate.X(), gate.I(3)),
	)

	amp := matrix.Apply(
		matrix.TensorProduct(gate.H(3), gate.H()),
		matrix.TensorProduct(gate.X(3), gate.I()),
		matrix.TensorProduct(gate.ControlledZ(3, []int{0, 1}, 2), gate.I()),
		matrix.TensorProduct(gate.X(3), gate.I()),
		matrix.TensorProduct(gate.H(3), gate.I()),
	)

	q := qubit.TensorProduct(
		qubit.Zero(3),
		qubit.One(),
	).Apply(
		gate.H(4),
		oracle,
		amp,
	)

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

}

Output:

[0001][  1](-0.1768 0.0000i): 0.0313
[0011][  3](-0.1768 0.0000i): 0.0313
[0101][  5](-0.1768 0.0000i): 0.0313
[0111][  7](-0.8839 0.0000i): 0.7813
[1001][  9](-0.1768 0.0000i): 0.0313
[1011][ 11](-0.1768 0.0000i): 0.0313
[1101][ 13](-0.1768 0.0000i): 0.0313
[1111][ 15](-0.1768 0.0000i): 0.0313
Example (POVM) 
package main

import (
	"fmt"
	"math"

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

func main() {
	E1 := gate.New(
		[]complex128{0, 0},
		[]complex128{0, 1},
	).Mul(complex(math.Sqrt(2)/(1.0+math.Sqrt(2)), 0))

	E2 := gate.New(
		[]complex128{1, -1},
		[]complex128{-1, 1},
	).Mul(complex(0.5, 0)).
		Mul(complex(math.Sqrt(2)/(1.0+math.Sqrt(2)), 0))

	E3 := gate.I().Sub(E1).Sub(E2)

	add := E1.Add(E2).Add(E3)
	fmt.Println(add.Equals(gate.I()))

	{
		q0 := qubit.Zero()
		q1 := qubit.Zero()
		q2 := qubit.Zero()

		fmt.Println("zero:")
		fmt.Println(q0.Apply(E1).InnerProduct(q0))
		fmt.Println(q1.Apply(E2).InnerProduct(q1))
		fmt.Println(q2.Apply(E3).InnerProduct(q2))
	}

	{
		q0 := qubit.Zero().Apply(gate.H())
		q1 := qubit.Zero().Apply(gate.H())
		q2 := qubit.Zero().Apply(gate.H())

		fmt.Println("H(zero):")
		fmt.Println(q0.Apply(E1).InnerProduct(q0))
		fmt.Println(q1.Apply(E2).InnerProduct(q1))
		fmt.Println(q2.Apply(E3).InnerProduct(q2))
	}

}

Output:

true
zero:
(0+0i)
(0.17157287525381+0i)
(0.5857864376269049+0i)
H(zero):
(0.17157287525381+0i)
(0+0i)
(0.5857864376269051+0i)
Example (QuantumTeleportation) 
package main

import (
	"fmt"

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

func main() {
	phi := qubit.New(1, 2)
	phi.Rand = rand.Const()

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

	bell := qubit.Zero(2).Apply(
		matrix.TensorProduct(gate.H(), gate.I()),
		gate.CNOT(2, 0, 1),
	)
	phi.TensorProduct(bell)

	phi.Apply(
		gate.CNOT(3, 0, 1),
		matrix.TensorProduct(gate.H(), gate.I(2)),
	)

	mz := phi.Measure(0)
	mx := phi.Measure(1)

	if mx.IsOne() {
		phi.Apply(matrix.TensorProduct(gate.I(2), gate.X()))
	}

	if mz.IsOne() {
		phi.Apply(matrix.TensorProduct(gate.I(2), gate.Z()))
	}

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

}

Output:

before:
[0][  0]( 0.4472 0.0000i): 0.2000
[1][  1]( 0.8944 0.0000i): 0.8000
after:
[110][  6]( 0.4472 0.0000i): 0.2000
[111][  7]( 0.8944 0.0000i): 0.8000
Example (QuantumTeleportation2) 
package main

import (
	"fmt"

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

func main() {
	phi := qubit.New(1, 2)
	phi.Rand = rand.Const()

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

	bell := qubit.Zero(2).Apply(
		matrix.TensorProduct(gate.H(), gate.I()),
		gate.CNOT(2, 0, 1),
	)
	phi.TensorProduct(bell)

	phi.Apply(
		gate.CNOT(3, 0, 1),
		matrix.TensorProduct(gate.H(), gate.I(2)),
		gate.CNOT(3, 1, 2),
		gate.CZ(3, 0, 2),
	)

	phi.Measure(0)
	phi.Measure(1)

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

}

Output:

before:
[0][  0]( 0.4472 0.0000i): 0.2000
[1][  1]( 0.8944 0.0000i): 0.8000
after:
[110][  6]( 0.4472 0.0000i): 0.2000
[111][  7]( 0.8944 0.0000i): 0.8000

Index

Examples

Constants

This section is empty.

Variables

This section is empty.

Functions

func Equals 

func Equals(s, v []State, eps ...float64) bool

Equals returns true if s equals v. If eps is not given, epsilon.E13 is used.

Types

type Qubit 

type Qubit struct {
	Rand func() float64 // Random number generator
	// contains filtered or unexported fields
}

Qubit is a qubit.

func New 

func New(z ...complex128) *Qubit

New returns a new qubit. z is a vector of complex128.

func One 

func One(n ...int) *Qubit

One returns a qubit in the one state. n is the number of qubits.

func TensorProduct 

func TensorProduct(qb ...*Qubit) *Qubit

func Zero 

func Zero(n ...int) *Qubit

Zero returns a qubit in the zero state. n is the number of qubits.

Example 
package main

import (
	"fmt"

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

func main() {
	z := qubit.Zero()
	fmt.Print("z : ")
	for _, s := range z.State() {
		fmt.Println(s)
	}

	z2 := qubit.Zero(2)
	fmt.Print("z2:")
	for _, s := range z2.State() {
		fmt.Println(s)
	}

}

Output:

z : [0][  0]( 1.0000 0.0000i): 1.0000
z2:[00][  0]( 1.0000 0.0000i): 1.0000

func (*Qubit) Amplitude 

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

Amplitude returns the amplitude of q.

func (*Qubit) Apply 

func (q *Qubit) Apply(m ...matrix.Matrix) *Qubit

Apply returns a qubit that is applied m.

func (*Qubit) BinaryString 

func (q *Qubit) BinaryString() string

BinaryString returns the binary string representation of q.

func (*Qubit) Clone 

func (q *Qubit) Clone() *Qubit

Clone returns a clone of q.

func (*Qubit) Dimension 

func (q *Qubit) Dimension() int

Dimension returns the dimension of q.

func (*Qubit) Equals 

func (q *Qubit) Equals(qb *Qubit, eps ...float64) bool

Equals returns true if q and qb are equal.

func (*Qubit) Fidelity 

func (q *Qubit) Fidelity(qb *Qubit) float64

Fidelity returns the fidelity of q and qb.

func (*Qubit) InnerProduct 

func (q *Qubit) InnerProduct(qb *Qubit) complex128

InnerProduct returns the inner product of q and qb.

func (*Qubit) Int 

func (q *Qubit) Int() int64

Int returns the integer representation of q.

func (*Qubit) IsOne 

func (q *Qubit) IsOne(eps ...float64) bool

IsOne returns true if q is one qubit.

func (*Qubit) IsZero 

func (q *Qubit) IsZero(eps ...float64) bool

IsZero returns true if q is zero qubit.

func (*Qubit) Measure 

func (q *Qubit) Measure(index int) *Qubit

Measure returns a measured qubit.

func (*Qubit) Normalize 

func (q *Qubit) Normalize() *Qubit

Normalize returns a normalized qubit.

func (*Qubit) NumberOfBit 

func (q *Qubit) NumberOfBit() int

NumberOfBit returns the number of qubits.

func (*Qubit) OuterProduct 

func (q *Qubit) OuterProduct(qb *Qubit) matrix.Matrix

OuterProduct returns the outer product of q and qb.

Example 
package main

import (
	"fmt"

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

func main() {
	v := qubit.New(1, 0)
	op := v.OuterProduct(v)
	fmt.Println(op)

}

Output:

[[(1+0i) (0+0i)] [(0+0i) (0+0i)]]
Example (OperatorSum) 
package main

import (
	"fmt"

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

func main() {
	v := qubit.New(1, 0)
	q := v.OuterProduct(v)
	e := gate.X().Dagger().Apply(q.Apply(gate.X()))

	fmt.Println(e)

}

Output:

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

func (*Qubit) Probability 

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

Probability returns the probability of q.

func (*Qubit) State 

func (q *Qubit) State(index ...[]int) []State

State returns the state of q with index.

Example 
package main

import (
	"fmt"

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

func main() {
	v := qubit.Zero(4).Apply(gate.H(4))

	for _, s := range v.State([]int{0, 1, 2, 3}) {
		fmt.Println(s)
	}

}

Output:

[0000][  0]( 0.2500 0.0000i): 0.0625
[0001][  1]( 0.2500 0.0000i): 0.0625
[0010][  2]( 0.2500 0.0000i): 0.0625
[0011][  3]( 0.2500 0.0000i): 0.0625
[0100][  4]( 0.2500 0.0000i): 0.0625
[0101][  5]( 0.2500 0.0000i): 0.0625
[0110][  6]( 0.2500 0.0000i): 0.0625
[0111][  7]( 0.2500 0.0000i): 0.0625
[1000][  8]( 0.2500 0.0000i): 0.0625
[1001][  9]( 0.2500 0.0000i): 0.0625
[1010][ 10]( 0.2500 0.0000i): 0.0625
[1011][ 11]( 0.2500 0.0000i): 0.0625
[1100][ 12]( 0.2500 0.0000i): 0.0625
[1101][ 13]( 0.2500 0.0000i): 0.0625
[1110][ 14]( 0.2500 0.0000i): 0.0625
[1111][ 15]( 0.2500 0.0000i): 0.0625
Example (Order) 
package main

import (
	"fmt"

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

func main() {
	v := qubit.Zero(4).Apply(gate.H(4))

	for _, s := range v.State([]int{0}, []int{1, 2, 3}) {
		fmt.Println(s)
	}

	for _, s := range v.State([]int{1, 2, 3}, []int{0}) {
		fmt.Println(s)
	}

}

Output:

[0 000][  0   0]( 0.2500 0.0000i): 0.0625
[0 001][  0   1]( 0.2500 0.0000i): 0.0625
[0 010][  0   2]( 0.2500 0.0000i): 0.0625
[0 011][  0   3]( 0.2500 0.0000i): 0.0625
[0 100][  0   4]( 0.2500 0.0000i): 0.0625
[0 101][  0   5]( 0.2500 0.0000i): 0.0625
[0 110][  0   6]( 0.2500 0.0000i): 0.0625
[0 111][  0   7]( 0.2500 0.0000i): 0.0625
[1 000][  1   0]( 0.2500 0.0000i): 0.0625
[1 001][  1   1]( 0.2500 0.0000i): 0.0625
[1 010][  1   2]( 0.2500 0.0000i): 0.0625
[1 011][  1   3]( 0.2500 0.0000i): 0.0625
[1 100][  1   4]( 0.2500 0.0000i): 0.0625
[1 101][  1   5]( 0.2500 0.0000i): 0.0625
[1 110][  1   6]( 0.2500 0.0000i): 0.0625
[1 111][  1   7]( 0.2500 0.0000i): 0.0625
[000 0][  0   0]( 0.2500 0.0000i): 0.0625
[001 0][  1   0]( 0.2500 0.0000i): 0.0625
[010 0][  2   0]( 0.2500 0.0000i): 0.0625
[011 0][  3   0]( 0.2500 0.0000i): 0.0625
[100 0][  4   0]( 0.2500 0.0000i): 0.0625
[101 0][  5   0]( 0.2500 0.0000i): 0.0625
[110 0][  6   0]( 0.2500 0.0000i): 0.0625
[111 0][  7   0]( 0.2500 0.0000i): 0.0625
[000 1][  0   1]( 0.2500 0.0000i): 0.0625
[001 1][  1   1]( 0.2500 0.0000i): 0.0625
[010 1][  2   1]( 0.2500 0.0000i): 0.0625
[011 1][  3   1]( 0.2500 0.0000i): 0.0625
[100 1][  4   1]( 0.2500 0.0000i): 0.0625
[101 1][  5   1]( 0.2500 0.0000i): 0.0625
[110 1][  6   1]( 0.2500 0.0000i): 0.0625
[111 1][  7   1]( 0.2500 0.0000i): 0.0625

func (*Qubit) String 

func (q *Qubit) String() string

String returns the string representation of q.

func (*Qubit) TensorProduct 

func (q *Qubit) TensorProduct(qb *Qubit) *Qubit

TensorProduct returns the tensor product of q and qb.

func (*Qubit) TraceDistance 

func (q *Qubit) TraceDistance(qb *Qubit) float64

TraceDistance returns the trace distance of q and qb.

type State 

type State struct {
	Amplitude    complex128
	Probability  float64
	Int          []int64
	BinaryString []string
}

State is a quantum state.

Example 
package main

import (
	"fmt"

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

func main() {
	s := qubit.State{
		Amplitude:    1,
		Probability:  1,
		Int:          []int64{4, 10, 8},
		BinaryString: []string{"0100", "1010", "1000"},
	}

	fmt.Println(s.Value())
	fmt.Println(s.Value(0))
	fmt.Println(s.Value(1))
	fmt.Println(s.Value(2))
	fmt.Println(s.String())

}

Output:

4 0100
4 0100
10 1010
8 1000
[0100 1010 1000][  4  10   8]( 1.0000 0.0000i): 1.0000

func (*State) Add 

func (s *State) Add(binary string)

func (State) Equals 

func (s State) Equals(v State, eps ...float64) bool

Equals returns true if s equals v. If eps is not given, epsilon.E13 is used.

func (State) String 

func (s State) String() string

func (State) Value 

func (s State) Value(index ...int) (int64, string)

Source Files

View all Source files

Jump to

Keyboard shortcuts

? : This menu
/ : Search site
f or F : Jump to
y or Y : Canonical URL
go.dev uses cookies from Google to deliver and enhance the quality of its services and to analyze traffic. Learn more.