qubit

package
v0.0.3 Latest Latest
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 Go to latest Published: Sep 9, 2023 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

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