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Merge pull request #20 from itsubaki/improve-cr-dagger
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Change CR params from k to theta
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@itsubaki
itsubaki committed May 17, 2022
2 parents 94812a3 + aabc56e commit 74c1226
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Showing 5 changed files with 120 additions and 107 deletions.
2 changes: 1 addition & 1 deletion pkg/math/matrix/matrix.go
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Original file line number Diff line number Diff line change
Expand Up @@ -95,7 +95,7 @@ func (m Matrix) Conjugate() Matrix {
return out
}

// Dagger returns conjugate transpose matrix
// Dagger returns conjugate transpose matrix.
func (m Matrix) Dagger() Matrix {
p, q := m.Dimension()

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86 changes: 45 additions & 41 deletions pkg/quantum/gate/gate.go
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Original file line number Diff line number Diff line change
Expand Up @@ -27,6 +27,11 @@ func Empty(n ...int) []matrix.Matrix {
return make([]matrix.Matrix, n[0])
}

// Theta returns 2 * pi / 2**k
func Theta(k int) float64 {
return 2 * math.Pi / math.Pow(2, float64(k))
}

func U(theta, phi, lambda float64) matrix.Matrix {
v := complex(theta/2, 0)
return matrix.Matrix{
Expand All @@ -35,39 +40,6 @@ func U(theta, phi, lambda float64) matrix.Matrix {
}
}

func RX(theta float64) matrix.Matrix {
v := complex(theta/2, 0)
return matrix.Matrix{
[]complex128{cmplx.Cos(v), -1i * cmplx.Sin(v)},
[]complex128{-1i * cmplx.Sin(v), cmplx.Cos(v)},
}
}

func RY(theta float64) matrix.Matrix {
v := complex(theta/2, 0)
return matrix.Matrix{
[]complex128{cmplx.Cos(v), -1 * cmplx.Sin(v)},
[]complex128{cmplx.Sin(v), cmplx.Cos(v)},
}
}

func RZ(theta float64) matrix.Matrix {
v := complex(0, theta/2)
return matrix.Matrix{
[]complex128{cmplx.Exp(-1 * v), 0},
[]complex128{0, cmplx.Exp(v)},
}
}

func R(k int) matrix.Matrix {
p := 2 * math.Pi / math.Pow(2, float64(k))
e := cmplx.Exp(complex(0, p))
return matrix.Matrix{
[]complex128{1, 0},
[]complex128{0, e},
}
}

func I(n ...int) matrix.Matrix {
return matrix.TensorProductN(matrix.Matrix{
[]complex128{1, 0},
Expand Down Expand Up @@ -119,6 +91,38 @@ func T(n ...int) matrix.Matrix {
}, n...)
}

func R(theta float64) matrix.Matrix {
e := cmplx.Exp(complex(0, theta))
return matrix.Matrix{
[]complex128{1, 0},
[]complex128{0, e},
}
}

func RX(theta float64) matrix.Matrix {
v := complex(theta/2, 0)
return matrix.Matrix{
[]complex128{cmplx.Cos(v), -1i * cmplx.Sin(v)},
[]complex128{-1i * cmplx.Sin(v), cmplx.Cos(v)},
}
}

func RY(theta float64) matrix.Matrix {
v := complex(theta/2, 0)
return matrix.Matrix{
[]complex128{cmplx.Cos(v), -1 * cmplx.Sin(v)},
[]complex128{cmplx.Sin(v), cmplx.Cos(v)},
}
}

func RZ(theta float64) matrix.Matrix {
v := complex(0, theta/2)
return matrix.Matrix{
[]complex128{cmplx.Exp(-1 * v), 0},
[]complex128{0, cmplx.Exp(v)},
}
}

func Controlled(u matrix.Matrix, n int, c []int, t int) matrix.Matrix {
g := I([]int{n}...)
f := fmt.Sprintf("%s%s%s", "%0", strconv.Itoa(n), "s")
Expand Down Expand Up @@ -288,13 +292,13 @@ func CS(n, c, t int) matrix.Matrix {
return ControlledS(n, []int{c}, t)
}

func ControlledR(k, n int, c []int, t int) matrix.Matrix {
func ControlledR(theta float64, n int, c []int, t int) matrix.Matrix {
g := I([]int{n}...)
d, _ := g.Dimension()
f := fmt.Sprintf("%s%s%s", "%0", strconv.Itoa(n), "s")

p := 2 * math.Pi / math.Pow(2, float64(k))
e := cmplx.Exp(complex(0, p))
// exp(i * theta)
e := cmplx.Exp(complex(0, theta))

for i := 0; i < d; i++ {
bits := []rune(fmt.Sprintf(f, strconv.FormatInt(int64(i), 2)))
Expand All @@ -316,8 +320,8 @@ func ControlledR(k, n int, c []int, t int) matrix.Matrix {
return g
}

func CR(k, n, c, t int) matrix.Matrix {
return ControlledR(k, n, []int{c}, t)
func CR(theta float64, n, c, t int) matrix.Matrix {
return ControlledR(theta, n, []int{c}, t)
}

// Swap returns unitary matrix of Swap operation.
Expand Down Expand Up @@ -355,16 +359,16 @@ func QFT(n int) matrix.Matrix {

k := 2
for j := i + 1; j < n; j++ {
g = g.Apply(CR(k, n, j, i))
g = g.Apply(CR(Theta(k), n, j, i))
k++
}
}

return g
}

// ControlledModExp2 returns unitary matrix of controlled modular exponentiation operation. |j>|k> -> |j>|a**(2**j) * k mod N>
// len(t) must be larger than log2(N)
// ControlledModExp2 returns unitary matrix of controlled modular exponentiation operation. |j>|k> -> |j>|a**(2**j) * k mod N>.
// len(t) must be larger than log2(N).
func ControlledModExp2(n, a, j, N, c int, t []int) matrix.Matrix {
m := I([]int{n}...)
d, _ := m.Dimension()
Expand Down
8 changes: 4 additions & 4 deletions pkg/quantum/gate/gate_test.go
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Original file line number Diff line number Diff line change
Expand Up @@ -208,7 +208,7 @@ func TestC(t *testing.T) {
{gate.C(gate.X(), 2, 0, 1), gate.CNOT(2, 0, 1)},
{gate.C(gate.Z(), 2, 0, 1), gate.CZ(2, 0, 1)},
{gate.C(gate.S(), 2, 0, 1), gate.CS(2, 0, 1)},
{gate.C(gate.R(100), 2, 0, 1), gate.CR(100, 2, 0, 1)},
{gate.C(gate.R(gate.Theta(4)), 2, 0, 1), gate.CR(gate.Theta(4), 2, 0, 1)},
{gate.C(gate.X(), 3, 0, 2), gate.CNOT(3, 0, 2)},
{gate.C(gate.X(), 3, 0, 1), gate.CNOT(3, 0, 1)},
{gate.C(gate.X(), 3, 1, 0), gate.CNOT(3, 1, 0)},
Expand Down Expand Up @@ -291,14 +291,14 @@ func TestIsUnitary(t *testing.T) {
{gate.Y(), true},
{gate.Z(), true},
{gate.U(1, 2, 3), true},
{gate.R(4), true},
{gate.R(gate.Theta(4)), true},
{gate.RX(1.23), true},
{gate.RY(1.23), true},
{gate.RZ(1.23), true},
{gate.ControlledS(2, []int{0}, 1), true},
{gate.ControlledR(10, 2, []int{0}, 1), true},
{gate.ControlledR(gate.Theta(4), 2, []int{0}, 1), true},
{gate.CS(2, 0, 1), true},
{gate.CR(10, 2, 0, 1), true},
{gate.CR(gate.Theta(4), 2, 0, 1), true},
{gate.QFT(2), true},
{gate.New(
[]complex128{1, 2},
Expand Down
83 changes: 38 additions & 45 deletions q.go
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Original file line number Diff line number Diff line change
Expand Up @@ -115,12 +115,12 @@ func (q *Q) Reset(qb ...Qubit) {
}
}

func (q *Q) I(qb ...Qubit) *Q {
return q.Apply(gate.I(), qb...)
func (q *Q) U(theta, phi, lambda float64, qb ...Qubit) *Q {
return q.Apply(gate.U(theta, phi, lambda), qb...)
}

func (q *Q) H(qb ...Qubit) *Q {
return q.Apply(gate.H(), qb...)
func (q *Q) I(qb ...Qubit) *Q {
return q.Apply(gate.I(), qb...)
}

func (q *Q) X(qb ...Qubit) *Q {
Expand All @@ -135,6 +135,10 @@ func (q *Q) Z(qb ...Qubit) *Q {
return q.Apply(gate.Z(), qb...)
}

func (q *Q) H(qb ...Qubit) *Q {
return q.Apply(gate.H(), qb...)
}

func (q *Q) S(qb ...Qubit) *Q {
return q.Apply(gate.S(), qb...)
}
Expand All @@ -143,8 +147,8 @@ func (q *Q) T(qb ...Qubit) *Q {
return q.Apply(gate.T(), qb...)
}

func (q *Q) U(theta, phi, lambda float64, qb ...Qubit) *Q {
return q.Apply(gate.U(theta, phi, lambda), qb...)
func (q *Q) R(theta float64, qb ...Qubit) *Q {
return q.Apply(gate.R(theta), qb...)
}

func (q *Q) RX(theta float64, qb ...Qubit) *Q {
Expand Down Expand Up @@ -199,26 +203,27 @@ func (q *Q) C(m matrix.Matrix, control, target Qubit) *Q {
return q.Controlled(m, []Qubit{control}, target)
}

func (q *Q) ControlledR(k int, control []Qubit, target Qubit) *Q {
func (q *Q) ControlledNot(control []Qubit, target Qubit) *Q {
n := q.NumberOfBit()
g := gate.ControlledR(k, n, Index(control...), target.Index())
g := gate.ControlledNot(n, Index(control...), target.Index())
q.qb.Apply(g)
return q
}

func (q *Q) CR(k int, control, target Qubit) *Q {
return q.ControlledR(k, []Qubit{control}, target)
func (q *Q) CNOT(control, target Qubit) *Q {
return q.ControlledNot([]Qubit{control}, target)
}

func (q *Q) InverseCR(k int, control, target Qubit) *Q {
n := q.NumberOfBit()
g := gate.ControlledR(k, n, []int{control.Index()}, target.Index()).Dagger()
q.qb.Apply(g)
return q
func (q *Q) CCNOT(control0, control1, target Qubit) *Q {
return q.ControlledNot([]Qubit{control0, control1}, target)
}

func (q *Q) CCCNOT(control0, control1, control2, target Qubit) *Q {
return q.ControlledNot([]Qubit{control0, control1, control2}, target)
}

func (q *Q) InvCR(k int, control, target Qubit) *Q {
return q.InverseCR(k, control, target)
func (q *Q) Toffoli(control0, control1, target Qubit) *Q {
return q.CCNOT(control0, control1, target)
}

func (q *Q) ControlledZ(control []Qubit, target Qubit) *Q {
Expand All @@ -236,27 +241,30 @@ func (q *Q) CCZ(control0, control1, target Qubit) *Q {
return q.ControlledZ([]Qubit{control0, control1}, target)
}

func (q *Q) ControlledNot(control []Qubit, target Qubit) *Q {
func (q *Q) ControlledR(theta float64, control []Qubit, target Qubit) *Q {
n := q.NumberOfBit()
g := gate.ControlledNot(n, Index(control...), target.Index())
g := gate.ControlledR(theta, n, Index(control...), target.Index())
q.qb.Apply(g)
return q
}

func (q *Q) CNOT(control, target Qubit) *Q {
return q.ControlledNot([]Qubit{control}, target)
func (q *Q) CR(theta float64, control, target Qubit) *Q {
return q.ControlledR(theta, []Qubit{control}, target)
}

func (q *Q) CCNOT(control0, control1, target Qubit) *Q {
return q.ControlledNot([]Qubit{control0, control1}, target)
func (q *Q) ControlledModExp2(a, j, N int, control Qubit, target []Qubit) *Q {
n := q.NumberOfBit()
g := gate.ControlledModExp2(n, a, j, N, control.Index(), Index(target...))
q.qb.Apply(g)
return q
}

func (q *Q) CCCNOT(control0, control1, control2, target Qubit) *Q {
return q.ControlledNot([]Qubit{control0, control1, control2}, target)
}
func (q *Q) CModExp2(a, N int, control []Qubit, target []Qubit) *Q {
for i := 0; i < len(control); i++ {
q.ControlledModExp2(a, i, N, control[i], target)
}

func (q *Q) Toffoli(control0, control1, target Qubit) *Q {
return q.CCNOT(control0, control1, target)
return q
}

func (q *Q) Condition(condition bool, m matrix.Matrix, qb ...Qubit) *Q {
Expand All @@ -275,21 +283,6 @@ func (q *Q) ConditionZ(condition bool, qb ...Qubit) *Q {
return q.Condition(condition, gate.Z(), qb...)
}

func (q *Q) ControlledModExp2(a, j, N int, control Qubit, target []Qubit) *Q {
n := q.NumberOfBit()
g := gate.ControlledModExp2(n, a, j, N, control.Index(), Index(target...))
q.qb.Apply(g)
return q
}

func (q *Q) CModExp2(a, N int, control []Qubit, target []Qubit) *Q {
for i := 0; i < len(control); i++ {
q.ControlledModExp2(a, i, N, control[i], target)
}

return q
}

func (q *Q) Swap(qb ...Qubit) *Q {
n := q.NumberOfBit()
l := len(qb)
Expand All @@ -310,7 +303,7 @@ func (q *Q) QFT(qb ...Qubit) *Q {

k := 2
for j := i + 1; j < l; j++ {
q.CR(k, qb[j], qb[i])
q.CR(gate.Theta(k), qb[j], qb[i])
k++
}
}
Expand All @@ -323,7 +316,7 @@ func (q *Q) InverseQFT(qb ...Qubit) *Q {
for i := l - 1; i > -1; i-- {
k := l - i
for j := l - 1; j > i; j-- {
q.InvCR(k, qb[j], qb[i])
q.CR(-1*gate.Theta(k), qb[j], qb[i])
k--
}

Expand Down
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