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https://github.com/itsubaki/q
Quantum Computation Simulator for Go
https://github.com/itsubaki/q
go quantum-computation quantum-computing quantum-information
Last synced: 3 months ago
JSON representation
Quantum Computation Simulator for Go
- Host: GitHub
- URL: https://github.com/itsubaki/q
- Owner: itsubaki
- License: mit
- Created: 2017-12-30T13:33:54.000Z (almost 7 years ago)
- Default Branch: main
- Last Pushed: 2024-05-12T13:24:15.000Z (6 months ago)
- Last Synced: 2024-05-12T14:34:21.541Z (6 months ago)
- Topics: go, quantum-computation, quantum-computing, quantum-information
- Language: Go
- Homepage: https://pkg.go.dev/github.com/itsubaki/q
- Size: 617 KB
- Stars: 224
- Watchers: 10
- Forks: 24
- Open Issues: 2
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
- go-awesome - q - quantum computer simulator (Open source library / Mathematical Calculations)
- awesome-quantum-software - Q - Quantum Computation Simulator written purely in GoLang. (Quantum simulators)
README
# q
[](https://pkg.go.dev/github.com/itsubaki/q)
[](https://goreportcard.com/report/github.com/itsubaki/q)
[](https://github.com/itsubaki/q/actions)
[](https://codecov.io/gh/itsubaki/q)
- quantum computation simulator
- pure Go implementation
- using only the standard library
## Example
### Bell state
```go
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.Equals(m1)) // 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
```go
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
```go
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
```go
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
```go
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`](./cmd/shor/main.go)
### Any quantum gate and its controlled gate
```go
h := gate.U(math.Pi/2, 0, math.Pi)
x := gate.U(math.Pi, 0, math.Pi)
qsim := q.New()
q0 := qsim.Zero()
q1 := qsim.Zero()
qsim.Apply(h, q0)
qsim.C(x, 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
```
## References
- Michael A. Nielsen, Issac L. Chuang. Quantum Computation and Quantum Information.