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CNOT / CX — Controlled-NOT

Flips the target qubit when the control qubit is |1⟩. The canonical entangling gate. Simulator 
qsim.CNOT(control, target Qubit) *Q
qsim.CX(control, target Qubit)   *Q  // alias
Gate package 
// n = total number of qubits in the system, c = control index, t = target index
gate.CNOT(n, c, t int) *matrix.Matrix
Example 
qsim := q.New()
q0 := qsim.Zero()
q1 := qsim.Zero()

qsim.H(q0)
qsim.CNOT(q0, q1) // Bell state

for _, s := range qsim.State() {
    fmt.Println(s)
}
// [00][  0]( 0.7071 0.0000i): 0.5000
// [11][  3]( 0.7071 0.0000i): 0.5000

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CCNOT — Toffoli Gate

Flips the target qubit when both control qubits are |1⟩. Universal for classical reversible computation. Simulator 
qsim.CCNOT(control0, control1, target Qubit) *Q
Gate package 
gate.CCNOT(n, c0, c1, t int) *matrix.Matrix

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CCCNOT — Four-Qubit Controlled-NOT

Flips the target when all three control qubits are |1⟩. Simulator 
qsim.CCCNOT(control0, control1, control2, target Qubit) *Q

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CZ / CCZ — Controlled-Z

Applies a phase flip to the target when the control(s) are |1⟩. Simulator 
qsim.CZ(control, target Qubit)              *Q  // single control
qsim.CCZ(control0, control1, target Qubit)  *Q  // two controls
Gate package 
gate.CZ(n, c, t int) *matrix.Matrix

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CR — Controlled-R

Applies the phase rotation R(theta) to the target qubit when the control is |1⟩. Core building block of QFT circuits. Simulator 
qsim.CR(theta float64, control, target Qubit) *Q
Gate package 
gate.CR(theta float64, n, c, t int) *matrix.Matrix

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C — Controlled Arbitrary Gate

Applies any 2×2 unitary g to target when control is |1⟩. Simulator 
qsim.C(g *matrix.Matrix, control, target Qubit) *Q
Gate package 
// Single control qubit, explicit system size
gate.C(u *matrix.Matrix, n int, c int, t int) *matrix.Matrix

// Arbitrary number of control qubits
gate.Controlled(u *matrix.Matrix, n int, c []int, t int) *matrix.Matrix

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CU — Controlled-U

Applies the universal gate U(theta, phi, lambda) to target conditioned on control. Simulator 
qsim.CU(theta, phi, lambda float64, control, target Qubit) *Q

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ControlledNot — General Multi-Control NOT

Flips each qubit in target when all qubits in control are |1⟩. Generalises CNOT, CCNOT, and CCCNOT to arbitrary numbers of controls and targets. Simulator 
qsim.ControlledNot(control []Qubit, target []Qubit) *Q
// Aliases:
qsim.ControlledX(control []Qubit, target []Qubit) *Q
Gate package 
gate.ControlledNot(n int, c []int, t int) *matrix.Matrix

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ControlledZ — General Multi-Control Z

Applies a phase flip to each qubit in target when all control qubits are |1⟩. Simulator 
qsim.ControlledZ(control []Qubit, target []Qubit) *Q
Gate package 
gate.ControlledZ(n int, c []int, t int) *matrix.Matrix

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Swap

Exchanges the quantum states of two qubits. When passed more than two qubits, Swap reverses the sequence (i.e., swaps the outermost pair first, then works inward). Simulator 
qsim.Swap(q0, q1)            // swap two qubits
qsim.Swap(q0, q1, q2, q3)   // swaps q0↔q3, then q1↔q2
Gate package 
// Returns an (2^n × 2^n) permutation matrix
gate.Swap(n, c, t int) *matrix.Matrix

​
QFT — Quantum Fourier Transform

Applies the quantum Fourier transform to the given qubits. Equivalent to a discrete Fourier transform on the computational-basis amplitudes. Used in phase estimation, Shor’s algorithm, and period finding. Simulator 
qsim.QFT(qb ...Qubit) *Q
Gate package 
// Returns the full (2^n × 2^n) QFT unitary matrix for n qubits
gate.QFT(n int) *matrix.Matrix

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InvQFT — Inverse Quantum Fourier Transform

Applies the inverse QFT. Converts frequency-domain amplitudes back to the computational basis. Used in the readout step of phase estimation. Simulator 
qsim.InvQFT(qb ...Qubit) *Q

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TensorProduct — Gate at Specified Indices

Embeds a single-qubit gate u into a larger n-qubit system, placing u at each qubit index listed in idx and identity on all remaining qubits. Gate package 
gate.TensorProduct(u *matrix.Matrix, n int, idx []int) *matrix.Matrix
Example 
// Apply H to qubits 0 and 2 in a 4-qubit system; identity on 1 and 3
g := gate.TensorProduct(gate.H(), 4, []int{0, 2})

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QFT Example: Grover’s Diffuser

The QFT and InvQFT are core subroutines in Shor’s algorithm. Here is a minimal demonstration of applying QFT and its inverse to confirm they are inverses of each other: 
package main

import (
    "fmt"

    "github.com/itsubaki/q"
)

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

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

    // Put qubits into superposition
    qsim.H(q0, q1, q2)

    // Apply QFT then InvQFT — the result should match the superposition state
    qsim.QFT(q0, q1, q2)
    qsim.InvQFT(q0, q1, q2)

    for _, s := range qsim.State() {
        fmt.Println(s)
    }
    // All 8 basis states appear with equal amplitude 1/√8 ≈ 0.3536
}

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