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A Bell state is a maximally entangled two-qubit quantum state. When you measure one qubit, the outcome of the other is immediately determined — no matter how far apart they are. This makes Bell states foundational to quantum teleportation, superdense coding, and quantum cryptography. The specific Bell state created here is: 
|Φ+⟩ = (|00⟩ + |11⟩) / √2
Both qubits are in a superposition of |00⟩ and |11⟩ with equal probability. They are never in |01⟩ or |10⟩.

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Creating a Bell state

1

Create the simulator and initialize two qubits

Instantiate a new simulator with q.New(), then allocate two qubits in the |0⟩ state using qsim.Zero().
qsim := q.New()

// generate qubits of |0>|0>
q0 := qsim.Zero()
q1 := qsim.Zero()
Both q0 and q1 start in the computational basis state |0⟩. The combined system is |00⟩.
2

Apply a Hadamard gate to q0

The Hadamard gate puts q0 into an equal superposition of |0⟩ and |1⟩:
H|0⟩ = (|0⟩ + |1⟩) / √2

qsim.H(q0)
After this step, the system is (|0⟩ + |1⟩)/√2 ⊗ |0⟩ = (|00⟩ + |10⟩)/√2.
3

Apply CNOT with q0 as control and q1 as target

The CNOT gate flips q1 only when q0 is |1⟩. This creates entanglement between the two qubits.
qsim.CNOT(q0, q1)
After CNOT:
  • |00⟩ stays |00⟩ (control is 0, target unchanged)
  • |10⟩ becomes |11⟩ (control is 1, target flipped)
The result is (|00⟩ + |11⟩)/√2 — a Bell state.
4

Inspect the state

Iterate over qsim.State() to print each basis state with its amplitude and probability:
for _, s := range qsim.State() {
  fmt.Println(s)
}

// [00][  0]( 0.7071 0.0000i): 0.5000
// [11][  3]( 0.7071 0.0000i): 0.5000
Each line has the format:
[binary representation][decimal index](amplitude real imaginary): probability
  • [00] — basis state in binary (|00⟩)
  • [ 0] — decimal index of the basis state
  • ( 0.7071 0.0000i) — complex amplitude; 1/√2 ≈ 0.7071
  • : 0.5000 — measurement probability (|0.7071|² = 0.5)
The state |01⟩ and |10⟩ do not appear because their amplitudes are zero.
5

Measure both qubits and verify correlation

Measuring collapses the superposition. Both qubits are measured independently, but because they are entangled they always yield the same outcome.
m0 := qsim.Measure(q0)
m1 := qsim.Measure(q1)
fmt.Println(m0.Equal(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
After measurement the state collapses deterministically to either |00⟩ or |11⟩, each with 50% probability. The amplitude becomes 1.0000 and the probability becomes 1.0000, confirming the wavefunction has fully collapsed.m0.Equal(m1) returns true every time — the two qubits always agree.

​
Complete example

qsim := q.New()

// generate qubits of |0>|0>
q0 := qsim.Zero()
q1 := qsim.Zero()

// apply quantum circuit
qsim.H(q0)
qsim.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.Equal(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

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