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You can simulate the standard quantum-teleportation protocol with three qubits, two classical measurement bits, and a simulator such as Qiskit Aer. One qubit holds a known test state, Alice’s qubit is entangled with Bob’s qubit, Alice measures her two qubits, and Bob applies conditional Pauli gates based on the two classical results. To verify the transfer, apply the inverse of the test state’s preparation to Bob’s qubit and check that the verification measurement is always 0 in an ideal simulation.
Teleportation transfers quantum-state information; it does not move matter, copy a qubit, or send information faster than light. The protocol consumes the shared entangled pair and requires ordinary classical communication.
What the circuit actually teleports
In the minimal protocol, the unknown state is represented by an input qubit. Alice and Bob first share an entangled Bell pair. Alice then performs a joint measurement on the input and her half of the pair. Those two classical results tell Bob which correction to apply to his qubit. After correction, Bob’s qubit has the same state the input had before Alice measured it.
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The three qubits
| Qubit | Role | Who controls it |
|---|---|---|
| q0 | Secret input state to be transferred | Alice initially prepares and later measures it |
| q1 | Alice’s half of the Bell pair | Alice entangles and measures it |
| q2 | Bob’s half of the Bell pair | Bob applies conditional corrections |
The circuit also needs two classical bits for Alice’s measurement outcomes. A third classical bit is convenient for the verification measurement at the end.
Gate sequence at a glance
With q0 as the input, q1 as Alice’s entangled qubit, and q2 as Bob’s, the protocol has four logical stages.
- Prepare the input. Apply any known state-preparation circuit to q0. A rotation sequence is useful for testing because it creates a state that is not simply 0, 1, or an equal superposition.
- Create the Bell pair. Apply a Hadamard gate to q1, then a controlled-NOT from q1 to q2. The pair is now entangled.
- Perform Alice’s Bell measurement. Apply CNOT from q0 to q1, then Hadamard to q0. Measure q0 and q1 in the computational basis.
- Correct Bob’s qubit. Send the two measured bits classically. Bob conditionally applies X and Z. Which measured bit controls which gate depends on your qubit, classical-register, and bit-order convention; the code below uses the mapping from the IBM Quantum Learning example described here.
The inverse of the input-preparation circuit is added only for testing. It is not part of teleportation and would not be available if the input state were genuinely unknown.
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A local Python installation with Qiskit and the Qiskit Aer simulator is sufficient. The example uses AerSimulator for shot-based execution, which repeats the circuit many times and returns measurement counts. Package APIs can change, so install versions that are compatible with one another and consult the installed package’s current documentation if an import or conditional-control method has been renamed.
pip install qiskit qiskit-aerRun the program in a Python file or notebook. No quantum processor is required for this tutorial.
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Build the circuit step by step
1. Allocate quantum and classical registers
Use separate one-bit classical registers for Alice’s two results. This makes the correction conditions unambiguous: m0 stores the measurement of q0 and m1 stores the measurement of q1. A separate verify register stores Bob’s final test bit.
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit_aer import AerSimulator
q = QuantumRegister(3, 'q')
m0 = ClassicalRegister(1, 'm0')
m1 = ClassicalRegister(1, 'm1')
verify = ClassicalRegister(1, 'verify')
qc = QuantumCircuit(q, m0, m1, verify)2. Prepare a known input state
For a reproducible test, prepare q0 with two rotations. The angles below are arbitrary test values, not a special teleportation requirement.
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theta = 0.7
phi = 1.1
qc.ry(theta, q[0])
qc.rz(phi, q[0])The state-preparation unitary is the sequence ry(theta) followed by rz(phi). To undo it later, the inverse gates must be applied in reverse order: rz(-phi) followed by ry(-theta).
3. Create the shared Bell pair
qc.h(q[1])
qc.cx(q[1], q[2])The Hadamard puts q1 into a superposition. The controlled-NOT correlates q2 with q1, producing the entangled pair that supplies the resource for teleportation. At this point q0 is still the input and q1-q2 are the shared pair.
4. Transform and measure Alice’s two qubits
qc.cx(q[0], q[1])
qc.h(q[0])
qc.measure(q[0], m0[0])
qc.measure(q[1], m1[0])The CNOT and Hadamard convert the joint information in q0 and q1 into two computational-basis bits. Measurement produces ordinary classical values, each either 0 or 1. It also removes the original coherent state from Alice’s side; this is why the protocol is transfer rather than cloning.
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5. Apply Bob’s conditional corrections
For the register assignment above, the IBM example applies Z to q2 when m0 is 1 and X to q2 when m1 is 1. In current Qiskit-style dynamic-circuit syntax, the conditions can be written as follows:
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with qc.if_test((m0, 1)):
qc.z(q[2])
with qc.if_test((m1, 1)):
qc.x(q[2])These two operations commute up to an irrelevant global phase when both conditions are true, so applying them in the displayed order is fine. The conceptual rule is that one measurement outcome selects the phase-flip correction Z and the other selects the bit-flip correction X. Other tutorials may label the measured bits in the opposite order or pack them into one classical register; in those circuits the apparent conditions can be swapped. Always trace which classical bit received each measurement before copying a conditional statement.
6. Undo the known preparation for verification
Now test whether Bob’s state equals the state originally prepared on q0:
qc.rz(-phi, q[2])
qc.ry(-theta, q[2])
qc.measure(q[2], verify[0])If teleportation and the corrections are correct, the inverse preparation maps Bob’s state to |0⟩. The final measurement should therefore be 0 on every shot in an ideal simulator. This inverse is a diagnostic operation added after the protocol; it is not a step Alice and Bob use to teleport an unknown state.
Complete runnable example
The following listing puts the pieces together and executes 1,024 shots.
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from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister, transpile
from qiskit_aer import AerSimulator
q = QuantumRegister(3, 'q')
m0 = ClassicalRegister(1, 'm0')
m1 = ClassicalRegister(1, 'm1')
verify = ClassicalRegister(1, 'verify')
qc = QuantumCircuit(q, m0, m1, verify)
theta = 0.7
phi = 1.1
# Known input state on q0
qc.ry(theta, q[0])
qc.rz(phi, q[0])
# Bell pair shared by Alice (q1) and Bob (q2)
qc.h(q[1])
qc.cx(q[1], q[2])
# Alice's Bell-basis measurement
qc.cx(q[0], q[1])
qc.h(q[0])
qc.measure(q[0], m0[0])
qc.measure(q[1], m1[0])
# IBM-example mapping for this register layout
with qc.if_test((m0, 1)):
qc.z(q[2])
with qc.if_test((m1, 1)):
qc.x(q[2])
# Verification only: undo the known input preparation on Bob's qubit
qc.rz(-phi, q[2])
qc.ry(-theta, q[2])
qc.measure(q[2], verify[0])
simulator = AerSimulator()
compiled = transpile(qc, simulator)
result = simulator.run(compiled, shots=1024).result()
counts = result.get_counts()
print(counts)Qiskit may print keys containing several classical-register fields, with spacing or ordering determined by the register layout. Do not judge success by looking for one memorized key string. Identify the field corresponding to verify and confirm that its value is 0 in every counted outcome. Alice’s m0 and m1 values should vary across runs; their variation is normal and does not indicate failure.
How the correction mapping works
Before correction, Bob’s qubit is one of four related versions of the input state. Alice’s two bits select the version. One bit indicates whether a bit flip is needed, represented by X; the other indicates whether a phase flip is needed, represented by Z. If both bits are 1, both corrections are applied.
There is no universal visual rule such as “the leftmost printed bit always controls X.” Qiskit displays classical bits according to register and string conventions, while circuit diagrams often draw q0 at the top and concatenate registers in another order. In the example, q0 is measured into m0 and q1 into m1, and the explicit conditions are Z-on-m0 and X-on-m1. If you instead use one two-bit register, verify whether the integer condition 1 refers to the least-significant bit and whether your framework’s displayed bit string reverses the register order. A correct protocol with a mismatched condition silently produces the wrong state, so this mapping check is the most important debugging step.
Verifying teleportation with shots
Why inverse preparation is a strong test
Directly comparing two arbitrary quantum states is not possible with one measurement. Because the test input is known, you can apply its inverse to Bob’s qubit. Correct teleportation followed by the inverse gives the definite state |0⟩, making a simple computational-basis measurement decisive in the ideal case.
- All verification shots should report verify = 0 in an ideal, noiseless simulator.
- The two Alice bits can be 00, 01, 10, or 11; their distribution is not itself the success criterion.
- A nonzero verification result indicates a circuit, mapping, simulator, or noise problem rather than a new teleportation outcome.
Testing simpler inputs first
If the rotation example fails, replace it temporarily with a single familiar preparation such as qc.h(q[0]) and use qc.h(q[2]) for the inverse test. You can also test |0⟩ by omitting input preparation; in that case the inverse is empty. Once those cases pass, restore the two-rotation state. This isolates correction and register-order errors from mistakes in manually constructing the inverse.
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Statevector simulation versus shot-based simulation
| Method | What it shows | Best use | Limitation |
|---|---|---|---|
| Statevector simulation | Complex amplitudes of the ideal quantum state | Inspecting superposition and entanglement without sampling noise | Measurements collapse the state, and the output is less intuitive for a protocol that includes classical feed-forward |
| Shot-based simulation | Repeated measurement samples and counts | Running the complete measure, communicate, correct, and verify workflow | Counts are statistical samples, so finite-shot histograms need not look perfectly uniform |
A statevector view is useful for learning what the Bell pair and intermediate transformations do. For the end-to-end beginner check, the shot-based circuit with inverse-preparation verification is usually clearer: inspect the verification bit and expect zero in the noiseless case.
Troubleshooting failures
Verification is sometimes 1
- Check the correction mapping first. Confirm that q0 was measured into m0 and q1 into m1, then confirm that your conditional gates match that convention.
- Check inverse order. The inverse of
ry(theta)followed byrz(phi)isrz(-phi)followed byry(-theta)when written as circuit operations. - Check classical-register conditions. A condition on a two-bit register tests its encoded integer value, not necessarily “this individual bit equals 1.” Separate one-bit registers avoid that ambiguity.
- Check that measurements occur before feed-forward. Bob’s corrections must be classically conditioned on Alice’s measured bits.
The program fails at if_test or c_if
Dynamic-circuit APIs differ between Qiskit releases. Use the conditional-control syntax supported by your installed version, but preserve the same logical conditions. If your version uses c_if, attach each condition to the appropriate one-bit classical register rather than guessing at a packed-register integer. Compile after adding the conditional operations so the simulator can validate the circuit.
The output keys look reversed
Multiple classical registers are commonly displayed in an order that differs from the order in which you read them. Name the registers, inspect the circuit diagram, and decode the key by register rather than assuming the leftmost character is m0. The physical protocol is unaffected by display order; only your interpretation and conditional code must agree.
Results are noisy on a real processor
A simulator with ideal gates is not a hardware benchmark. Real processors introduce gate, readout, and coherence errors, and their control software must support mid-circuit measurement and real-time conditional operations. A hardware result can therefore contain nonzero verification counts even when the circuit logic is correct. Hardware outcomes depend on the selected device, calibration, transpilation, and run conditions; do not treat a single tutorial run as a general accuracy statistic.
What this experiment proves—and what it does not
- It demonstrates that an unknown quantum state can be reconstructed at Bob’s location using a pre-shared entangled pair plus two classical bits.
- It does not transmit a physical object from Alice to Bob.
- It does not create a second copy of the input state. Alice’s original is disturbed by measurement.
- It does not eliminate the classical communication delay. Bob cannot choose the correct operation before receiving Alice’s results.
- It does not require a quantum computer for the first demonstration; an ideal simulator is enough to validate the gate sequence.
Adapting the circuit to an unknown input
In a real protocol, Alice need not know the amplitudes of q0. The teleportation gates and measurements are unchanged. What changes is the verification method: Alice and Bob cannot apply an inverse-preparation circuit they do not know. Instead, experiments use state tomography, randomized measurements, or comparisons against a separately prepared reference state. For a beginner simulator, a known preparation remains preferable because it turns success into a direct 0/1 measurement test.
A practical checklist
- Allocate exactly three qubits and at least two classical measurement bits.
- Record the role of every qubit and classical bit before writing conditions.
- Prepare a known input state on q0.
- Create the Bell pair with H on q1 and CNOT q1 to q2.
- Apply CNOT q0 to q1, then H on q0.
- Measure q0 and q1 into explicitly named classical bits.
- Apply the X and Z corrections according to your actual bit mapping; in the example, Z is controlled by m0 and X by m1.
- For testing only, apply the exact inverse input preparation to q2.
- Run enough shots to see stable counts and inspect the verification bit, not just the printed key order.
- If moving to hardware, expect noise and confirm that the platform supports dynamic feed-forward.
Following this sequence gives a complete three-qubit teleportation demonstration while keeping the essential distinction clear: entanglement supplies the quantum resource, classical bits select the correction, and the simulator’s zero verification result confirms that Bob received the prepared state.
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