Teleportation with feed-forward

The protocol that needs dynamic circuits: two classical bits move one qubit of state.

You will learn to

Explain each of the four stages of teleportation.
Say why the two classical bits are necessary (no faster-than-light signalling).
Verify the protocol with a measurement in the right basis.

1. Share a Bell pair between q1 (sender) and q2 (receiver).
2. The sender entangles the message qubit q0 with q1: CNOT then H.
3. Measure q0 and q1: two classical bits.
4. The receiver applies X if c[1] = 1 and Z if c[0] = 1. q2 now carries the original state.

Try it

Teleport ry(0.6)|0⟩

The last gate undoes the preparation on q2, so a perfect teleport always reads c[2] = 0. Simulate: the last bit is 0 in every shot. Remove either correction and it is no longer.

OPENQASM 3.0;
include "stdgates.inc";
qubit[3] q;
bit[3] c;
ry(0.6) q[0];
h q[1];
cx q[1], q[2];
cx q[0], q[1];
h q[0];
c[0] = measure q[0];
c[1] = measure q[1];
if (c[1] == true) {
  x q[2];
}
if (c[0] == true) {
  z q[2];
}
ry(-0.6) q[2];
c[2] = measure q[2];

Open in the IDE Open in the Playground

Before the corrections, q2 is in one of four states depending on the two bits: the message, or the message with an X, a Z, or both applied. Without the bits the receiver sees a completely mixed qubit; nothing about the message has travelled. The bits travel classically, so no information moves faster than light.

Quiz 1 · 10 XP

What has the receiver before the two classical bits arrive?

Quiz 2 · 10 XP

Teleportation is also written with deferred measurement (CX/CZ corrections, no if). Why prefer the dynamic version on hardware?

Key takeaway

Teleportation moves a qubit's state with one Bell pair and two classical bits. The dynamic version, with if-corrections, is the one hardware actually runs.

Docs: teleportation example

Up next: Deutsch–Jozsa: one query instead of many · Quantum Algorithms

OPENQASM 3.0; include "stdgates.inc"; qubit[3] q; bit[3] c; ry(0.6) q[0]; h q[1]; cx q[1], q[2]; cx q[0], q[1]; h q[0]; c[0] = measure q[0]; c[1] = measure q[1]; if (c[1] == true) { x q[2]; } if (c[0] == true) { z q[2]; } ry(-0.6) q[2]; c[2] = measure q[2];