After I saw a 5-qubit GHZ state on Twitter, I tried out a 14-qubit GHZ state. If you are unfamiliar with the concepts of superposition and quantum entanglement, please follow the previous link for oversimplified definitions.

Because quantum computers are still in their infancy and suffer high error rates (the reasons of which are also in the previous article), the resultant histogram showed no evidence of quantum entanglement. The experiment clearly breaks down with a number of qubits less than 14.

Therefore, I proposed a follow-up experiment to determine at what point this experiment breaks down. For consistency, all of the experiments, even the smaller ones, were run on the same hardware: ibmq_16_melbourne through IBM Q Experience. All of the experiments were written in OpenQASM 2.0 (Quantum Assembly Language). This was the result of the 14-qubit GHZ state. The probability of seeing all zeroes or all ones, the only accurate outputs, is less than 1%. Therefore, in the previous article, I showed this 3-qubit GHZ state on the same hardware. In contrast to the 14 qubits, the success rate here is greater than 94%. As far as current quantum computers go, that’s actually really good. At 4 qubits, the success rate drops to about 65%, or almost two-thirds. By 5 qubits, which is what I saw on Twitter, we switch from a two-thirds probability of success to a two-thirds probability of failure. With 6 qubits, the failure rate is about 8-in-9. If you run the experiment nine times, only one might be accurate. The error rate for 7 qubits is about the same as for 6 qubits. The chance of failure increases by 1%, leaving only a 10% probability of measuring an accurate result.

With the current state of quantum computers, we have to conclude that GHZ states are limited to three qubits. Even at four qubits, Bob and Charlie are going to disagree about their measurements one-third of the time. By five qubits, they will be arguing most of the time. And somewhere before 14 qubits they will essentially be arguing all the time.