# What do the "gate errors rates" mean physically for IBM's quantum computers?

I wish to simulate the gate errors from IBM's various quantum computers. However I am not sure what the gate error rate physically means. An error rate of say 0.01 for a particular means one in every 100 trials the gate will not return the desired outcome. But if I wish to simulate this myself I need to know what outcome is produced. Is it simply a random outcome? For example if I am implementing a CNOT gate on the state |11>, what happens when the gate fails? What is the state after this?

• I don't think this is what it error rate means, since the gate takes a quantum state as input, and outputs another quantum state, so what do you mean by "outcome". As far ask I know, error rate is one minus fidelity. It is usually determined by methods of randomized benchmarking. Oct 6, 2020 at 12:51
• Hi Yael, by output I mean what the quantum state would be. I have updated the question to reflect this
– LOC
Oct 6, 2020 at 20:40
• An error rate of 0.01 does not mean that one in every 100 trials the gate will not return the desired outcome. Take for example a gate that never produces the desired outcome, but produces another state, which is close to the desired outcome. Also, the outcome can be a mixed state. I recommend to gain good understanding of the definitions of fidelity and quantum channels, these are well explained in the textbook of Nielsen and Chuang. Oct 8, 2020 at 7:08

Different quantum channels can cause the same gate error. One option is to assume that the gate error is caused by a depolarizing channel, followed by thermal relaxation. This is the assumption made in NoiseModel.from_backend, whose documentation can help you: https://qiskit.org/documentation/stubs/qiskit.providers.aer.noise.NoiseModel.from_backend.html#qiskit.providers.aer.noise.NoiseModel.from_backend.