Skip to main content
Quantum Computing

Return to Question

deleted 2 characters in body
Source Link
Quantum Guy 123
Quantum Guy 123
  • 1.5k
  • 5
  • 18

The fidelity of a qubit is nicely defined here and gate fidelity as "the average fidelity of the output state over pure input states" (defined here).

How can one combine the fidelity'sfidelies of two (or more) gates to get a combined total gate fidelity? As in, if a qubit is operated on by two (or more) gates, how can we calculate the expected fidelity of the qubit (compared to its original state) after being operated on by those gates if all we know is the gate fidelity of each gate?

I imagine it is deducible from the definition of qubit fidelity... I haven't been able to figure it out. I also did a lot of searching online and couldn't find anything. I prefer the definition on the wikipedia page: $F(\rho, \sigma)=\left|\left\langle\psi_{\rho} \mid \psi_{\sigma}\right\rangle\right|^{2}$ for comparing the input state to the output state. It is easy to work with. A solution explained in these terms is much preferred.

The fidelity of a qubit is nicely defined here and gate fidelity as "the average fidelity of the output state over pure input states" (defined here).

How can one combine the fidelity's of two (or more) gates to get a combined total gate fidelity? As in, if a qubit is operated on by two (or more) gates, how can we calculate the expected fidelity of the qubit (compared to its original state) after being operated on by those gates if all we know is the gate fidelity of each gate?

I imagine it is deducible from the definition of qubit fidelity... I haven't been able to figure it out. I also did a lot of searching online and couldn't find anything. I prefer the definition on the wikipedia page: $F(\rho, \sigma)=\left|\left\langle\psi_{\rho} \mid \psi_{\sigma}\right\rangle\right|^{2}$ for comparing the input state to the output state. It is easy to work with. A solution explained in these terms is much preferred.

The fidelity of a qubit is nicely defined here and gate fidelity as "the average fidelity of the output state over pure input states" (defined here).

How can one combine the fidelies of two (or more) gates to get a combined total gate fidelity? As in, if a qubit is operated on by two (or more) gates, how can we calculate the expected fidelity of the qubit (compared to its original state) after being operated on by those gates if all we know is the gate fidelity of each gate?

I imagine it is deducible from the definition of qubit fidelity... I haven't been able to figure it out. I also did a lot of searching online and couldn't find anything. I prefer the definition on the wikipedia page: $F(\rho, \sigma)=\left|\left\langle\psi_{\rho} \mid \psi_{\sigma}\right\rangle\right|^{2}$ for comparing the input state to the output state. It is easy to work with. A solution explained in these terms is much preferred.

Source Link
Quantum Guy 123
Quantum Guy 123
  • 1.5k
  • 5
  • 18

How to Aggregate Multiple Gate Fidelities

The fidelity of a qubit is nicely defined here and gate fidelity as "the average fidelity of the output state over pure input states" (defined here).

How can one combine the fidelity's of two (or more) gates to get a combined total gate fidelity? As in, if a qubit is operated on by two (or more) gates, how can we calculate the expected fidelity of the qubit (compared to its original state) after being operated on by those gates if all we know is the gate fidelity of each gate?

I imagine it is deducible from the definition of qubit fidelity... I haven't been able to figure it out. I also did a lot of searching online and couldn't find anything. I prefer the definition on the wikipedia page: $F(\rho, \sigma)=\left|\left\langle\psi_{\rho} \mid \psi_{\sigma}\right\rangle\right|^{2}$ for comparing the input state to the output state. It is easy to work with. A solution explained in these terms is much preferred.