When should I use VD?#

Advantages#

  • VD can exponentially reduce the contributions of non-dominant eigenvectors in the density matrix, bringing the effective state closer to the ideal noise-free state as the number of copies \(M\) increases.

  • VD can be used complementarily with other error mitigation and calibration techniques, allowing for higher levels of errors reduction.

  • The explicit preparation of the \(\rho\) density matrix is not required, thus allowing for higher suppression and more computational efficiency.

  • VD is a unique error mitigation strategy in that is uses additional available qubits instead of requiring many additional circuits or shots. This makes the technique useful when the circuit of interest is smaller than half the device size.

Disadvantages#

  • The last advantage is also a disadvantage as VD requires additional qubits on devices that are already limited in size.

  • Real errors and noise on the hardware will lead to population in states that are not orthogonal to the target state, which results in a drift of the dominant eigenvector. This results in limiting the potential error mitigation of VD: instead of a quadratic suppression in errors there will be a constant factor improvement instead [57].

  • Currently the implementation of VD only allows for measurement on \(Z\) observables.

  • The VD implementation occasional results in a divide by zero error. This occurs only when the number of iterations is even and typically when that number is fairly low (under 100). In order to circumvent this known issue, if an even number \(K\) of iterations is passed to the function then this value will be reduced by 1. This ensures that the circuits are never run more times than expected.

  • The current implementation only allows for \(M = 2\) number of copies.