run_symmetrized_readout(program, trials, symm_type=3, meas_qubits=None)¶
Run a quil program in such a way that the readout error is made symmetric. Enforcing symmetric readout error is useful in simplifying the assumptions in some near term error mitigation strategies, see
measure_observablesfor more information.
The simplest example is for one qubit. In a noisy device, the probability of accurately reading the 0 state might be higher than that of the 1 state; due to e.g. amplitude damping. This makes correcting for readout more difficult. In the simplest case, this function runs the program normally
(trials//2)times. The other half of the time, it will insert an
Xgate prior to any
MEASUREinstruction and then flip the measured classical bit back. Overall this has the effect of symmetrizing the readout error.
The details. Consider preparing the input bitstring
|i>(in the computational basis) and measuring in the Z basis. Then the Confusion matrix for the readout error is specified by the probabilities
p(j|i) := Pr(measured = j | prepared = i ).
In the case of a single qubit i,j in [0,1] then: there is no readout error if p(0|0) = p(1|1) = 1. the readout error is symmetric if p(0|0) = p(1|1) = 1 - epsilon. the readout error is asymmetric if p(0|0) != p(1|1).
If your quantum computer has this kind of asymmetric readout error then
qc.run_symmetrized_readoutwill symmetrize the readout error.
The readout error above is only asymmetric on a single bit. In practice the confusion matrix on n bits need not be symmetric, e.g. for two qubits p(ij|ij) != 1 - epsilon for all i,j. In these situations a more sophisticated means of symmetrization is needed; and we use orthogonal arrays (OA) built from Hadamard matrices.
The symmetrization types are specified by an int; the types available are: -1 – exhaustive symmetrization uses every possible combination of flips 0 – trivial that is no symmetrization 1 – symmetrization using an OA with strength 1 2 – symmetrization using an OA with strength 2 3 – symmetrization using an OA with strength 3 In the context of readout symmetrization the strength of the orthogonal array enforces the symmetry of the marginal confusion matrices.
By default a strength 3 OA is used; this ensures expectations of the form
<b_k . b_j . b_i>for bits any bits i,j,k will have symmetric readout errors. Here expectation of a random variable x as is denote
<x> = sum_i Pr(i) x_i. It turns out that a strength 3 OA is also a strength 2 and strength 1 OA it also ensures
<b_j . b_i>and
<b_i>have symmetric readout errors for any bits b_j and b_i.
Program) – The program to run symmetrized readout on.
int) – The minimum number of times to run the program; it is recommend that this number should be in the hundreds or thousands. This parameter will be mutated if necessary.
int) – the type of symmetrization
- Return type
A numpy array of shape (trials, len(ro-register)) that contains 0s and 1s.