Randomized Benchmarking for Non-Markovian Noise

Towards a general framework of Randomized Benchmarking for non-Markovian Noise

“…We have established a Randomized Benchmarking (RB) framework for non-Markovian noise with gate sets forming a finite group which admits a multiplicity-free representation. Despite this being a more general and abstract case than that of unitary 2-designs [29], it renders a much clearer functional form of the Average Sequence Fidelity (ASF) as described in terms of so-called quality maps, which carry average noise through the environment mediating temporal correlations. Quality maps naturally generalize the concept of quality parameters [32], from Markovian to non-Markovian RB, as the central quantities capturing average noise rates within the ASF.…”

“…In general, the functional form of the ASF depends not only on the specific gate set to be benchmarked, but also on the assumptions made about the noise. Both a class of non-Clifford gate sets has been considered [8,12,31,32,[35][36][37][38] and the assumptions on the noise relaxed, e.g., for time-dependent [4,5,39], gate-dependent [4,33,34,40,41] or non-Markovian noise [27][28][29], although to this day, arguably the least explored regime is that of non-Markovian noise.…”

“…A first signature of non-Markovianity in a RB experiment is the display of deviations from an exponential decay in the ASF [29]. However, deviations might not be evident or significant, making the experiment blind to non-Markovianity, or the noise might be time-dependent but Markovian, not displaying multi-time correlations but rather some arbitrary temporal dependence changing the exponential rates of decay of the ASF data.…”

“…With this setup, the only difference for the case of non-Markovian RB is that now the noise Λ acts jointly on a system S and an environment E, with respective dimensions d S and d E , at every step of the RB sequence, and the gates G are now assumed to act solely on S [29]. Keep in mind that if we employ the superoperator representation, the environment will have implicit two copies 8 .…”

Hidden Quantum Memory: Is Memory There When Somebody Looks?

“…Introduction.-Our ability to understand and control memory effects in the evolution of open quantum systems is becoming increasingly important as technology allows us to manipulate interactions with increasing levels of speed, precision and complexity [1,2]. Control over memory can be advantageous in various tasks, such as the creation, manipulation and preservation of coherences and correlations [3,4], reservoir engineering to simulate complex dynamics [5][6][7][8][9][10][11][12][13][14][15][16], sophisticated randomised benchmarking and quantum error correction [17][18][19], optimal dynamical decoupling [20][21][22], designing quantum circuit architectures [23][24][25][26][27][28][29], and improving the efficiency of thermodynamic machines [30][31][32].…”