Error mitiga­tion inclu­ding noise learning at the software and hardware levels

Error mitiga­tion refers to techni­ques that reduce the impact of noise in quantum compu­ta­ti­ons without requi­ring full quantum error correc­tion (QEC). Unlike QEC, these methods do not need additio­nal qubits or fault-tolerant opera­ti­ons and are thus parti­cu­larly useful and neces­sary in the realm of NISQ hardware. The sources of noise comprise gate errors, decohe­rence leading to a loss of quantum infor­ma­tion, readout errors that cause measu­re­ment bit-flips and cross­talk due to unwan­ted qubit inter­ac­tions. In the context of QML, gate errors may lead to quantum kernel Gram matri­ces that are no longer positive semi-definite or corrupted parame­ter optimiza­tion due to noisy gradi­ent estima­tes. Error mitiga­tion techni­ques are then requi­red to restore the kernel semi-positive-defini­ten­ess or to allow for unbia­sed cost function evalua­tions. However, the appli­ca­tion of many error mitiga­tion methods comes at the cost of sampling and circuit overhead and are thus only feasi­ble for shallow- to medium-sized circuits.