Efficiently improving the performance of noisy quantum computers

Abstract

Using near-term quantum computers to achieve a quantum advantage requires efficient strategies to improve the performance of the noisy quantum devices presently available. We develop and experimentally validate two efficient error mitigation protocols named "Noiseless Output Extrapolation" and "Pauli Error Cancellation" that can drastically enhance the performance of quantum circuits composed of noisy cycles of gates. By combining popular mitigation strategies such as probabilistic error cancellation and noise amplification with efficient noise reconstruction methods, our protocols can mitigate a wide range of noise processes that do not satisfy the assumptions underlying existing mitigation protocols, including non-local and gate-dependent processes. We test our protocols on a four-qubit superconducting processor at the Advanced Quantum Testbed. We observe significant improvements in the performance of both structured and random circuits, with up to 86% improvement in variation distance over the unmitigated outputs. Our experiments demonstrate the effectiveness of our protocols, as well as their practicality for current hardware platforms.

The learnability of Pauli noise

“…and curve fitting gives √ λ IZ λ ZZ (similar results have been obtained in [9,[21][22][23]). To learn λ IZ , we may consider applying the same technique in Fig.…”

“…Applying this to the data of IZ and ZZ in Fig. 6 (a), we have λ S IZ /λ S ZZ ≤ 0.9879 (23). If we make a physical assumption that the state preparation noise is a random bit-flip during the qubit initialization, one can conclude the bit-flip rate on the first qubit is lower bounded by 0.61(12)% [34].…”

“…a is unlearnable if and only if G changes the pattern of P a , i.e., pt(G(P a )) = pt(P a ). The fact that certain Pauli fidelity is SPAM-robustly unlearnable is observed in some recent works [9,[21][22][23], under the name of "degeneracy". Our work is the first to give a rigorous argument for this by establishing connection to gate set tomography.…”

“…However, even under this simplified setting of Pauli noise learning, all prior experimental attempts can only partially characterize the noise channel of a single CNOT/CZ gate [21][22][23], which only has 15 degrees of freedom. A natural question is whether this limitation is caused by the fundamental unlearnability of the noise channel, and if so, which part of the noise channel and how many degrees of freedom among the 15 are unlearnable?…”

“…In addition, we also explore ways to overcome the unlearnability barrier. It has been recognized that the unlearnability does not apply if the initial state |0 ⊗n can be prepared perfectly [15,23], and it has been suggested that state preparation noise could be much smaller than gate and/or measurement noise in practice [26][27][28], which would make gate noise fully learnable up to small error. We develop an algorithm based on cycle benchmarking that fully learns gate-dependent Pauli noise channel assuming perfect initial state preparation, and experimentally demonstrate the method on IBM's CNOT gate.…”