Quantum Bayesian Error Mitigation Employing Poisson Modelling over the
  Hamming Spectrum for Quantum Error Mitigation
The field of quantum computing has experienced a rapid expansion in recent
years, with ongoing exploration of new technologies, a decrease in error rates,
and a growth in the number of qubits available in quantum processors. However,
near-term quantum algorithms are still unable to be induced without compounding
consequential levels of noise, leading to non-trivial erroneous results.
Quantum Error Correction and Mitigation are rapidly advancing areas of research
in the quantum computing landscape, with a goal of reducing errors. IBM has
recently emphasized that Quantum Error Mitigation is the key to unlocking the
full potential of quantum computing. A recent work, namely HAMMER, demonstrated
the existence of a latent structure regarding post-circuit induction errors
when mapping to the Hamming spectrum. However, they assumed that errors occur
solely in local clusters, whereas we observe that at higher average Hamming
distances this structure falls away. Our study demonstrates that the correlated
structure is not just limited to local patterns, but it also encompasses
certain non-local clustering patterns that can be accurately characterized
through a Poisson distribution model. This model takes into account the input
circuit, the current state of the device, including calibration statistics, and
the qubit topology. Using this quantum error characterizing model, we developed
an iterative algorithm over the generated Bayesian network state-graph for
post-induction error mitigation. Our Q-Beep approach delivers state-of-the-art
results, thanks to its problem-aware modeling of the error distribution's
underlying structure and the implementation of an Bayesian network state-graph.
This has resulted in an increase of up to 234.6% in circuit execution accuracy
on BV circuits and an average improvement of 71.0% in the quality of QAOA
solutions when tested on 16 IBMQ quantum processors.
Samuel Stein Nathan Wiebe Yufei Ding James Ang Ang Li