Q-BEEP: Quantum Bayesian Error Mitigation Employing Poisson Modeling over the Hamming Spectrum

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 Quantum Error Mitigation are rapidly advancing areas of research in the quantum computing landscape, with a goal of reducing quantum errors. IBM has recently emphasized that Quantum Error Mitigation is the key to unlocking the full potential of quantum computing in a published article. 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-theart 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 Bernstein-Vazirani circuits and an average improvement of 71.0% in the quality of QAOA solutions when tested on 16 real-world IBMQ quantum processors. For other benchmarks such as those in QASMBench, a fidelity improvement of up to 17.8% is attained. Q-Beep is a light-weight post-processing technique that can be performed offline and remotely, making it a useful tool for quantum vendors to adopt and provide more reliable circuit induction results. Q-Beep will be released on GitHub.