Quantum Bayesian Error Mitigation Employing Poisson Modelling over the Hamming Spectrum for Quantum Error Mitigation

• URL: http://arxiv.org/abs/2207.07237v2
• Date: Fri, 9 Sep 2022 17:27:06 GMT
• Title: Quantum Bayesian Error Mitigation Employing Poisson Modelling over the Hamming Spectrum for Quantum Error Mitigation
• Authors: Samuel Stein, Nathan Wiebe, Yufei Ding, James Ang, Ang Li
• Abstract summary: In situ error mitigation and post induction error mitigation are promising fields of research within the quantum algorithm scene. We show that such a correlation structure is not only local but extends certain non local clustering patterns. We develop an iterative algorithm over the generated Bayesian network state graph for post induction error mitigation.
• Score: 16.130519404795407
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum computing technology has grown rapidly in recent years, with new technologies being explored, error rates being reduced, and quantum processors qubit capacity growing. 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 (in situ error mitigation) and Quantum Error Mitigation (post induction error mitigation) are promising fields of research within the quantum algorithm scene, aiming to alleviate quantum errors, increasing the overall fidelity and hence the overall quality of circuit induction. Earlier this year, a pioneering work, namely HAMMER, published in ASPLOS 22 demonstrated the existence of a latent structure regarding post circuit induction errors when mapping to the Hamming spectrum. However, they intuitively assumed that errors occur in local clusters, and that at higher average Hamming distances this structure falls away. In this work, we show that such a correlation structure is not only local but extends certain non local clustering patterns which can be precisely described by a Poisson distribution model taking the input circuit, the device run time status (i. e. calibration statistics), and qubit topology into consideration. Using this quantum error characterizing model, we developed an iterative algorithm over the generated Bayesian network state graph for post induction error mitigation. Thanks to more precise modeling of the error distribution latent structure and the new iterative method, our Q Beep approach provides state of the art performance and can boost circuit execution fidelity by up to 234.6% on Bernstein Vazirani circuits and on average 71.0% on QAOA solution quality, using 16 practical IBMQ quantum processors. For other benchmarks such as those in QASMBench, the fidelity improvement is up to 17.8%.

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