Imperfect measurements contribute greatly to errors in the state of the art quantum devices. Recently, various methods of characterization and mitigation of the readout noise were proposed. They usually work well in experiments involving only a few qubits. Yet, due to the exponential scaling of required resources, they are unfeasible to implement for larger systems.
In the first part of the talk, I will describe how to circumvent this curse of dimensionality and implement noise-mitigation efficiently in problems requiring estimation of multiple low-dimensional marginal probability distributions. I will start by introducing a correlated measurement noise model that can be efficiently described and characterized. Characterization of the model is done using the modified technique of Quantum Overlapping Tomography and standard Detector Tomography. I will also show that our noise model admits noise-mitigation on the level of marginal probability distributions. The noise-mitigation can be performed up to some controllable error arising from correlations in measurement noise and statistical fluctuations. At the end of the first part of the talk, I will discuss the results of the estimation of the ground state of multiple 2-local Hamiltonians performed experimentally on up to 11 qubits on IBM's and Rigetti's devices. The results show the effectiveness of our noise-mitigation strategy and confirm that our noise-model is accurate.
In the second part of the talk, I will describe how the readout noise affects the performance of the Quantum Approximate Optimization Algorithm (QAOA). QAOA is an example of a variational quantum algorithm which is one of the candidates for the demonstration of quantum speedup in near-term quantum devices. The algorithm requires simultaneous estimation of a number of few-body Hamiltonians and therefore is compatible with our error-mitigation scheme.
I will start by explaining that the measurement noise can affect QAOA in two ways. First, it can corrupt the total energy estimation in the optimization stage, which will lead the optimization to the wrong parameters region. Second, it can significantly corrupt the energy estimation at the end of the optimization, which leads to the wrong solution. Then, I will explain how noise-mitigation can reduce both effects. To support those claims, I will present results of exhaustive numerical simulations which indicate that for numerous problems, including random MAX 2SAT and Sherrington-Kirkpatrick model, the noise-mitigation improves the quality of optimization and final estimation in QAOA. Finally, I will discuss the sampling complexity of QAOA in the context of error-mitigation. In particular, I will show that estimators of error-mitigated local Hamiltonians are effectively uncorrelated for a broad class of states appearing in QAOA. This allows for a significant reduction of sample complexity of the problem of estimation of the total energy with the system size, even when readout error mitigation is used.
1. F.B. Maciejewski, Z. Zimborás, and M. Oszmaniec, Quantum 4, 257 (2020).
Filip Maciejewski and Michał Oszmaniec
Zoom meeting details
Topic: Quantum Information and Quantum Computing Working Group
Time: September 03, 2020, 4:00 PM Warsaw
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Meeting ID: 92227103826
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