Quantum State Characterization for Benchmarking NISQ Devices

Zoom Seminar presentation by Dr. Ahmad Farooq

Reliable and efficient reconstruction of the quantum states under the processing of noisy measurement data is a vital tool in fundamental and applied quantum information sciences owing to communication, sensing, and computing. Noisy intermediate-scale quantum (NISQ) computers are expected to perform tasks that surpass the capability of the most powerful classical computers available today. However, noisy quantum gates and decoherence limit a clean enough improvement over the existing classical computing devices for complex algorithms. With the advent of the NISQ era, we come across a paradox: How will we validate a quantum device confirming that it is producing the desired result? For characterization, certification, and benchmarking of these noisy devices, quantum state tomography comes into play, which is the gold standard for reconstructing a quantum state. The quantum state tomography problem becomes intractable due to an exponential growth of the system size with an increase in the number of qubits under consideration. Adaptive learning based on the simultaneous perturbation stochastic approximation algorithm for the tomography of general quantum states is proposed. The salient features of this algorithm are efficient post-processing in the dimension d of the state, robustness against measurement, and channel noise. Most of the tomography algorithms employ entangled bases in the measurement setting. To implement entangled bases on NISQ devices, we apply sets of unitary transformations followed by the computational basis measurement. The controlled-NOT (CNOT) gate is an essential transformation required for implementing these sets of entangled measurements. Implementing a CNOT gate on quantum devices introduces a larger error due to experimental difficulties. Moreover, the circuit depth is quite high for a large number of qubit systems, which results in the decoherence of qubits. The introduction of local basis measurement for state reconstruction can be a massive catalyst for benchmarking quantum devices. For this purpose, 2n+1 local basis measurements, which scale linearly with the number of qubits, are introduced to perfectly reconstruct the unknown quantum state.

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