Joint Quantum-State and Measurement Tomography with Incomplete Measurements

Abstract

Estimation of quantum states and measurements is crucial for the implementation of quantum information protocols. The standard method for each is quantum tomography. However, quantum tomography suffers from systematic errors caused by imperfect knowledge of the system. We present a procedure to simultaneously characterize quantum states and measurements that mitigates systematic errors by use of a single high-fidelity state preparation and a limited set of high-fidelity unitary operations. Such states and operations are typical of many state-of-the-art systems. For this situation we design a set of experiments and an optimization algorithm that alternates between maximizing the likelihood with respect to the states and measurements to produce estimates of each. In some cases, the procedure does not enable unique estimation of the states. For these cases, we show how one may identify a set of density matrices compatible with the measurements and use a semi-definite program to place bounds on the state's expectation values. We demonstrate the procedure on data from a simulated experiment with two trapped ions.

arXiv commentupdated to be almost identical to published version. 13 two-column pages, 5 figures

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Cited by in corpus (25)

• Gate Set Tomography
• Cross-Platform Verification of Intermediate Scale Quantum Devices
• Learning Quantum Systems
• Quantum gate teleportation between separated qubits in a trapped-ion processor
• Detector Tomography on IBM 5-qubit Quantum Computers and Mitigation of Imperfect Measurement
• Robust and resource-efficient microwave near-field entangling ${}^9$Be${}^{+}$ gate
• Quantum amplification of boson-mediated interactions
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• Joint Quantum-State and Measurement Tomography with Incomplete Measurements
• Ground-state energy estimation of the water molecule on a trapped ion quantum computer
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• Direct Characterization of Quantum Measurements using Weak Values
• Self-consistent quantum measurement tomography based on semidefinite programming
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• Quantum tomography of noisy ion-based qudits
• Quantum reservoir computing for photonic entanglement witnessing
• Quantum tomography of Rydberg atom graphs by configurable ancillas
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• Universal framework for simultaneous tomography of quantum states and SPAM noise
• Unitary quantum process tomography with unreliable pure input states
• Experimental Demonstration of Swift Analytical Universal Control over Nearby Transitions
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• Tomography of a single-atom-resolved detector in the presence of shot-to-shot number fluctuations