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Threshold Quantum State Tomography

Daniele Binosi, Diego Maragnano, Giovanni Garberoglio, Maurizio Dapor, Marco Liscidini

Published Jan 1, 2024• 0 citations
Publisher

Abstract

We introduce a new approach to quantum state tomography (QST) in which the number of measurements can be dramatically smaller than in traditional QST without compromising fidelity. We show experimental results up to 7 qubits.
DOI
10.1364/cleo_fs.2024.fm4r.3

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Quantum state tomography (QST) aims at reconstructing the state of a quantum system. However, in conventional QST, the number of measurements scales exponentially with the number of qubits. Here, we propose a QST protocol, in which the introduction of a threshold allows one to drastically reduce the number of measurements required for the reconstruction of the state density matrix without compromising the result accuracy. In addition, one can also use the same approach to reconstruct an approximated density matrix tailoring the number of measurements on the available resources. We experimentally demonstrate this protocol by performing the tomography of states up to 7 qubits. We show that our approach can lead to results in agreement with those obtained by QST even when the number of measurements is reduced by more than two orders of magnitude.
Quantum state tomography (QST) is a fundamental technique in quantum information science, aiming to reconstruct the density matrix of an unknown quantum state from experimental measurements. However, traditional QST methods often suffer from significant computational demands and are highly susceptible to measurement noise, hindering their practical application, particularly with near-term quantum computers. This work proposes a novel approach to QST utilizing variational quantum algorithms (VQAs). VQAs iteratively optimize a parameterized quantum circuit to minimize a cost function related to the fidelity between the desired state and the state predicted by the circuit. This approach dramatically reduces the number of required measurements and offers the potential for achieving high-fidelity state reconstruction with lower quantum resource requirements. We detail the theoretical framework, outlining the core algorithms and mathematical formulations. The key advantage lies in the ability to learn the state directly, mitigating the limitations of traditional methods. We explore the optimization landscape and discuss strategies for improving convergence and robustness. The results demonstrate a promising path toward scalable and robust QST on quantum devices.
Quantum state tomography (QST) is plagued by the ``curse of dimensionality'' due to the exponentially-scaled complexity in measurement and data post-processing. Efficient QST schemes for large-scale mixed states are currently missing. In this work, we propose an efficient and robust mixed-state tomography scheme based on the locally purified state ansatz. We demonstrate the efficiency and robustness of our scheme on various randomly initiated states with different purities. High tomography fidelity is achieved with much smaller numbers of positive-operator-valued measurement (POVM) bases than the conventional least-square (LS) method. On the superconducting quantum experimental circuit [Phys. Rev. Lett. 119, 180511 (2017)], our scheme accurately reconstructs the Greenberger-Horne-Zeilinger (GHZ) state and exhibits robustness to experimental noises. Specifically, we achieve the fidelity F≃0.92F \simeq 0.92F≃0.92 for the 10-qubit GHZ state with just Nm=500N_m = 500Nm​=500 POVM bases, which far outperforms the fidelity F≃0.85F \simeq 0.85F≃0.85 by the LS method using the full Nm=310=59049N_m = 3^{10} = 59049Nm​=310=59049 bases. Our work reveals the prospects of applying tensor network state ansatz and the machine learning approaches for efficient QST of many-body states.