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arXiv:2401.12864 · APL Quantum

A tailor-made quantum state tomography approach

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

Published Jul 26, 2024• 10 citations
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Abstract

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.

DOI
10.1063/5.0219143

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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 aims at reconstructing the state of a quantum system. The standard approach is based on a tomographically complete set of observables and a maximum likelihood estimation of the density matrix. However, the number of measurements scales exponentially with the number of qubits or qudits of the system. By leveraging some properties of any physical density matrix, we propose a method in which the number of necessary measurements depends on the state under investigation but without the need for any a priori information. In some cases, this can lead to a significant reduction of the resources necessary for state characterization.
Quantum state tomography (QST) is a crucial tool for characterizing quantum states. However, performing full QST becomes impractical for reconstructing multiqubit density matrices since datasets and computational costs grow exponentially with qubit number. To bypass full QST, we introduce selective and efficient QST (SEEQST)—a method that enables efficient estimation of multiple selected elements of an arbitrary multiqubit density matrix. We show that any N -qubit density matrix can be partitioned into 2 N disjoint subsets, each containing 2 N elements. With SEEQST, any such subset can be accurately estimated from just two experiments with only single-qubit measurements. The complexity for estimating any subset remains constant regardless of Hilbert-space dimension, so, if desired, SEEQST can reconstruct the full density matrix, using 2 N + 1 − 1 experiments, where standard methods would use 3 N experiments. We provide a circuit decomposition for the SEEQST experiments, demonstrating that their maximum circuit depth scales logarithmically with N assuming all-to-all connectivity.
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.
We propose an efficient quantum state tomography method inspired by compressed sensing and threshold quantum state tomography that can drastically reduce the number of measurement settings to reconstruct the density matrix of an NNN-qudit system. We validate our algorithm with demonstrations on IBMQ and show the efficient and accurate reconstruction of $N\ensuremath{\le}7$ qubit systems, reproducing GHZ, W\mathrm{W}W, and random states with O(1)O(1)O(1), O(N2)O({N}^{2})O(N2), and O(N)O(N)O(N) settings.
Quantum state tomography (QST) is a crucial technique for characterizing the state of quantum systems. However, traditional QST requires a large number of measurements, leading to significant experimental overhead in terms of time, resources, and data acquisition. This work proposes a novel approach to QST by leveraging compressed sensing (CS) techniques. CS allows for accurate reconstruction of the quantum state from a significantly reduced set of measurements, thereby mitigating the experimental burden. We employ sparsity regularization, a key component of CS, to minimize the number of measurements needed. The theoretical framework and the underlying principles are presented, focusing on the mathematical formulation of the problem and the optimization strategies involved. This method offers a pathway to more efficient and cost-effective QST, particularly for complex quantum states or when limited experimental resources are available. We demonstrate the potential of this approach through a detailed mathematical analysis.