The deployment of intermediate- and large-scale quantum devices necessitates the development of efficient full state tomographical techniques for quantum benchmarks. Here, we introduce a matrix filling-based method for tomography of pure quantum states, called the matrix-completion quantum state tomography. This method requires only 2n + 1 local Pauli operators and minimal post-processing for n-qubit states. Numerical results show that our method is highly efficient on superconducting real quantum devices and achieves better fidelity estimates of multiqubit quantum states as compared to contemporary pure state tomography methods. These desirable features of the matrix-completion quantum state tomography protocol make it suitable for the benchmarking of intermediate- and large-scale quantum devices dealing mainly with pure quantum states.
The deployment of intermediate- and large-scale quantum devices necessitates the development of efficient full state tomographical techniques for quantum benchmarks. Here, we introduce a matrix filling-based method for tomography of pure quantum states, called the matrix-completion quantum state tomography. This method requires only 2n + 1 local Pauli operators and minimal post-processing for n-qubit states. Numerical results show that our method is highly efficient on superconducting real quantum devices and achieves better fidelity estimates of multiqubit quantum states as compared to contemporary pure state tomography methods. These desirable features of the matrix-completion quantum state tomography protocol make it suitable for the benchmarking of intermediate- and large-scale quantum devices dealing mainly with pure quantum states.
This paper introduces a novel and efficient technique for quantum state estimation, coined as low-rank matrix-completion quantum state tomography for characterizing pure quantum states, as it requires only non-entangling bases and 2n+1 local Pauli operators. This significantly reduces the complexity of the process and increases the accuracy of the state estimation, as it eliminates the need for the entangling bases, which are experimentally difficult to implement on quantum devices. The required minimal post-processing, improved accuracy and efficacy of this matrix-completion-based method make it an ideal benchmarking tool for investigating the properties of quantum systems, enabling researchers to verify the accuracy of quantum devices, characterize their performance, and explore the underlying physics of quantum phenomena. Our numerical results demonstrate that this method outperforms contemporary techniques in its ability to accurately reconstruct multi-qubit quantum states on real quantum devices, making it an invaluable contribution to the field of quantum state characterization and an essential step toward the reliable deployment of intermediate- and large-scale quantum devices.
We propose a quantum tomography scheme for pure states which adopts machine learning methods, along with a built-in fidelity estimation approach to assess the reliability of the tomographic state. We prove the validity of the scheme theoretically and perform numerically simulated experiments on several typical target quantum states such as W, cluster and dimer states. We find that the required number of measurements to meet the convergence criterion does not grow exponentially in the number of qubits, thus the scheme achieves high efficiency that is crucial for large-scale quantum states tomography in a laboratory.
In quantum information transformation and quantum computation, the most critical issues are security and accuracy. These features, therefore, stimulate research on quantum state characterization. A characterization tool, quantum state tomography, reconstructs the density matrix of an unknown quantum state. Theoretically, reconstructing an unknown state using this method can be arbitrarily accurate. However, this is not so practical owing to the huge burden of measurements and data processing for large numbers of qubits. Even comprising an efficient estimator and a precise algorithm, an optimal tomographic framework can also be overburdened owing to the exponential growth of the measurements. Moreover, the consequential postprocessing of huge amounts of data challenges the capacity of computers. Thus, it is crucial to build an efficient framework that requires fewer measurements but yields an expected accuracy. To this end, we built a tomography schema by which only a few Pauli measurements enable an accurate tomographic reconstruction. Subsequently, this schema was verified as efficient and accurate through numerical simulations on the tomography of multiqubit quantum states. Furthermore, it was proven to be robust through numerical simulations on a noisy superconducting qubit system. Therefore, the tomography schema paves an alternative effective way to reconstruct the density matrix of a quantum state owing to its efficiency and accuracy, which are essential for quantum state tomography.
In quantum information transformation and quantum computation, the most critical issues are security and accuracy. These features, therefore, stimulate research on quantum state characterization. A characterization tool, Quantum state tomography, reconstructs the density matrix of an unknown quantum state. Theoretically, reconstructing an unknown state using this method can be arbitrarily accurate. However, this is less practical owing to the huge burden of measurements and data processing for large numbers of qubits. Even comprising an efficient estimator and a precise algorithm, an optimal tomographic framework can also be overburdened owing to the exponential growth of the measurements. Moreover, the consequential postprocessing of huge amounts of data challenges the capacity of computers. Thus, it is crucial to build an efficient framework that requires fewer measurements but yields an expected accuracy. To this end, we built a tomography schema by which only a few Pauli measurements enable an accurate tomographic reconstruction. Subsequently, this schema was verified as efficient and accurate through numerical simulations on the tomography of multi-qubit quantum states. Furthermore, this schema was proven to be robust through numerical simulations on a noisy superconducting qubit system. Therefore, the tomography schema paves an alternatively effective way to reconstruct the density matrix of a quantum state owing to its efficiency and accuracy, which are essential for quantum state tomography.
ventional full state tomography reaches its limit already for a few qubits and hence novel methods for the verification and benchmarking of quantum devices are called for. We show how the complete reconstruction of density matrices is possible even if one relies only on local information about the state. This results in an experimental effort that is linear in the number of qubits and efficient post-processing – in stark contrast to the exponential scaling of standard tomography. Whenever full tomography is not needed but instead less information required, one would expect that even fewer measurements suffice. Taking entanglement content of solid state samples and bosons in lattices as an example, we show how it may be quantified unconditionally using already routinely performed measurements only.
Quantum state tomography is an essential tool for the characterization and verification of quantum states. However, as it cannot be directly applied to systems with more than a few qubits, efficient tomography of larger states on mid-sized quantum devices remains an important challenge in quantum computing. We develop a tomography approach that requires moderate computational and quantum resources for the tomography of states that can be approximated by Gibbs states of local Hamiltonians. The proposed method, Hamiltonian Learning Tomography, uses a Hamiltonian learning algorithm to get a parametrized ansatz for the Gibbs Hamiltonian, and optimizes it with respect to the results of local measurements. We demonstrate the utility of this method with a high fidelity reconstruction of the density matrix of 4 to 10 qubits in a Gibbs state of the transverse-field Ising model, in numerical simulations as well as in experiments on IBM Quantum superconducting devices accessed via the cloud. Code implementation of the our method is freely available as an open source software in Python.