Estimating quantum state properties is essential across a wide range of applications, from studying quantum many-body physics to benchmarking quantum hardware. We present Qurrium, a Python package built on Qiskit that implements randomized measurement protocols for estimating purity, second-order Rényi entropy, expectation values of Pauli observables, and state overlap. In this paper, we focus on the classical shadow protocol and demonstrate two workflows in Qurrium. One is the end-to-end workflow that integrates quantum circuit preparation, simulation, measurement, and analysis. The other is the standalone estimation workflow that accepts pre-collected measurement data from any hardware platform in Qurrium's data format. We demonstrate both workflows through examples of a cluster state and an Ising time-evolved state. Furthermore, we report results obtained from a superconducting quantum processor developed by Academia Sinica and analyzed using the standalone estimation workflow. Qurrium is built on Qiskit, the dominant framework in quantum computing software, making it directly accessible to the large community of researchers already working with Qiskit. The source code is openly available at https://github.com/qurrium/qurrium and the example code is provided at https://github.com/qurrium/classical-shadow-examples.
Estimating quantum state properties is essential across a wide range of applications, from studying quantum many-body physics to benchmarking quantum hardware. We present Qurrium, a Python package built on Qiskit that implements randomized measurement protocols for estimating purity, second-order Rényi entropy, expectation values of Pauli observables, and state overlap. In this paper, we focus on the classical shadow protocol and demonstrate two workflows in Qurrium. One is the end-to-end workflow that integrates quantum circuit preparation, simulation, measurement, and analysis. The other is the standalone estimation workflow that accepts pre-collected measurement data from any hardware platform in Qurrium's data format. We demonstrate both workflows through examples of a cluster state and an Ising time-evolved state. Furthermore, we report results obtained from a superconducting quantum processor developed by Academia Sinica and analyzed using the standalone estimation workflow. Qurrium is built on Qiskit, the dominant framework in quantum computing software, making it directly accessible to the large community of researchers already working with Qiskit. The source code is openly available at https://github.com/qurrium/qurrium and the example code is provided at https://github.com/qurrium/classical-shadow-examples.
We introduce RandomMeas.jl , a modular and high-performance open-source software package written in Julia for implementing and analyzing randomized measurement protocols in quantum computing. Randomized measurements provide a powerful framework for extracting properties of quantum states and processes such as expectation values, entanglement, and fidelities using simple experimental procedures combined with classical post-processing, most prominently via the classical shadow formalism. RandomMeas.jl covers the full randomized measurement workflow, from the generation of measurement settings for use on a quantum computer, the optional classical simulation of randomized measurements with tensor networks, to a suite of estimators for physical properties based on classical shadows. The package includes advanced features such as robust and shallow shadow techniques, batch estimators, and built-in statistical uncertainty estimation. Its unified, composable design enables the scalable application and further development of randomized measurements protocols across theoretical and experimental contexts.
We present qlbm , a Python software package designed to facilitate the development, simulation, and analysis of Quantum Lattice Boltzmann Methods (QBMs). qlbm is a modular framework that introduces a quantum component abstraction hierarchy tailored to the implementation of novel QBMs. The framework interfaces with state-of-the-art quantum software infrastructure to enable efficient simulation and validation pipelines, and leverages novel execution and pre-processing techniques that significantly reduce the computational resources required to develop quantum circuits. We demonstrate the versatility of the software by showcasing multiple QBMs in 2D and 3D with complex boundary conditions, integrated within automated benchmarking utilities. Accompanying the source code are extensive test suites, thorough online documentation resources, analysis tools, visualization methods, and demos that aim to increase the accessibility of QBMs while encouraging reproducibility and collaboration. Program summary Program Title: qlbm CPC Library link to program files: https://doi.org/10.17632/28hkvsg7p2.1 Developer's repository link: https://github.com/QCFD-Lab/qlbm Licensing provisions: MPL-2.0 Programming language: Python3 Supplementary material: The documentation of is available at https://qcfd-lab.github.io/qlbm/ . Nature of problem: The advent of quantum algorithms for computational fluid dynamics brings with it challenges that are new to the established field of computational physics. These challenges include the lack of standardized implementations of the still nascent quantum methods, the intense computational demands of developing and simulating quantum algorithms on hardware available today, and the absence of tools that integrate novel developments into established infrastructure. Because of these current limitations, physicists and mathematicians expend superfluous resources on tasks that more mature computational physics branches have surmounted long ago. Solution method: QLBM is a software package that provides an end-to-end development environment for quantum lattice Boltzmann methods. The modular design and flexible quantum circuit library provide a base for extending and generalizing quantum algorithms. Performance enhancements exploit the paradigm of quantum computing simulations to accelerate the speed at which researchers can verify the validity of their methods. Its integration with state-of-the-art quantum computing software and visualization tools increases the algorithms' accesibility. These features allow QLBM to effectively generate, simulate, and analyze quantum circuits for 2D and 3D computational fluid dynamics problems.
Accurately estimating expectation values of quantum observables with as few measurements as possible is crucial to many quantum computing applications. We introduce a framework that covers many of existing measurement strategies and introduce heuristics that can be used to enhance randomized schemes, including those based on Pauli grouping with inverse probability weighting and variants of the classical shadow algorithm. We show how to maximize information gain from such schemes, while carefully optimizing the distribution of possible measurements, and show that simple grouping algorithms can get close to, and in some cases exceed, state-of-the-art accuracy for unbiased estimation of expectation values on a standard quantum chemistry benchmark. We show how these randomized methods may be compared to more recent measurement schemes, such as shadow grouping, derandomized shadow, and overlapped grouping measurement, we show how the same strategies can be used to augment these schemes, and we demonstrate that we can reduce measurement costs by up to a factor of two by allowing Clifford measurement circuits for otherwise Clifford-less methods.
Improving the performance of quantum algorithms is a fundamental task to achieve quantum advantage. In many cases, extracting information from quantum systems poses an important challenge for practical implementations of real-world quantum computers, given the high resource cost of performing state tomography. In this scenario, randomized measurements have emerged as a promising tool. In particular, the classical shadow protocol allows one to retrieve expected values of low-weight Pauli observables by performing only local measurements. In this paper, we present an implementation of the recently introduced feedback-based algorithm for quantum optimization using the Ket quantum programming platform to solve the MaxCut optimization problem. We employ classical shadows for the feedback routine of parameter estimation and compare this approach with the direct estimation of observables. Our results show that depending on the graph geometry of the MaxCut problem, the number of measurements required to estimate expected values of observables with classical shadows can be up to 16 times lower than with direct-observable estimation. Furthermore, by analyzing complete graphs, we numerically confirm logarithmic growth in the required number of measurements relative to the number of observables, reinforcing that classical shadows can be a useful tool for estimating low-locality Pauli observables in quantum algorithms.
We propose ShadowGPT, a novel approach for solving quantum many-body problems by learning from randomized measurement data collected from quantum experiments. The model is a generative pretrained transformer (GPT) trained on simulated classical shadow data of ground states of quantum Hamiltonians, obtained through randomized Pauli measurements. Once trained, the model can predict a range of ground state properties across the Hamiltonian parameter space. We demonstrate its effectiveness on the transverse-field Ising model and the Z2×Z2 cluster-Ising model, accurately predicting ground state energy, correlation functions, and entanglement entropy. This approach highlights the potential of combining quantum data with classical machine learning to address complex quantum many-body challenges.
QuTiP, the Quantum Toolbox in Python (Johansson et al., 2012, Johansson et al., 2013), has been at the forefront of open-source quantum software for the past 13 years. It is used as a research, teaching, and industrial tool, and has been downloaded millions of times by users around the world. Here we introduce the latest developments in QuTiP v5, which are set to have a large impact on the future of QuTiP and enable it to be a modern, continuously developed and popular tool for another decade and more. We summarize the code design and fundamental data layer changes as well as efficiency improvements, new solvers, applications to quantum circuits with QuTiP-QIP, and new quantum control tools with QuTiP-QOC. Additional flexibility in the data layer underlying all “quantum objects” in QuTiP allows us to harness the power of state-of-the-art data formats and packages like JAX, CuPy, and more. We explain these new features with a series of both well-known and new examples. The code for these examples is available in a static form on GitHub ( https://github.com/qutip/qutip-paper-v5-examples ) and as continuously updated and documented notebooks in the qutip-tutorials package ( https://github.com/qutip/qutip-tutorials ).