Quantum State Modeling for System Engineers

Sample-based Krylov Quantum Diagonalization by IBM https://lnkd.in/eEBBt7jJ Abstract: Approximating the ground state of many-body systems is a key computational bottleneck underlying important applications in physics and chemistry. It has long been viewed as a promising application for quantum computers. The most widely known quantum algorithm for ground state approximation, quantum phase estimation, is out of reach of current quantum processors due to its high circuit-depths. Quantum diagonalization algorithms based on subspaces represent alternatives to phase estimation, which are feasible for pre-fault-tolerant and early-fault-tolerant quantum computers. Here, we introduce a quantum diagonalization algorithm which combines two key ideas on quantum subspaces: a classical diagonalization based on quantum samples, and subspaces constructed with quantum Krylov states. We prove that our algorithm converges in polynomial time under the working assumptions of Krylov quantum diagonalization and sparseness of the ground state. We then show numerical investigations of lattice Hamiltonians, which indicate that our method can outperform existing Krylov quantum diagonalization in the presence of shot noise, making our approach well-suited for near-term quantum devices. Finally, we carry out the largest ground-state quantum simulation of the single-impurity Anderson model on a system with 41 bath sites, using 85 qubits and up to 6·103 two-qubit gates on a Heron quantum processor, showing excellent agreement with density matrix renormalization group calculations. 

Dual-capability machine learning models for quantum Hamiltonian parameter estimation and dynamics prediction Quantum computing increasingly relies on accurately knowing a system’s Hamiltonian (the mathematical description of its energy and interactions), and on predicting how quantum states evolve over time. Both are indispensable for applications like quantum error correction, control protocols, and simulations. Yet, determining Hamiltonian parameters from experimental data is challenging in large or noisy systems. Simultaneously, the high-dimensional nature of quantum states complicates dynamical forecasts. An et al. propose a single machine learning framework that can solve both tasks—learning time-dependent Hamiltonian parameters from local observable measurements and predicting those same observables given the Hamiltonian parameters. The authors use a recurrent neural network based on long short-term memory (LSTM) units, which efficiently handle time-series data, and crucially augment it with an encoding network to handle various initial states. This architecture allows the same model to perform two modes: (1) “forward” mode, which uses the Hamiltonian’s time dependence to predict local observables, and (2) “inverse” mode, which infers unknown Hamiltonian parameters by observing the time evolution of those observables. The training datasets are generated from quantum many-body simulations with random driving fields or random parameters, letting the network learn a general mapping. They demonstrate robust performance under different system sizes, noise regimes, and both integrable and nonintegrable dynamics. Finally, they validate the approach experimentally on a nuclear magnetic resonance (NMR) setup for predicting observables and on a superconducting quantum chip for deducing unknown detuning parameters. Through both simulation and real-device experiments, the model maintained high accuracy: it correctly matched local spin dynamics well beyond its training window and inferred Hamiltonian parameters with minimal error. On an NMR device, it accurately predicted the trajectory of two qubits over extended times. On a superconducting qubit platform, it reliably extracted time-varying detuning strengths that otherwise hinder quantum logic gates. This dual-capability framework opens avenues for streamlined data-driven methods in quantum system diagnostics and real-time feedback, benefiting tasks like parameter estimation, noise characterization, and control optimization in quantum information processing. Paper: https://lnkd.in/dPJxDY7x #MachineLearning #QuantumHamiltonian #QuantumDynamics #RecurrentNeuralNetworks #QuantumControl #ParameterEstimation #NMR #SuperconductingQubits #QuantumComputing #LongShortTermMemory #ManyBodyPhysics #QuantumSimulation #DeepLearning #AIforScience #Research

Quantum State Estimation - Pleased to share our newly accepted paper entitled "Efficient Quantum State Estimation with Low-rank Matrix Completion" on EPJ Quantum Technology (Springer) Quantum state tomography is essential for reconstructing the quantum states of a system, a critical step in quantum computing and information processing. However, the primary challenge lies in the exponential scaling of required measurements with the system size (d²), where d is the dimension, making it impractical for large systems. To address this, we have developed efficient low-rank approximation techniques that reduce the number of measurements to approximately 2n+1, where n is the number of qubits. These techniques use local Pauli basis measurements instead of entangled basis measurements, which are easier to prepare and implement. Implementing entangled basis measurements on real quantum hardware is challenging due to noise and the complexity of two-qubit gates. The implications are profound for benchmarking quantum computers. With fewer measurements required, it becomes feasible to efficiently and accurately characterize and verify the performance of larger quantum systems. This breakthrough accelerates the development and scaling of utility-scale quantum computers, bringing us closer to realizing their full potential. Shehbaz Tariq