Related papers: Certifying and learning local quantum Hamiltonians
Low-energy estimation and state preparation for general $k$-local Hamiltonians are fundamental challenges in quantum complexity theory. For constant relative accuracy, Buhrman et al. (PRL 2025) recently broke the natural Grover bound…
We show how quantum metrology protocols that seek to estimate the parameters of a Hamiltonian that exhibits a quantum phase transition can be efficiently simulated on an exponentially smaller quantum computer. Specifically, by exploiting…
Quantum process characterization is a fundamental task in quantum information processing, yet conventional methods, such as quantum process tomography, require prohibitive resources and lack scalability. Here, we introduce an efficient…
We present and experimentally implement a real-time protocol for calibrating the frequency of a resonantly driven qubit, achieving exponential scaling in calibration precision with the number of measurements, up to the limit imposed by…
The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation…
Learning the unknown interactions that govern a quantum system is crucial for quantum information processing, device benchmarking, and quantum sensing. The problem, known as Hamiltonian learning, is well understood under the assumption that…
We present efficient quantum algorithms for simulating time-dependent Hamiltonian evolution of general input states using an oracular model of a quantum computer. Our algorithms use either constant or adaptively chosen time steps and are…
With the development of quantum many-body simulator, Hamiltonian tomography has become an increasingly important technique for verification of quantum devices. Here we investigate recovering the Hamiltonians of two spin chains with 2-local…
The ground state energy and the free energy of Quantum Local Hamiltonians are fundamental quantities in quantum many-body physics, however, it is QMA-Hard to estimate them in general. In this paper, we develop new techniques to find…
We show that it is possible to uniquely reconstruct a generic many-body local Hamiltonian from a single pair of initial and final states related by time evolution with the Hamiltonian. We then propose a practical version of the protocol…
Estimating spectral gaps of quantum many-body Hamiltonians is a highly challenging computational task, even under assumptions of locality and translation-invariance. Yet, the quest for rigorous gap certificates is motivated by their broad…
Preparing thermal and ground states is an essential quantum algorithmic task for quantum simulation. In this work, we construct the first efficiently implementable and exactly detailed-balanced Lindbladian for Gibbs states of arbitrary…
Bayesian inference is a widely used technique for real-time characterization of quantum systems. It excels in experimental characterization in the low data regime, and when the measurements have degrees of freedom. A decisive factor for its…
We present an efficient quantum algorithm for simulating the evolution of a sparse Hamiltonian H for a given time t in terms of a procedure for computing the matrix entries of H. In particular, when H acts on n qubits, has at most a…
The efficient simulation of quantum dynamics and ground states is a central challenge in physics and a key frontier for quantum advantage. While short-time evolution in one-dimensional systems can often be simulated classically, extending…
We consider the problem of learning an $M$-sparse Hamiltonian and the related problem of Hamiltonian sparsity testing. Through a detailed analysis of Bell sampling, we reduce the total evolution time required by the state-of-the-art…
Learning the structure of the entanglement Hamiltonian (EH) is central to characterizing quantum many-body states in analog quantum simulation. We describe a protocol where spatial deformations of the many-body Hamiltonian, physically…
We give a classical $1/(qk+1)$-approximation for the maximum eigenvalue of a $k$-sparse fermionic Hamiltonian with strictly $q$-local terms, as well as a $1/(4k+1)$-approximation when the Hamiltonian has both $2$-local and $4$-local terms.…
An observer-based Hamiltonian identification algorithm for quantum systems is proposed. For the 2-level case an exponential convergence result based on averaging arguments and some relevant transformations is provided. The convergence for…
Here, we study quantitative homogenization of first-order convex Hamilton-Jacobi equations with $(u/\varepsilon)$-periodic Hamiltonians which typically appear in dislocation dynamics. Firstly, we establish the optimal convergence rate by…