Hybrid quantum systems with different particle species are fundamental in quantum materials and quantum information science. In this work, we establish a rigorous theoretical framework proving that, given access to an unknown spin-boson type Hamiltonian, our algorithm achieves Heisenberg-limited estimation for all coupling parameters up to error
ε with a total evolution time
O(ε−1) using only
O(polylog(ε−1)) measurements. It is also robust against small state preparation and measurement errors. In addition, we provide an alternative algorithm based on distributed quantum sensing, which significantly reduces the evolution time per measurement. To validate our method, we demonstrate its efficiency in hybrid Hamiltonian learning and spectrum learning, with broad applications in AMO, condensed matter and high energy physics. Our results provide a scalable and robust framework for precision Hamiltonian characterization in hybrid quantum platforms.
An adiabatic quantum algorithm is essentially given by three elements: An initial Hamiltonian with known ground state, a problem Hamiltonian whose ground state corresponds to the solution of the given problem and an evolution schedule such that the adiabatic condition is satisfied. A correct choice of these elements is crucial for an efficient adiabatic quantum computation. In this paper we propose a hybrid quantum-classical algorithm to solve optimization problems with an adiabatic machine assuming restrictions on the class of available problem Hamiltonians. The scheme is based on repeated calls to the quantum machine into a classical iterative structure. In particular we present a technique to learn the encoding of a given optimization problem into a problem Hamiltonian and we prove the convergence of the algorithm. Moreover the output of the proposed algorithm can be used to learn efficient adiabatic algorithms from examples.
The Learning-With-Errors (LWE) problem is a fundamental computational challenge with implications for post-quantum cryptography and computational learning theory. Here we propose a quantum-classical hybrid algorithm with Ising model to address LWE, transforming it into the Shortest Vector Problem and using variable qubits to encode lattice vectors into an Ising Hamiltonian. By identifying low-energy Hamiltonian levels, the solution is extracted, making the method suitable for noisy intermediate-scale quantum devices. The required number of qubits is less than m(m + 1), where m is the number of samples. Our heuristic algorithm’s time complexity depends on the specific quantum eigensolver used to find low-energy levels, and the performance when using the Quantum Approximate Optimization Algorithm is investigated. We validate the algorithm by solving a 2-dimensional LWE problem on a 5-qubit quantum device, demonstrating its potential for solving meaningful LWE instances on near-term quantum devices. Evaluating the security of post-quantum cryptography is critically important to ensure resilience against quantum attacks. In this paper, the authors study a complex computational task at the heart of post-quantum cryptography with a hybrid quantum-classical algorithm, heuristically finding some advantages.