We illustrate the predictive ability of our model by numerical simulations for small molecules with and without noise inevitable in near-term quantum computers. The results show that our scheme reproduces well the first and second excitation energies as well as the transition dipole moment between the ground states and excited states only from the ground states as inputs. We expect our contribution will enhance the applications of quantum computers in the study of quantum chemistry and quantum materials.Ĭlassical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over more traditional methods have not been firmly established. In this work, we prove that classical ML algorithms can efficiently predict ground state properties of gapped Hamiltonians in finite spatial dimensions, after learning from data obtained by measuring other Hamiltonians in the same quantum phase of matter. In contrast, under widely accepted complexity theory assumptions, classical algorithms that do not learn from data cannot achieve the same guarantee. We also prove that classical ML algorithms can efficiently classify a wide range of quantum phases of matter. Our arguments are based on the concept of a classical shadow, a succinct classical description of a many-body quantum state that can be constructed in feasible quantum experiments and be used to predict many properties of the state.
Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, 2D random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases. The variational quantum eigensolver (VQE) is one of the most promising algorithms to find eigenstates of a given Hamiltonian on noisy intermediate-scale quantum devices (NISQ). The practical realization is limited by the complexity of quantum circuits. Here we present an approach to reduce quantum circuit complexity in VQE for electronic structure calculations. Our ClusterVQE algorithm splits the initial qubit space into clusters which are further distributed on individual (shallower) quantum circuits. The clusters are obtained based on mutual information reflecting maximal entanglement between qubits, whereas inter-cluster correlation is taken into account via a new “dressed” Hamiltonian. ClusterVQE therefore allows exact simulation of the problem by using fewer qubits and shallower circuit depth at the cost of additional classical resources, making it a potential leader for quantum chemistry simulations on NISQ devices.
Proof-of-principle demonstrations are presented for several molecular systems based on quantum simulators as well as IBM quantum devices.Īccurate molecular force fields are of paramount importance for the efficient implementation of molecular dynamics techniques at large scales.
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