Daily Papers

Excited electronic states are difficult to accurately and tractably model, particularly those exhibiting multiexcitonic character. Scalable single-reference excited state methods typically fail to describe such states as they suffer from the defects of the mean-field approximation and/or neglect higher-rank excitation operators. To address this, we derive the [T] perturbative correction to the quantum self-consistent equation-of-motion unitary coupled cluster singles and doubles (q-sc-EOM-UCCSD) method. The method captures triple excitation effects through a classical step of second-order in many-body perturbation theory following a q-sc-EOM-UCCSD calculation on a quantum computer. The perturbative correction developed has a O(N^7) classical computational time scaling. We incorporate [T] into a hybrid compute strategy wherein eigenvectors of the effective Hamiltonian from the hybrid quantum-classical q-sc-EOM-UCCSD algorithm are relayed to a classical computer which performs the postprocessing required for the [T] correction. The benefits of [T] are quantified in a benchmark covering a variety of electronically excited states of the isoelectronic CH^+ and BH molecules. We find that the addition of the [T] correction to both trotterized and full operator variants of q-sc-EOM-CCSD can offer dramatic improvements over baseline q-sc-EOM-UCCSD. Our assessment clearly demonstrates the importance of considering higher-rank excitation operators in q-sc-EOM-UCCSD, quantifies the overall success of the [T] correction, and discusses some of its limitations.

We introduce AQCtensor, a novel algorithm to produce short-depth quantum circuits from Matrix Product States (MPS). Our approach is specifically tailored to the preparation of quantum states generated from the time evolution of quantum many-body Hamiltonians. This tailored approach has two clear advantages over previous algorithms that were designed to map a generic MPS to a quantum circuit. First, we optimize all parameters of a parametric circuit at once using Approximate Quantum Compiling (AQC) - this is to be contrasted with other approaches based on locally optimizing a subset of circuit parameters and "sweeping" across the system. We introduce an optimization scheme to avoid the so-called ``orthogonality catastrophe" - i.e. the fact that the fidelity of two arbitrary quantum states decays exponentially with the number of qubits - that would otherwise render a global optimization of the circuit impractical. Second, the depth of our parametric circuit is constant in the number of qubits for a fixed simulation time and fixed error tolerance. This is to be contrasted with the linear circuit Ansatz used in generic algorithms whose depth scales linearly in the number of qubits. For simulation problems on 100 qubits, we show that AQCtensor thus achieves at least an order of magnitude reduction in the depth of the resulting optimized circuit, as compared with the best generic MPS to quantum circuit algorithms. We demonstrate our approach on simulation problems on Heisenberg-like Hamiltonians on up to 100 qubits and find optimized quantum circuits that have significantly reduced depth as compared to standard Trotterized circuits.