Tailored and Externally Corrected Coupled Cluster with Quantum Inputs.

We propose to use wave function overlaps obtained from a quantum computer as inputs for the classical split-amplitude techniques, tailored and externally corrected coupled cluster, to achieve balanced treatment of static and dynamic correlation effects in molecular electronic structure simulations. By combining insights from statistical properties of matchgate shadows, which are used to measure quantum trial state overlaps, with classical correlation diagnostics, we can provide quantum resource estimates well into the classically no longer exactly solvable regime. We find that rather imperfect wave functions and remarkably low shot counts are sufficient to cure qualitative failures of plain coupled cluster singles doubles and to obtain chemically precise dynamic correlation energy corrections. We provide insights into which wave function preparation schemes have a chance of yielding quantum advantage, and we test our proposed method using overlaps measured on Google's Sycamore device.

Reducing the Runtime of Fault-Tolerant Quantum Simulations in Chemistry through Symmetry-Compressed Double Factorization.

Quantum phase estimation based on qubitization is the state-of-the-art fault-tolerant quantum algorithm for computing ground-state energies in chemical applications. In this context, the 1-norm of the Hamiltonian plays a fundamental role in determining the total number of required iterations and also the overall computational cost. In this work, we introduce the symmetry-compressed double factorization (SCDF) approach, which combines a CDF of the Hamiltonian with the symmetry shift technique, significantly reducing the 1-norm value. The effectiveness of this approach is demonstrated numerically by considering various benchmark systems, including the FeMoco molecule, cytochrome P450, and hydrogen chains of different sizes. To compare the efficiency of SCDF to other methods in absolute terms, we estimate Toffoli gate requirements, which dominate the execution time on fault-tolerant quantum computers. For the systems considered here, SCDF leads to a sizable reduction of the Toffoli gate count in comparison to other variants of DF or even tensor hypercontraction, which is usually regarded as the most efficient approach for qubitization.

Estimation of Electrostatic Interaction Energies on a Trapped-Ion Quantum Computer.

We present the first hardware implementation of electrostatic interaction energies by using a trapped-ion quantum computer. As test system for our computation, we focus on the reduction of NO to N2O catalyzed by a nitric oxide reductase (NOR). The quantum computer is used to generate an approximate ground state within the NOR active space. To efficiently measure the necessary one-particle density matrices, we incorporate fermionic basis rotations into the quantum circuit without extending the circuit length, laying the groundwork for further efficient measurement routines using factorizations. Measurements in the computational basis are then used as inputs for computing the electrostatic interaction energies on a classical computer. Our experimental results strongly agree with classical noise-less simulations of the same circuits, finding electrostatic interaction energies within chemical accuracy despite hardware noise. This work shows that algorithms tailored to specific observables of interest, such as interaction energies, may require significantly fewer quantum resources than individual ground state energies would require in the straightforward supermolecular approach.

Efficient quantum analytic nuclear gradients with double factorization.

Efficient representations of the Hamiltonian, such as double factorization, drastically reduce the circuit depth or the number of repetitions in error corrected and noisy intermediate-scale quantum (NISQ) algorithms for chemistry. We report a Lagrangian-based approach for evaluating relaxed one- and two-particle reduced density matrices from double factorized Hamiltonians, unlocking efficiency improvements in computing the nuclear gradient and related derivative properties. We demonstrate the accuracy and feasibility of our Lagrangian-based approach to recover all off-diagonal density matrix elements in classically simulated examples with up to 327 quantum and 18 470 total atoms in QM/MM simulations with modest-sized quantum active spaces. We show this in the context of the variational quantum eigensolver in case studies, such as transition state optimization, ab initio molecular dynamics simulation, and energy minimization of large molecular systems.