Oumarou Oumarou

Quantum Krylov subspace diagonalization is a prominent candidate for early fault-tolerant quantum simulation of many-body and molecular systems, but so far, the focus has been mainly on computing ground-state energies. We go beyond this by deriving analytical first-order derivatives for quantum Krylov methods and show how to obtain relaxed one and two particle reduced density matrices of the Krylov eigenstates. The direct approach to measuring these matrices requires a number of distinct measurement that scales quadratically with the Krylov dimension D. Here, we show how to reduce this scaling to a constant. This is done by leveraging quantum signal processing to prepare Krylov eigenstates, including excited states, in depth linear in D. We also compare several measurement schemes for efficiently obtaining the expectation value of an operator with states prepared using quantum signal processing. We validate our approach by computing the nuclear gradient of a small molecule and estimating its variance.

An important measure of the development of quantum computing platforms has been the simulation of increasingly complex physical systems. Before fault-tolerant quantum computing, robust error-mitigation strategies were necessary to continue this growth. Here, we validate recently introduced error-mitigation strategies that exploit the expectation that the ideal output of a quantum algorithm would be a pure state. We consider the task of simulating electron systems in the seniority-zero subspace where all electrons are paired with their opposite spin. This affords a computational stepping stone to a fully correlated model. We compare the performance of error mitigations on the basis of doubling quantum resources in time or in space on up to 20 qubits of a superconducting qubit quantum processor. We observe a reduction of error by one to two orders of magnitude below less sophisticated techniques such as postselection. We study how the gain from error mitigation scales with the system size and observe a polynomial suppression of error with increased resources. Extrapolation of our results indicates that substantial hardware improvements will be required for classically intractable variational chemistry simulations.

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.