Chemical basis of Trotter-Suzuki errors in quantum chemistry simulation

Abstract

Although the simulation of quantum chemistry is one of the most anticipated applications of quantum computing, the scaling of known upper bounds on the complexity of these algorithms is daunting. Prior work has bounded errors due to Trotterization in terms of the norm of the error operator and analyzed scaling with respect to the number of spin orbitals. However, we find that these error bounds can be loose by up to sixteen orders of magnitude for some molecules. Furthermore, numerical results for small systems fail to reveal any clear correlation between ground state error and number of spin orbitals. We instead argue that chemical properties, such as the maximum nuclear charge in a molecule and the filling fraction of orbitals, can be decisive for determining the cost of a quantum simulation. Our analysis motivates several strategies to use classical processing to further reduce the required Trotter step size and to estimate the necessary number of steps, without requiring additional quantum resources. Finally, we demonstrate improved methods for state preparation techniques which are asymptotically superior to proposals in the simulation literature.

Error Sensitivity to Environmental Noise in Quantum Circuits for Chemical State Preparation

“…However, our aim is to characterize the effects of noise, so all errors are reported as the difference in error between the pristine (noiseless) and noisy circuits. As noted in the introduction, Trotter errors have been analyzed in several previous studies 12, [25][26][27] .…”

“…The approximation becomes exact as η approaches infinity. The effects of Trotterization order have been studied elsewhere 12,[25][26][27] . As the focus of the present study is the effects of decoherence, most of our quantum circuits estimate the molecular energy using a Trotter number of one.…”

“…Each of these methods seems to display practical benefits and drawbacks that lend them best to different situations. These and other studies have investigated gate ordering, gate cancellation, and the effects of various Trotterization approximations 26,27 .…”

Boson sampling for molecular vibronic spectra

“…Particularly significant is the exponential speed up achieved for the prime factorization of large numbers [3], a problem for which no efficient classical algorithm is currently known. Another attractive area for quantum computers is quantum simulation [4][5][6][7][8][9] where it has recently been shown that the dynamics of chemical reactions [10] as well as molecular electronic structure [11] are attractive applications for quantum devices. For all these instances, the realization of a quantum computer would challenge the Extended Church-Turing thesis (ECT), which claims that a Turing machine can efficiently simulate any physically realizable system, and even disprove it if prime factorization was finally demonstrated to be not efficiently solvable on classical machines.…”

Quantum Information and Computation for Chemistry

“…The following years saw a sequence of developments in analyzing the asymptotic scaling of resources needed for performing quantum chemical simulations on a quantum computer, in terms of the numbers of electrons and spin-orbitals. In spite of seemingly pessimistic initial estimates (Wecker et al, 2014a), developments in recent years have led to significant improvements in resource estimates for simulating quantum chemistry Poulin et al, 2015;Babbush et al, 2015a). Recently, Reiher and co-workers carried out a detailed study of the computational cost, including quantum error correction, for FeMoCo, a model of the nitrogenase enzyme (Reiher et al, 2016) that suggests that it is indeed feasible to employ future error-corrected architectures for the simulation of realistic chemical systems of scientific and industrial interest.…”