On the Chemical Basis of Trotter-Suzuki Errors in Quantum Chemistry Simulation

By Ryan Babbush, Jarrod R. McClean, Dave Wecker, Alán Aspuru-Guzik, Nathan Wiebe. 2014

183 citations recorded by the source corpus.

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 discretization of the time evolution (known as ``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 16 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 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.

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Citations in the corpus

Quantum algorithms to simulate many-body physics of correlated fermions. (2017, methodology): “In order to implement time evolution of the Hubbard model on a quantum computer, we decompose it into a product of available quantum gates based on the TrotterSuzuki formula [57, 58]; the desired accuracy determines the number of time steps [59, 60].”
Quantum Chemistry in the Age of Quantum Computing. (2018, unknown): “ ˆis the corresponding FGSs. For pure states i 1 0 and 2 = 1. Importantly, any expectation value of an operator can be computed from the covariance matrix as: iptr ˆ j 1 ::: j 2p = Pf jj 1:::;j 2p ; (50) where 1 j 1 <:::<j 2p2N, jj 1:::j 2p is the corresponding submatrix of and Pf( 1) = 2NN! P”
Hamiltonian Simulation in the Interaction Picture (2018, methodology): “This means that the cost of the simulation method is largely insensitive to the nuclear charges present in the simulation, unlike Trotter-Suzuki simulation methods which sensitively depend on the nuclear charges [24].”
Quantum information processing with superconducting circuits: a review (2016, methodology): “In practice one uses higher order Trotter formulas to minimise the errors [389, 396].”
Elucidating reaction mechanisms on quantum computers (2016, methodology): “[19] Ryan Babbush, Jarrod McClean, Dave Wecker, Alán Aspuru-Guzik, and Nathan Wiebe, “Chemical basis of trotter-suzuki errors in quantum chemistry simulation,” Physical Review A 91, 022311 (2015).”
Entanglement Induced Barren Plateaus (2020, methodology): “With these observations, the results then follow from the use of standard inequalities and the Haar expectation value of random states given, for example, in [31].”
Toward the first quantum simulation with quantum speedup (2017, methodology): “To address this, we report empirical error estimates by extrapolating the error seen in direct classical simulations of small instances [as also explored in previous work on simulating manybody dynamics (28) and quantum chemistry (29, 30)].”
Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator (2018, background): “[47] Ryan Babbush, Jarrod McClean, Dave Wecker, Alán Aspuru-Guzik, and Nathan Wiebe, “Chemical basis of Trotter-Suzuki errors in quantum chemistry simulation,” Physical Review A 91, 022311 (2015).”
Potential of quantum computing for drug discovery (2018, methodology): “The ﬁrst methods used the dynamical evolution under the target Hamiltonian, which was implemented using techniques such as Trotterization [8, 90, 92, 98–100, 103, 104] and approximate decomposition into a sum of unitaries using a Taylor expansion ( Taylorization ) [91, 174].”