@article {3400, title = {Quantum Algorithms for Simulating Nuclear Effective Field Theories}, year = {2023}, month = {12/8/2023}, abstract = {

Quantum computers offer the potential to simulate nuclear processes that are classically intractable. With the goal of understanding the necessary quantum resources, we employ state-of-the-art Hamiltonian-simulation methods, and conduct a thorough algorithmic analysis, to estimate the qubit and gate costs to simulate low-energy effective field theories (EFTs) of nuclear physics. In particular, within the framework of nuclear lattice EFT, we obtain simulation costs for the leading-order pionless and pionful EFTs. We consider both static pions represented by a one-pion-exchange potential between the nucleons, and dynamical pions represented by relativistic bosonic fields coupled to non-relativistic nucleons. We examine the resource costs for the tasks of time evolution and energy estimation for physically relevant scales. We account for model errors associated with truncating either long-range interactions in the one-pion-exchange EFT or the pionic Hilbert space in the dynamical-pion EFT, and for algorithmic errors associated with product-formula approximations and quantum phase estimation. Our results show that the pionless EFT is the least costly to simulate and the dynamical-pion theory is the costliest. We demonstrate how symmetries of the low-energy nuclear Hamiltonians can be utilized to obtain tighter error bounds on the simulation algorithm. By retaining the locality of nucleonic interactions when mapped to qubits, we achieve reduced circuit depth and substantial parallelization. We further develop new methods to bound the algorithmic error for classes of fermionic Hamiltonians that preserve the number of fermions, and demonstrate that reasonably tight Trotter error bounds can be achieved by explicitly computing nested commutators of Hamiltonian terms. This work highlights the importance of combining physics insights and algorithmic advancement in reducing quantum-simulation costs.

}, url = {https://arxiv.org/abs/2312.05344}, author = {James D. Watson and Jacob Bringewatt and Alexander F. Shaw and Andrew M. Childs and Alexey V. Gorshkov and Zohreh Davoudi} } @article {2913, title = {Hamiltonian simulation with random inputs}, journal = {Phys. Rev. Lett. 129, 270502}, volume = {129}, year = {2022}, month = {12/30/2022}, abstract = {

The algorithmic error of digital quantum simulations is usually explored in terms of the spectral norm distance between the actual and ideal evolution operators. In practice, this worst-case error analysis may be unnecessarily pessimistic. To address this, we develop a theory of average-case performance of Hamiltonian simulation with random initial states. We relate the average-case error to the Frobenius norm of the multiplicative error and give upper bounds for the product formula (PF) and truncated Taylor series methods. As applications, we estimate average-case error for digital Hamiltonian simulation of general lattice Hamiltonians and k-local Hamiltonians. In particular, for the nearest-neighbor Heisenberg chain with n spins, the error is quadratically reduced from O(n) in the worst case to O(n\−\−\√) on average for both the PF method and the Taylor series method. Numerical evidence suggests that this theory accurately characterizes the average error for concrete models. We also apply our results to error analysis in the simulation of quantum scrambling.

}, doi = {https://doi.org/10.1103/PhysRevLett.129.270502}, url = {https://arxiv.org/abs/2111.04773}, author = {Qi Zhao and You Zhou and Alexander F. Shaw and Tongyang Li and Andrew M. Childs} } @article {2696, title = {Quantum Algorithms for Simulating the Lattice Schwinger Model}, journal = {Quantum}, volume = {4}, year = {2020}, month = {8/5/2020}, type = {INT-PUB-20-008}, abstract = {

The Schwinger model (quantum electrodynamics in 1+1 dimensions) is a testbed for the study of quantum gauge field theories. We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In particular, we perform a tight analysis of low-order Trotter formula simulations of the Schwinger model, using recently derived commutator bounds, and give upper bounds on the resources needed for simulations in both scenarios. In lattice units, we find a Schwinger model on N/2 physical sites with coupling constant x\−1/2 and electric field cutoff x\−1/2Λ can be simulated on a quantum computer for time 2xT using a number of T-gates or CNOTs in O\˜(N3/2T3/2x\−\−\√Λ) for fixed operator error. This scaling with the truncation Λ is better than that expected from algorithms such as qubitization or QDRIFT. Furthermore, we give scalable measurement schemes and algorithms to estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density. Finally, we bound the root-mean-square error in estimating this observable via simulation as a function of the diamond distance between the ideal and actual CNOT channels. This work provides a rigorous analysis of simulating the Schwinger model, while also providing benchmarks against which subsequent simulation algorithms can be tested.\ 

}, doi = {https://doi.org/10.22331/q-2020-08-10-306}, url = {https://arxiv.org/abs/2002.11146}, author = {Alexander F. Shaw and Pavel Lougovski and Jesse R. Stryker and Nathan Wiebe} }