02470nas a2200169 4500008004100000245007100041210006900112260001400181520193200195100002202127700002202149700002402171700002302195700002502218700002002243856003702263 2023 eng d00aQuantum Algorithms for Simulating Nuclear Effective Field Theories0 aQuantum Algorithms for Simulating Nuclear Effective Field Theori c12/8/20233 a
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.
1 aWatson, James, D.1 aBringewatt, Jacob1 aShaw, Alexander, F.1 aChilds, Andrew, M.1 aGorshkov, Alexey, V.1 aDavoudi, Zohreh uhttps://arxiv.org/abs/2312.0534401557nas a2200169 4500008004100000245004600041210004600087260001500133490000800148520110300156100001301259700001401272700002401286700001701310700002301327856003701350 2022 eng d00aHamiltonian simulation with random inputs0 aHamiltonian simulation with random inputs c12/30/20220 v1293 aThe 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.
1 aZhao, Qi1 aZhou, You1 aShaw, Alexander, F.1 aLi, Tongyang1 aChilds, Andrew, M. uhttps://arxiv.org/abs/2111.0477301946nas a2200157 4500008004100000245006600041210006600107260001300173490000600186520147300192100002401665700002101689700002301710700001801733856003701751 2020 eng d00aQuantum Algorithms for Simulating the Lattice Schwinger Model0 aQuantum Algorithms for Simulating the Lattice Schwinger Model c8/5/20200 v43 aThe 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.
1 aShaw, Alexander, F.1 aLougovski, Pavel1 aStryker, Jesse, R.1 aWiebe, Nathan uhttps://arxiv.org/abs/2002.11146