Low-Depth Quantum Simulation of Materials

By Ryan Babbush, Nathan Wiebe, Jarrod R. McClean, James D. McClain, Hartmut Neven, Garnet Kin-Lic Chan. 2017

345 citations recorded by the source corpus.

Quantum simulation of the electronic structure problem is one of the most researched applications of quantum computing. The majority of quantum algorithms for this problem encode the wavefunction using N Gaussian orbitals, leading to Hamiltonians with O(N^4) second-quantized terms. We avoid this overhead and extend methods to condensed phase materials by utilizing a dual form of the plane wave basis which diagonalizes the potential operator, leading to a Hamiltonian representation with O(N^2) second-quantized terms. Using this representation, we can implement single Trotter steps of the Hamiltonians with linear gate depth on a planar lattice. Properties of the basis allow us to deploy Trotter- and Taylor-series-based simulations with respective circuit depths of O(N^(7/2)) and O(N^(8/3)) for fixed charge densities. Variational algorithms also require significantly fewer measurements in this basis, ameliorating a primary challenge of that approach. While our approach applies to the simulation of arbitrary electronic structure problems, the basis sets explored in this work will be most practical for treating periodic systems, such as crystalline materials, in the near term. We conclude with a proposal to simulate the uniform electron gas (jellium) using a low-depth variational ansatz realizable on near-term quantum devices. From these results, we identify simulations of low-density jellium as a promising first setting to explore quantum supremacy in electronic structure.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Physical and Theoretical Chemistry

View Paper: https://www.semanticscholar.org/paper/0dd1d2d714813d540d9d855e91c0f446a7b96760

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Citations in the corpus

Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity (2018, methodology): “(42) encompass a wide range of fermionic Hamiltonians, including the molecular electronic structure (aka “ quantum chemistry ” ) Hamiltonian in any basis that diagonalizes the Coulomb potential [39].”
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].”
Efficient and noise resilient measurements for quantum chemistry on near-term quantum computers (2019, background): “Although there are a variety of approaches to simulating indistinguishable fermions with distinguishable qubits [23–25], the Jordan-Wigner transformation is the most widely used, due to its simplicity and to the fact that it allows for the explicit construction of a number of useful circuit primitiv”
Hartree-Fock on a superconducting qubit quantum computer (2020, background): “Accordingly, the most eﬃcient quantum algorithms for chemistry [12–15] require that one perform the simulation in more structured bases with asymptotically fewer terms [16–18], necessitating that U κ (cid:63) is applied explicitly at the beginning of the computation.”
Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator (2018, background): “For instance, it has been argued that a parameterized Trotter approximation [7, 81], to the adiabatic state preparation algorithm may serve as an effective ansatz [40, 41, 51].”