Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity

By Ryan Babbush, Craig Gidney, Dominic W. Berry, Nathan Wiebe, Jarrod R. McClean, Alexandru Paler, Austin G. Fowler, Hartmut Neven. Physical Review X, 2018

484 citations recorded by the source corpus.

We construct quantum circuits which exactly encode the spectra of correlated electron models up to errors from rotation synthesis. By invoking these circuits as oracles within the recently introduced "qubitization" framework, one can use quantum phase estimation to sample states in the Hamiltonian eigenbasis with optimal query complexity $O(\lambda / \epsilon)$ where $\lambda$ is an absolute sum of Hamiltonian coefficients and $\epsilon$ is target precision. For both the Hubbard model and electronic structure Hamiltonian in a second quantized basis diagonalizing the Coulomb operator, our circuits have T gate complexity $O({N + \log (1/\epsilon}))$ where $N$ is number of orbitals in the basis. This enables sampling in the eigenbasis of electronic structure Hamiltonians with T complexity $O(N^3 /\epsilon + N^2 \log(1/\epsilon)/\epsilon)$. Compared to prior approaches, our algorithms are asymptotically more efficient in gate complexity and require fewer T gates near the classically intractable regime. Compiling to surface code fault-tolerant gates and assuming per gate error rates of one part in a thousand reveals that one can error correct phase estimation on interesting instances of these problems beyond the current capabilities of classical methods using only about a million superconducting qubits in a matter of hours.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/f5448598a5ba2de65c03c3757710344b33404cd0

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Citations in the corpus

Variational quantum algorithms (2020, background): “Since long-term algorithms for material simulation require phase estimation [235–237], these lie beyond the scope of near-term devices.”
Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator (2018, background): “[49] Ryan Babbush, Craig Gidney, Dominic Berry, Nathan Wiebe, Jarrod McClean, Alexandru Paler, Austin Fowler, and Hartmut Neven, “Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity,” arXiv.”
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.”
A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery (2018, methodology): “h increases the computation time to 10 seconds. Although this seems fast, many quantum computations have T counts that are signicantly higher than 108. While the T count of Hubbard model simulations [2] is indeed in this range, quantum chemistry simulations can be more demanding. In particular, the ”
Potential of quantum computing for drug discovery (2018, methodology): “Current estimates using the qubitization technique indicate that calculations on systems of a thousand spin orbitals might require on the order of a million physical qubits with error rates of one in ten thousands using state-of-the-art techniques for error correction, as described in [177].”
Halving the cost of quantum addition (2017, background): “temporary logical-ANDs to cut the T-count of a chemistry algorithm in preparation by nearly 50% [2].”
Generalized Quantum Signal Processing (2023, methodology): “This insight enables faster phase estimation using existing approaches to qubitization [19].”