Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
Oct 23, 2018
36 pages
Published in:
- Phys.Rev.X 8 (2018) 4, 041015
- Published: Oct 23, 2018
Citations per year
Abstract: (APS)
We construct quantumcircuits that exactly encode the spectra of correlated electronmodels up to errors from
rotation synthesis. By invoking these circuits as oracles within the recently introduced “qubitization”
framework, one can use quantumphase estimation to sample states in the Hamiltonian eigenbasis with optimal
query complexityOð.=.Þ, where . is an absolute sumof Hamiltonian coefficients and . is the target precision.
For both theHubbardmodel and electronic structureHamiltonian in a second quantized basis diagonalizing the
Coulomboperator, our circuits have T-gate complexityO(N þ logð1=.Þ), whereN is the number of orbitals in
the basis. This scenario enables sampling in the eigenbasis of electronic structure Hamiltonians with T
complexity O(N3=. þ N2 logð1=.Þ=.). Compared to prior approaches, our algorithms are asymptotically
more efficient in gate complexity and require fewerTgates 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.- Quantum Information, Science & Technology
- Condensed Matter, Materials & Applied Physics
- Electronic structure
- Quantum algorithms
- Quantum error correction
- Quantum simulation
- Quantum walks
- Surface code quantum computing
- quantum error correction
- surface code
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