Quantum Materials Corp. (fka QTMM)

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Fast Quantum Algorithm for Spectral Properties

David Poulin, Alexei Kitaev, Damian S. Steiger, Matthew B. Hastings, Matthias Troyer
(Submitted on 29 Nov 2017)

We present two techniques that can greatly reduce the number of gates required for ground state preparation in quantum simulations. The first technique realizes that to prepare the ground state of some Hamiltonian, it is not necessary to implement the time-evolution operator: any unitary operator which is a function of the Hamiltonian will do. We propose one such unitary operator which can be implemented exactly, circumventing any Taylor or Trotter approximation errors. The second technique is tailored to lattice models, and is targeted at reducing the use of generic single-qubit rotations, which are very expensive to produce by distillation and synthesis fault-tolerantly. In particular, the number of generic single-qubit rotations used by our method scales with the number of parameters in the Hamiltonian, which contrasts with a growth proportional to the lattice site required by other techniques.

https://arxiv.org/abs/1711.11025

Excuse me while I whip this out!

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. In either case, these procedures make the scheme fully compatible with the Zeno ground state preparation outlined above [16]. Had we instead chosen to perform adiabatic evolution with the operator W(g) itself, we would have had to worry about the spectral gap to the states orthogonal to the space spanned by the |?± k i. But by completing a deterministic projection as described in this paragraph, we are guaranteed to always remain in this invariant subspace.