Go-No go criteria for performing quantum chemistry calculations on
quantum computers
- URL: http://arxiv.org/abs/2306.02620v2
- Date: Tue, 5 Dec 2023 09:37:05 GMT
- Title: Go-No go criteria for performing quantum chemistry calculations on
quantum computers
- Authors: Thibaud Louvet, Thomas Ayral, Xavier Waintal
- Abstract summary: We propose two criteria for evaluating the two leading quantum approaches for this class of problems.
We find a crippling effect of noise with an overall scaling of the precision that is generically it less favourable than in the corresponding classical algorithms.
The second criterion applies to the Quantum Phase Estimation (QPE) algorithm that is often presented as the go-to replacement of VQE upon availability of (noiseless) fault-tolerant quantum computers.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum chemistry is envisioned as an early and disruptive application for
quantum computers. We propose two criteria for evaluating the two leading
quantum approaches for this class of problems. The first criterion applies to
the Variational Quantum Eigensolver (VQE) algorithm. It sets an upper bound to
the level of noise that can be tolerated in quantum hardware as a function of
the targetted precision and problem size. We find a crippling effect of noise
with an overall scaling of the precision that is generically {\it less}
favourable than in the corresponding classical algorithms. Indeed, the studied
molecule is unrelated to the hardware dynamics, hence to its noise; conversely
the hardware noise populates states of arbitrary energy of the studied
molecule. The second criterion applies to the Quantum Phase Estimation (QPE)
algorithm that is often presented as the go-to replacement of VQE upon
availability of (noiseless) fault-tolerant quantum computers. QPE suffers from
the orthogonality catastrophe that generically leads to an exponentially small
success probability when the size of the problem grows. Our criterion allows
one to estimate quantitatively the importance of this phenomenon from the
knowledge of the variance of the energy of the input state used in the
calculation.
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