Simulation of noisy Clifford circuits without fault propagation
- URL: http://arxiv.org/abs/2309.15345v1
- Date: Wed, 27 Sep 2023 01:30:03 GMT
- Title: Simulation of noisy Clifford circuits without fault propagation
- Authors: Nicolas Delfosse and Adam Paetznick
- Abstract summary: We propose a simulation algorithm for all Clifford circuits that does not require fault propagation.
Our algorithm, which we name adjoint-based code (ABC) simulation, relies on the fact that propagation forward is the adjoint of propagation backward.
- Score: 3.1727619150610837
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The design and optimization of a large-scale fault-tolerant quantum computer
architecture relies extensively on numerical simulations to assess the
performance of each component of the architecture. The simulation of
fault-tolerant gadgets, which are typically implemented by Clifford circuits,
is done by sampling circuit faults and propagating them through the circuit to
check that they do not corrupt the logical data. One may have to repeat this
fault propagation trillions of times to extract an accurate estimate of the
performance of a fault-tolerant gadget. For some specific circuits, such as the
standard syndrome extraction circuit for surface codes, we can exploit the
natural graph structure of the set of faults to perform a simulation without
fault propagation. We propose a simulation algorithm for all Clifford circuits
that does not require fault propagation and instead exploits the mathematical
structure of the spacetime code of the circuit. Our algorithm, which we name
adjoint-based code (ABC) simulation, relies on the fact that propagation
forward is the adjoint of propagation backward in the sense of Proposition 3
from [14]. We use this result to replace the propagation of trillions of
fault-configurations by the backward propagation of a small number of Pauli
operators which can be precomputed once and for all.
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