2023
DOI: 10.22331/q-2023-03-17-952
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Parity Quantum Optimization: Benchmarks

Abstract: We present benchmarks of the parity transformation for the Quantum Approximate Optimization Algorithm (QAOA). We analyse the gate resources required to implement a single QAOA cycle for real-world scenarios. In particular, we consider random spin models with higher order terms, as well as the problems of predicting financial crashes and finding the ground states of electronic structure Hamiltonians. For the spin models studied our findings imply a significant advantage of the parity mapping compared to the sta… Show more

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Cited by 11 publications
(8 citation statements)
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“…, 2N − 1}. This identification is implicitly used in other canonical mappings [41,42,50,56], and we refer to the associated Pauli operators S i as Majorana strings. To complete the mapping, these Majorana strings are paired into qubit mode operators A i and A † i .…”
Section: B Fermion-to-qubit Mappingsmentioning
confidence: 99%
“…, 2N − 1}. This identification is implicitly used in other canonical mappings [41,42,50,56], and we refer to the associated Pauli operators S i as Majorana strings. To complete the mapping, these Majorana strings are paired into qubit mode operators A i and A † i .…”
Section: B Fermion-to-qubit Mappingsmentioning
confidence: 99%
“…In this section, we show that consecutive decompositions of many multi-qubit gates can lead to cancellations, using a Quantum Approximate Optimisation (QAOA) circuit with a parity encoded binary optimisation problem. We do not provide the details of parity encoded QAOA, please refer to [28,29] for the Lechner-Hauke-Zoller (LHZ) construction and [30][31][32] for the parity architecture.…”
Section: Specific Example Of Parity Encoded Mappingmentioning
confidence: 99%
“…One of the most promising candidates to show quantum advantage in the NISQ-era in solving combinatorial optimization problems is the Quantum Approximate Optimization Algorithm (QAOA) [23]. As the parity mapping exhibits various benefits for the implementation for such optimization algorithms [24], [25], we apply our findings to the QAOA and in particular show how the new encoding approach leads to a constant-depth implementation of the QAOA in the parity architecture while implicitly preserving all parity constraints by using logical bit-flip operators in the mixing Hamiltonian [26]. So far, parity QAOA was either implemented in constant depth by enforcing (at least part of) the parity constraints via an additional energy penalty in the cost function [24], [27], [28] or fulfilling the constraints implicitly at the cost of a linear circuit depth [27].…”
Section: Introductionmentioning
confidence: 99%