01576nas a2200157 4500008004100000245010800041210006900149260001400218490000600232520106400238100001701302700001601319700002701335700001901362856003701381 2020 eng d00aOptimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning0 aOptimal fermiontoqubit mapping via ternary trees with applicatio c5/26/20200 v43 a

We introduce a fermion-to-qubit mapping defined on ternary trees, where any single Majorana operator on an n-mode fermionic system is mapped to a multi-qubit Pauli operator acting nontrivially on ⌈log3(2n+1)⌉ qubits. The mapping has a simple structure and is optimal in the sense that it is impossible to construct Pauli operators in any fermion-to-qubit mapping acting nontrivially on less than log3(2n) qubits on average. We apply it to the problem of learning k-fermion reduced density matrix (RDM), a problem relevant in various quantum simulation applications. We show that using the ternary-tree mapping one can determine the elements of all k-fermion RDMs, to precision ϵ, by repeating a single quantum circuit for ≲(2n+1)kϵ−2 times. This result is based on a method we develop here that allows one to determine the elements of all k-qubit RDMs, to precision ϵ, by repeating a single quantum circuit for ≲3kϵ−2 times, independent of the system size. This improves over existing schemes for determining qubit RDMs.

1 aJiang, Zhang1 aKalev, Amir1 aMruczkiewicz, Wojciech1 aNeven, Hartmut uhttps://arxiv.org/abs/1910.1074602646nas a2200241 4500008004100000245008200041210006900123260001500192520190700207100002902114700002302143700001802166700002302184700001502207700002002222700002702242700002402269700001902293700002002312700001702332700001802349856003702367 2017 eng d00aOn the readiness of quantum optimization machines for industrial applications0 areadiness of quantum optimization machines for industrial applic c2017/08/313 a

There have been multiple attempts to demonstrate that quantum annealing and, in particular, quantum annealing on quantum annealing machines, has the potential to outperform current classical optimization algorithms implemented on CMOS technologies. The benchmarking of these devices has been controversial. Initially, random spin-glass problems were used, however, these were quickly shown to be not well suited to detect any quantum speedup. Subsequently, benchmarking shifted to carefully crafted synthetic problems designed to highlight the quantum nature of the hardware while (often) ensuring that classical optimization techniques do not perform well on them. Even worse, to date a true sign of improved scaling with the number problem variables remains elusive when compared to classical optimization techniques. Here, we analyze the readiness of quantum annealing machines for real-world application problems. These are typically not random and have an underlying structure that is hard to capture in synthetic benchmarks, thus posing unexpected challenges for optimization techniques, both classical and quantum alike. We present a comprehensive computational scaling analysis of fault diagnosis in digital circuits, considering architectures beyond D-wave quantum annealers. We find that the instances generated from real data in multiplier circuits are harder than other representative random spin-glass benchmarks with a comparable number of variables. Although our results show that transverse-field quantum annealing is outperformed by state-of-the-art classical optimization algorithms, these benchmark instances are hard and small in the size of the input, therefore representing the first industrial application ideally suited for near-term quantum annealers.

1 aPerdomo-Ortiz, Alejandro1 aFeldman, Alexander1 aOzaeta, Asier1 aIsakov, Sergei, V.1 aZhu, Zheng1 aO'Gorman, Bryan1 aKatzgraber, Helmut, G.1 aDiedrich, Alexander1 aNeven, Hartmut1 ade Kleer, Johan1 aLackey, Brad1 aBiswas, Rupak uhttps://arxiv.org/abs/1708.09780