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Monolayer WTe2, an inversion-symmetric transition metal dichalcogenide, has recently been established as a quantum spin Hall insulator and found superconducting upon gating. Here we show that generally a superconducting inversion-symmetric quantum spin Hall material whose normal state is ``effectively gapped", such as gated monolayer WTe2, can be an inversion-protected topological crystalline superconductor featuring ``higher-order topology" if the superconductivity is parity-odd. We explicitly demonstrate how the bulk-boundary correspondence naturally emerges in such type of superconductors within a two-dimensional minimal model. We then study the pairing symmetry of superconducting WTe2 with a microscopic model, and find two types of self-consistently obtained exotic pairings. First is an odd-parity pairing that possesses a nontrivial bulk symmetry indicator and hosts two Majorana Kramers pairs localizing at opposite corners. Even when the conventional pairing is energetically favored, we find that an intermediate in-plane field exceeding the Pauli limit stabilizes an equal-spin pairing aligning with the field. Our findings suggest gated monolayer WTe2 is a playground for exotic odd-parity superconductivity, and possibly the first material realization for inversion-protected Majorana corner modes without utilizing proximity effect. 

Query complexity is a common tool for comparing quantum and classical computation, and it has produced many examples of how quantum algorithms differ from classical ones. Here we investigate in detail the role that oracles play for the advantage of quantum algorithms. We do so by using a simulation framework, Quantum Simulation Logic (QSL), to construct oracles and algorithms that solve some problems with the same success probability and number of queries as the quantum algorithms. The framework can be simulated using only classical resources at a constant overhead as compared to the quantum resources used in quantum computation. Our results clarify the assumptions made and the conditions needed when using quantum oracles. Using the same assumptions on oracles within the simulation framework we show that for some specific algorithms, such as the Deutsch-Jozsa and Simon’s algorithms, there simply is no advantage in terms of query complexity. This does not detract from the fact that quantum query complexity provides examples of how a quantum computer can be expected to behave, which in turn has proved useful for finding new quantum algorithms outside of the oracle paradigm, where the most prominent example is Shor’s algorithm for integer factorization.