Classical approximation complexity asks what solution quality can be guaranteed with polynomial-time computation. The classes APX, PTAS, and FPTAS distinguish a fixed approximation ratio, approximation to any fixed accuracy, and approximation schemes whose running time is also polynomial in inverse accuracy. Their rand...
Evaluating expectation values is a critical task for variational quantum eigensolvers, and for parameterized quantum circuits and other quantum algorithms more generally. We consider the well-studied case of the Quantum Approximate Optimization Algorithm (QAOA) for the MaxCut problem. Recent work of Wang et al. [arXiv:...
This work proves that the barrier to reaching the classical threshold does not arise from a need for entanglement, and separates the effects of relaxation tightness and energy approximation from operational accessibility.
This work studies quantum random access optimization (QRAO), a special case of the Pauli correlation encoding (PCE) framework that assigns up to three binary variables to the Pauli observables of each qubit, with the packing choices determining the compressed Hamiltonian to be optimized.
It is shown that, when the cost phases are engineered so that these paths add coherently, a number of circuit alternations growing only logarithmically with problem size suffices to convert the sum of their absolute contributions into a lower bound on the target amplitude, yielding a certified success probability indep...
Chinonso Onah, Stuart Hadfield, K. Michielsen· arXiv.org· 2 citations
This work defines the universal margin as the smallest correlator magnitude that can be guaranteed with prescribed signs for every target sign assignment, and shows that it is exactly $\Delta_{\rm Maj}(n)=\tan\!\left(\frac{\pi}{4n}\right)=\Theta(1/n)$, whereas uniformly random sign assignments retain $\Theta(1/\sqrt n)...
A noise-aware adaptive approach to quantum approximate optimization, Noise-Directed Adaptive Warm-Starting (ND-AWS), that builds on recent concepts such as Warm-Start QAOA and Noise-Directed Adaptive Remapping by leveraging bitflip gauge transformations, and exploits amplitude-damping-like noise components.
Filip B. Maciejewski, Stuart Hadfield, Oscar Wallis et al.· 4 citations
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