8 research outputs found
Expectation Values from the Single-Layer Quantum Approximate Optimization Algorithm on Ising Problems
We report on the energy-expectation-value landscapes produced by the
single-layer () Quantum Approximate Optimization Algorithm (QAOA) when
being used to solve Ising problems. The landscapes are obtained using an
analytical formula that we derive. The formula allows us to predict the
landscape for any given Ising problem instance and consequently predict the
optimal QAOA parameters for heuristically solving that instance using the
single-layer QAOA. We have validated our analytical formula by showing that it
accurately reproduces the landscapes published in recent experimental reports.
We then applied our methods to address the question: how well is the
single-layer QAOA able to solve large benchmark problem instances? We used our
analytical formula to calculate the optimal energy-expectation values for
benchmark MAX-CUT problems containing up to vertices and
edges. We also calculated the optimal energy expectations for general Ising
problems with up to vertices and edges. Our results
provide an estimate for how well the single-layer QAOA may work when run on a
quantum computer with thousands of qubits. In addition to providing performance
estimates when optimal angles are used, we are able to use our analytical
results to investigate the difficulties one may encounter when running the QAOA
in practice for different classes of Ising instances. We find that depending on
the parameters of the Ising Hamiltonian, the expectation-value landscapes can
be rather complex, with sharp features that necessitate highly accurate
rotation gates in order for the QAOA to be run optimally on quantum hardware.
We also present analytical results that explain some of the qualitative
landscape features that are observed numerically.Comment: 24 pages, 15 figure
Readiness of Quantum Optimization Machines for Industrial Applications
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 of 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 testing
near-term quantum annealers and other quantum algorithmic strategies for
optimization problems.Comment: 22 pages, 12 figures. Content updated according to Phys. Rev. Applied
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