Solving various NP-Hard problems using exponentially fewer qubits on a Quantum Computer
arxiv(2023)
摘要
NP-hard problems are not believed to be exactly solvable through general
polynomial time algorithms. Hybrid quantum-classical algorithms to address such
combinatorial problems have been of great interest in the past few years. Such
algorithms are heuristic in nature and aim to obtain an approximate solution.
Significant improvements in computational time and/or the ability to treat
large problems are some of the principal promises of quantum computing in this
regard. The hardware, however, is still in its infancy and the current Noisy
Intermediate Scale Quantum (NISQ) computers are not able to optimize
industrially relevant problems. Moreover, the storage of qubits and
introduction of entanglement require extreme physical conditions. An issue with
quantum optimization algorithms such as QAOA is that they scale linearly with
problem size. In this paper, we build upon a proprietary methodology which
scales logarithmically with problem size - opening an avenue for treating
optimization problems of unprecedented scale on gate-based quantum computers.
In order to test the performance of the algorithm, we first find a way to apply
it to a handful of NP-hard problems: Maximum Cut, Minimum Partition, Maximum
Clique, Maximum Weighted Independent Set. Subsequently, these algorithms are
tested on a quantum simulator with graph sizes of over a hundred nodes and on a
real quantum computer up to graph sizes of 256. To our knowledge, these
constitute the largest realistic combinatorial optimization problems ever run
on a NISQ device, overcoming previous problem sizes by almost tenfold.
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关键词
fewer qubits,quantum,np-hard
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