arXiv subjects

Rizwanul Alam

Publications and source records attributed to Rizwanul Alam.

3 recordsLinked to original sources

arXiv2023

Combinatorial optimization with quantum imaginary time evolution

We use Quantum Imaginary Time Evolution (QITE) to solve polynomial unconstrained binary optimization (PUBO) problems. We show that a linear Ansatz yields good results for a wide range of PUBO problems, often outperforming standard classical methods, such as the Goemans-Williamson (GW) algorithm. We obtain numerical results for the Low Autocorrelation Binary Sequences (LABS) and weighted MaxCut combinatorial optimization problems, thus extending an earlier demonstration of successful application of QITE on MaxCut for unweighted graphs. We find the performance of QITE on the LABS problem with a separable Ansatz comparable with p=10 QAOA, and do not see a significant advantage with an entangling Ansatz. On weighted MaxCut, QITE with a separable Ansatz often outperforms the GW algorithm on graphs up to 150 vertices.

quant-ph↗

arXiv2023

Approximate Boltzmann Distributions in Quantum Approximate Optimization

Approaches to compute or estimate the output probability distributions from the quantum approximate optimization algorithm (QAOA) are needed to assess the likelihood it will obtain a quantum computational advantage. We analyze output from QAOA circuits solving 7,200 random MaxCut instances, with $n=14-23$ qubits and depth parameter $p \leq 12$, and find that the average basis state probabilities follow approximate Boltzmann distributions: The average probabilities scale exponentially with their energy (cut value), with a peak at the optimal solution. We describe the rate of exponential scaling or "effective temperature" in terms of a series with a leading order term $T \sim C_\mathrm{min}/n\sqrt{p}$, with $C_\mathrm{min}$ the optimal solution energy. Using this scaling we generate approximate output distributions with up to 38 qubits and find these give accurate accounts of important performance metrics in cases we can simulate exactly.

quant-ph↗

arXiv2023

Solving MaxCut with Quantum Imaginary Time Evolution

We introduce a method to solve the MaxCut problem efficiently based on quantum imaginary time evolution (QITE). We employ a linear Ansatz for unitary updates and an initial state involving no entanglement, as well as an imaginary-time-dependent Hamiltonian interpolating between a given graph and a subgraph with two edges excised. We apply the method to thousands of randomly selected graphs with up to fifty vertices. We show that our algorithm exhibits a 93% and above performance converging to the maximum solution of the MaxCut problem for all considered graphs. Our results compare favorably with the performance of classical algorithms, such as the greedy and Goemans-Williamson algorithms. We also discuss the overlap of the final state of the QITE algorithm with the ground state as a performance metric, which is a quantum feature not shared by other classical algorithms. This metric can be improved by introducing higher-order Ansaetze and entangled initial states.

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