[Paper Review] Unsupervised Machine Learning on a Hybrid Quantum Computer

Johannes Otterbach, Riccardo Manenti+28 more|arXiv (Cornell University)|Dec 15, 2017

Quantum Computing Algorithms and ArchitectureComputer Science220 citations

TL;DR

The paper demonstrates a hybrid quantum-classical approach using a 19-qubit gate-model quantum processor to perform clustering via QAOA with Bayesian optimization, achieving optimal or near-optimal MaxCut solutions on random instances despite noise.

ABSTRACT

Machine learning techniques have led to broad adoption of a statistical model of computing. The statistical distributions natively available on quantum processors are a superset of those available classically. Harnessing this attribute has the potential to accelerate or otherwise improve machine learning relative to purely classical performance. A key challenge toward that goal is learning to hybridize classical computing resources and traditional learning techniques with the emerging capabilities of general purpose quantum processors. Here, we demonstrate such hybridization by training a 19-qubit gate model processor to solve a clustering problem, a foundational challenge in unsupervised learning. We use the quantum approximate optimization algorithm in conjunction with a gradient-free Bayesian optimization to train the quantum machine. This quantum/classical hybrid algorithm shows robustness to realistic noise, and we find evidence that classical optimization can be used to train around both coherent and incoherent imperfections.

Motivation & Objective

• Demonstrate a hybrid quantum-classical approach to an unsupervised learning task (clustering) using a gate-model quantum processor.
• Translate clustering into a MaxCut problem and solve it with the Quantum Approximate Optimization Algorithm (QAOA).
• Show robustness of the quantum/classical hybrid method to realistic noise and imperfections.
• Employ Bayesian optimization to train the variational parameters of the quantum circuit.
• Provide evidence that classical optimization can mitigate coherent and incoherent gate imperfections.

Proposed method

• Encode clustering as a weighted MaxCut problem via the Bhattacharyya-based distance representation.
• Implement a single iteration (p=1) of QAOA with a cost Hamiltonian H_C = -1/2 sum_{i,j} w_{ij} (1 - σ_i^z σ_j^z).
• Use a Bayesian optimization loop to select QAOA angles (γ, β) to maximize the best observed MaxCut value.
• Run the QAOA circuit on Rigetti’s 19Q processor with a depth corresponding to six two-qubit gates for the cost unitary.
• Compare experimental results to a noiseless quantum virtual machine simulation and to random bit-string sampling.
• Describe circuit compilation and hardware details including CZ gate implementation and connectivity.

Experimental results

Research questions

• RQ1 Can a hybrid quantum-classical algorithm using QAOA efficiently solve clustering formulated as a MaxCut problem on near-term devices?
• RQ2 Does Bayesian optimization of QAOA angles enable robust performance in the presence of realistic gate noise and device imperfections?
• RQ3 How does the hybrid algorithm perform relative to random sampling and noiseless simulations for MaxCut-based clustering?
• RQ4 What are the circuit depth and hardware requirements to implement the clustering problem on a 19-qubit device?
• RQ5 Does the approach generalize across different random problem instances (weights) for MaxCut-based clustering?

Key findings

• The algorithm reaches the optimal MaxCut value for most fixed, random problem instances within 55 Bayesian optimization steps.
• The method shows robustness to realistic noise, with most runs converging to optimal or near-optimal solutions.
• Experimental results (blue) outperform random bit-string sampling (green) and align with noiseless simulation (orange).
• Kolmogorov–Smirnov tests reject the random-sampling null hypothesis for both experimental and noiseless results at >99% and >99.99% confidence, respectively.
• A 19-qubit gate-model processor suffices to demonstrate the clustering via a p=1 QAOA run with Bayesian optimization over angles up to 55 steps.
• Runtime is approximately 10 minutes for 55 Bayesian optimization steps with 2500 measurements per step, including communication and compilation overhead.