High Dimensional Quantum Machine Learning With Small Quantum Computers

Abstract

Quantum computers hold great promise to enhance machine learning, but their current qubit counts restrict the realisation of this promise. In an attempt to placate this limitation techniques can be applied for evaluating a quantum circuit using a machine with fewer qubits than the circuit naively requires. These techniques work by evaluating many smaller circuits on the smaller machine, that are then combined in a polynomial to replicate the output of the larger machine. This scheme requires more circuit evaluations than are practical for general circuits. However, we investigate the possibility that for certain applications many of these subcircuits are superfluous, and that a much smaller sum is sufficient to estimate the full circuit. We construct a machine learning model that may be capable of approximating the outputs of the larger circuit with much fewer circuit evaluations. We successfully apply our model to the task of digit recognition, using simulated quantum computers much smaller than the data dimension. The model is also applied to the task of approximating a random 10 qubit PQC with simulated access to a 5 qubit computer, even with only relatively modest number of circuits our model provides an accurate approximation of the 10 qubit PQCs output, superior to a neural network attempt. The developed method might be useful for implementing quantum models on larger data throughout the NISQ era.

arXiv comment13 pages, 7 figures

References in corpus (22)

• Quantum Computing in the NISQ era and beyond
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Supervised learning with quantum enhanced feature spaces
• Barren plateaus in quantum neural network training landscapes
• Quantum machine learning in feature Hilbert spaces
• The effect of data encoding on the expressive power of variational quantum machine learning models
• Power of data in quantum machine learning
• Trading classical and quantum computational resources
• Differentiable Learning of Quantum Circuit Born Machine
• Simulating Large Quantum Circuits on a Small Quantum Computer
• CutQC: Using Small Quantum Computers for Large Quantum Circuit Evaluations
• Avoiding barren plateaus using classical shadows
• Quantum federated learning through blind quantum computing
• Gradients of parameterized quantum gates using the parameter-shift rule and gate decomposition
• Constructing a virtual two-qubit gate by sampling single-qubit operations
• Quantum simulation with hybrid tensor networks
• Quantum Circuit Cutting with Maximum Likelihood Tomography
• Quantum machine learning of large datasets using randomized measurements
• Overhead for simulating a non-local channel with local channels by quasiprobability sampling
• Quantum advantage and noise reduction in distributed quantum computing
• $i$-QER: An Intelligent Approach towards Quantum Error Reduction
• Divide and Conquer for Combinatorial Optimization and Distributed Quantum Computation

Cited by in corpus (15)

• Barren Plateaus in Variational Quantum Computing
• Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group
• Review of Distributed Quantum Computing. From single QPU to High Performance Quantum Computing
• Investigating the effect of circuit cutting in QAOA for the MaxCut problem on NISQ devices
• Hybrid quantum cycle generative adversarial network for small molecule generation
• Cutting multi-control quantum gates with ZX calculus
• How quantum computing can enhance biomarker discovery
• Networked Quantum Services
• Hyperparameter Importance of Quantum Neural Networks Across Small Datasets
• Distributed Quantum Neural Networks via Partitioned Features Encoding
• Distributed Quantum Computing for Chemical Applications
• Distributed quantum machine learning via classical communication
• Reduce&chop: Shallow circuits for deeper problems
• Quantum channel decomposition with pre- and post-selection
• CutReg: A loss regularizer for enhancing the scalability of QML via adaptive circuit cutting