Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage (2208.13673v2)

Abstract: While recent breakthroughs have proven the ability of noisy intermediate-scale quantum (NISQ) devices to achieve quantum advantage in classically-intractable sampling tasks, the use of these devices for solving more practically relevant computational problems remains a challenge. Proposals for attaining practical quantum advantage typically involve parametrized quantum circuits (PQCs), whose parameters can be optimized to find solutions to diverse problems throughout quantum simulation and machine learning. However, training PQCs for real-world problems remains a significant practical challenge, largely due to the phenomenon of barren plateaus in the optimization landscapes of randomly-initialized quantum circuits. In this work, we introduce a scalable procedure for harnessing classical computing resources to provide pre-optimized initializations for PQCs, which we show significantly improves the trainability and performance of PQCs on a variety of problems. Given a specific optimization task, this method first utilizes tensor network (TN) simulations to identify a promising quantum state, which is then converted into gate parameters of a PQC by means of a high-performance decomposition procedure. We show that this learned initialization avoids barren plateaus, and effectively translates increases in classical resources to enhanced performance and speed in training quantum circuits. By demonstrating a means of boosting limited quantum resources using classical computers, our approach illustrates the promise of this synergy between quantum and quantum-inspired models in quantum computing, and opens up new avenues to harness the power of modern quantum hardware for realizing practical quantum advantage.

Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage

The paper "Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage" addresses a pivotal challenge in quantum computing, specifically leveraging noisy intermediate-scale quantum (NISQ) devices to solve computational problems that are of practical interest. The authors propose a novel approach that integrates classical tensor networks (TNs) to significantly enhance the performance and trainability of parameterized quantum circuits (PQCs), circumventing the notorious issue of barren plateaus in optimization landscapes.

The research underscores the role of TNs, particularly matrix product states (MPS), as a classical computational resource that can pre-optimize PQCs, thereby improving convergence and model quality. The synergy lies in initializing PQCs with parameters derived from MPS models, which are adeptly converted into quantum gate parameters via a detailed decomposition protocol. This approach leverages the expressivity bound of MPS set by its bond dimension, thus scaling classical resources to yield improved quantum circuit initialization. Importantly, the authors demonstrate that such pre-optimized circuits retain stability in gradient variences, effectively bypassing barren plateaus encountered with randomly initialized circuits.

Strong numerical results are presented across various domains, including generative modeling and Hamiltonian ground state search tasks. The performance improvements of PQCs when initialized using TNs are robust, revealing improvements both in speed and accuracy compared to their randomly initialized counterparts. Specifically, PQCs show drastic enhancements in loss function convergence when trained with classically optimized TN initializations, effectively translating increases in classical bond dimension to enhanced quantum performance.

The implications of this paper are profound. Practically, it allows for optimizing quantum resources by integrating classical computation power, making current quantum hardware more viable and competitive in solving real-world problems. Theoretically, it suggests new avenues in hybrid quantum-classical algorithms that could bridge the gap toward quantum advantage in practical applications. As quantum technology evolves, further developments could see broader applications of TN methodologies, extending beyond MPS to more sophisticated TN architectures and increasing the interaction between quantum hardware and classical simulation.

Future research could explore refining the TN-PQC synergy to address larger qubit systems, exploring other TN architectures like tree tensor networks or projected entangled pair states for tasks with varying correlation structures. Understanding the mapping of more complex TNs into quantum circuits could further augment quantum solution quality by better adapting the TN topology to circuit architecture demands.

In conclusion, the paper presents a compelling solution to enhancing quantum computing's practical capabilities by harnessing classical resources. Through the synergistic integration of TNs with PQCs, this research paves the way for tangible advances towards achieving practical quantum advantage, making quantum algorithms more scalable and effective in diverse scientific and industrial applications.