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

Manuel S. Rudolph, Jacob Miller+4 more|arXiv (Cornell University)|Aug 29, 2022

Quantum Computing Algorithms and Architecture9 citations

TL;DR

This paper proposes a synergistic framework that uses tensor network (TN) simulations to pre-optimize initial parameters for parametrized quantum circuits (PQCs), significantly improving their trainability and performance. By leveraging classical computing to generate high-quality initial quantum states via matrix product states (MPS), and then decomposing them into efficient quantum gate sequences, the method avoids barren plateaus and enables deep quantum circuits to converge reliably on high-quality solutions with minimal quantum resource usage.

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.

Motivation & Objective

• To address the challenge of barren plateaus in training parametrized quantum circuits (PQCs) on near-term quantum hardware.
• To improve the trainability and performance of PQCs for practical quantum advantage in quantum simulation and machine learning.
• To demonstrate that classical tensor network simulations can provide high-quality initial parameterizations for PQCs, reducing reliance on random initialization.
• To show that increased classical resources (via higher bond dimension in TNs) can be translated into enhanced quantum circuit performance.
• To move beyond the adversarial 'classical vs. quantum' mindset by leveraging complementary strengths of classical and quantum computing.

Proposed method

• The method begins by simulating the target quantum problem using a matrix product state (MPS) tensor network model on classical hardware, with a tunable bond dimension χ to control classical resource usage.
• The resulting MPS wavefunction is then decomposed into a sequence of SU(4) two-qubit gates using a layer-efficient decomposition protocol, forming a quantum circuit initialization.
• This classically pre-optimized quantum circuit is then extended with additional parametrized gates to further improve performance, which are trained on actual quantum hardware.
• The framework avoids barren plateaus by initializing the PQC in a region of parameter space with favorable gradient properties, as evidenced by stable gradient variances and magnitudes.
• The approach enables deep quantum circuits—previously untrainable due to vanishing gradients—to converge reliably to high-quality solutions.
• The method is evaluated on Hamiltonian minimization and generative modeling tasks, showing superior convergence and lower training loss compared to randomly initialized PQCs.

Experimental results

Research questions

• RQ1 Can classical tensor network simulations provide effective initial parameterizations that improve the trainability of parametrized quantum circuits?
• RQ2 To what extent can increased classical computational resources (via higher bond dimension χ) mitigate barren plateaus in PQCs?
• RQ3 Does pre-optimization via tensor networks lead to faster convergence and better final performance in quantum machine learning and quantum simulation tasks?
• RQ4 Can this synergistic framework enable deep quantum circuits to overcome the exponential gradient decay typical of randomly initialized PQCs?
• RQ5 How does the performance of TN-initialized PQCs compare to randomly initialized PQCs in terms of optimization dynamics and final solution quality?

Key findings

• PQCs initialized using tensor network simulations exhibit gradient variances and magnitudes that remain nearly constant with increasing circuit depth and qubit count, in contrast to the exponential decay seen in randomly initialized PQCs.
• The method successfully avoids barren plateaus, enabling deep quantum circuits—previously untrainable due to vanishing gradients—to converge reliably to high-quality solutions.
• On Hamiltonian minimization and generative modeling tasks, TN-initialized PQCs achieved significantly lower training losses than randomly initialized counterparts using identical quantum resources.
• The performance of the PQC improves with increasing bond dimension χ in the classical TN simulation, indicating a scalable path to better initialization.
• Even at 100 qubits, the framework maintains favorable scaling, with performance trends favoring larger χ values to sustain gradient stability.
• The approach demonstrates that classical computing resources can be strategically used to enhance quantum circuit performance, effectively short-cutting the path to practical quantum advantage.