Schmidt Spectrum Optimisation Achieves Scalable Quantum State Preparation for Near-Term Hardware

The efficient creation of complex quantum states represents a major challenge in the development of quantum technologies, and researchers continually seek methods to simplify the necessary quantum circuits. Josh Green, Joshua Snow, and Jingbo Wang from The University of Western Australia now present a new algorithm that optimises the preparation of many-body quantum states, represented as Matrix Product States, by focusing on the Schmidt spectrum, a measure of entanglement. Their approach systematically minimises circuit depth while maintaining the inherent structure of these states, a crucial step towards scalable quantum computation on existing hardware. By optimising circuits to reduce entropy, the team achieves state-of-the-art performance, improving the accuracy of state preparation by up to an order of magnitude compared with current methods, and importantly, overcomes limitations in the time-complexity of previous techniques.

Efficient Quantum State Preparation with SOSO

This paper introduces Sequential Optimization of Schmidt (SOSO), a novel method for efficiently preparing quantum states represented as Matrix Product States (MPS) using shallow quantum circuits. SOSO addresses the difficulty of mapping complex quantum states onto quantum hardware with limited circuit depth, a challenge faced by existing methods. The core innovation lies in a loss function based on the Schmidt decomposition of the MPS, explicitly targeting the entanglement structure of the state. The method sequentially builds the quantum circuit layer by layer, utilising local SU(4) gates to efficiently manipulate entanglement, and employs gradient descent with automatic differentiation for optimisation.

Experiments demonstrate that SOSO achieves high fidelity state preparation with significantly shallower circuits compared to other methods, showing improved scalability for larger systems. Benchmarking on ground states of quantum many-body systems confirms its ability to accurately represent complex states, consistently outperforming existing approaches in both fidelity and circuit depth. The importance of a good initial parameter setting, or warm-start, is highlighted, with SOSO serving as an effective initialization for further optimization. This work represents a significant advancement in quantum state preparation, offering a more efficient and scalable approach crucial for realising near-term quantum applications like quantum simulation and machine learning. The use of Schmidt decomposition as a guiding principle for circuit optimization provides new insights into entanglement optimization, reinforcing the importance of good initialization strategies for training quantum circuits.

Schmidt Spectrum Optimisation for Quantum Circuits

Scientists developed Schmidt Spectrum Optimisation (SSO), a new algorithm for designing shallow-depth quantum circuits capable of preparing many-body states represented as Matrix Product States (MPS). SSO systematically disentangles a target MPS using optimised local unitaries, then reverses this process to create a state preparation circuit. By directly optimising the Schmidt spectra of intermediate states, the algorithm effectively reduces entanglement while minimising circuit depth, a crucial factor for near-term quantum hardware implementation. Benchmarking across a range of MPS approximations to ground states of local Hamiltonians demonstrates state-of-the-art shallow-depth performance, improving accuracy by up to an order of magnitude over existing methods.

Furthermore, SSO mitigates the adverse time-complexity scaling observed in previous disentangling-based approaches, avoiding the exponential scaling of computational resources with the number of circuit layers. This improvement stems from the direct optimisation of Schmidt spectra, leading to a more efficient and scalable disentangling process. The method’s ability to efficiently prepare complex quantum states represents a significant step towards realising the potential of near-term quantum computers, offering a substantial improvement in both accuracy and scalability compared to previous techniques.

Schmidt Spectrum Optimisation For Quantum State Preparation

The research team developed Schmidt Spectrum Optimisation (SSO), a new algorithm for designing shallow-depth circuits to prepare many-body quantum states represented as Matrix Product States (MPS). SSO systematically minimises circuit depth while preserving the inherent structure of MPS representations, enabling scalable state preparation on near-term quantum hardware. The core principle involves disentangling the target MPS using optimised local unitaries, then reversing this process to create a state preparation circuit. SSO defines a loss function directly on the Schmidt spectra of intermediate states and uses automatic differentiation to optimise each circuit layer, systematically reducing entropy.

Experiments demonstrate that SSO achieves state-of-the-art shallow-depth performance, improving accuracy by up to an order of magnitude over existing methods across a range of MPS approximations to ground states of local Hamiltonians. On a 48-qubit quantum Ising chain, SSO achieved a fidelity of 0.9980 within just two layers, while the Matrix Product Disentangler (MPD) algorithm exhibited pathological behaviour. Across tests on various Hamiltonians, SSO consistently reduced the error in the prepared state by approximately one order of magnitude compared to MPD. Measurements of the maximum bond dimension during disentangling revealed a significant advantage for SSO, maintaining a lower dimension compared to MPD, directly impacting the computational cost and scalability of the state preparation process. These results confirm that SSO mitigates the adverse time-complexity scaling observed in previous disentangling-based approaches, paving the way for more efficient and scalable quantum state preparation.

Schmidt Optimisation For Shallow Quantum Circuits

This research presents Schmidt Spectrum Optimisation, a new algorithm for designing shallow-depth quantum circuits capable of preparing many-body states represented as Matrix Product States. The method systematically disentangles a target state using optimised layers of quantum gates, then reverses this process to create a state preparation circuit. By directly optimising the Schmidt spectra of intermediate states, the algorithm effectively reduces entanglement while minimising circuit depth, a crucial factor for implementation on near-term quantum hardware. The team demonstrated that this approach significantly improves upon existing methods for state preparation, achieving higher accuracy and mitigating the computational challenges associated with increasing circuit depth.

The highest fidelity state preparation circuits were achieved when combining the algorithm with full optimisation of the circuit operators. The success of this backwards disentangling approach, starting from the target state, alleviates common issues with optimisation algorithms that can plateau prematurely. While the current work focuses on shallow-depth circuits, the principles developed could potentially be extended to explore more complex circuit designs in future research, representing a significant advancement in the field of quantum state preparation.