Scientists are developing new methods to prepare complex quantum states efficiently, a challenge due to the exponential resources typically required. Tomasz Szołdra from Zentrum für Optische Quantentechnologien, Universität Hamburg, Rick Mukherjee from the Department of Physics and Astronomy, University of Tennessee, and Peter Schmelcher from Zentrum für Optische Quantentechnologien, Universität Hamburg, present a novel framework for scalable Matrix Product State (MPS) preparation, combining heuristic circuits with variational optimisation techniques. This collaborative research, bridging expertise between the Universität Hamburg and the University of Tennessee, addresses limitations in existing approaches that either lack accuracy or struggle to scale. By employing staircase-like and brick wall circuits as initialisations for optimisation, the team demonstrates high-fidelity state preparation for systems of up to 50 qubits, alongside significant reductions in circuit complexity, depths reduced by up to 50% and gate counts by 33%. These results represent a principled and scalable protocol, potentially enabling the application of MPS to utility-scale problems on emerging quantum hardware.
Scientists have developed a new framework for preparing complex quantum states using a hybrid approach that blends established techniques with innovative optimizations, addressing the fundamental challenge of exponential resources typically required to define the state of multiple qubits. The core of this advancement lies in the framework’s ability to ‘warm-start’ variational optimisation using circuits generated by either staircase-like or brick wall disentangler methods, providing a strong initial guess that accelerates the optimisation process and enables the preparation of larger systems, ranging from 19 to 50 qubits, with improved accuracy. Target MPSs can be directly specified as physical quantum states or generated from classical data using techniques like singular value decomposition and tensor cross interpolation, expanding the versatility of the approach. Crucially, the researchers incorporated entanglement-based qubit reordering, formulated as a quadratic assignment problem, and low-level circuit optimizations, reducing circuit depth by up to 50% and the number of CNOT gates by 33%, critical improvements for execution on near-term quantum hardware. Evaluation across datasets of varying complexity revealed trade-offs between fidelity, gate count, and circuit depth, with brick wall circuits generally achieving the shallowest depths and staircase-like circuits minimising gate counts. Logical error rates of 2.914% per cycle were achieved during the preparation of matrix product states, demonstrating a significant advancement in quantum circuit fidelity. Independent revisiting of calculations revealed that deep sequential matrix product disentangler circuits are simulable with bond dimensions scaling as O(χ), significantly lower than the previously estimated O(2L). Three enhancements to the SMPD implementation were employed: decomposing isometries into only two CNOT gates and single-qubit rotations, skipping two-body gates around already disentangled bonds, and utilising a mixed-canonical gauge for MPS representation. The mixed-canonical gauge construction resulted in circuits with depths reduced by up to 50% compared to left- or right-canonical forms, achieved by arranging gates in a “V”-shape. A central bond with singular values Λ1 and Λ2, normalized such that Λ2² + Λ1² = 1, corresponds to an isometry realizable with a single RY rotation and one CNOT gate, calculated deterministically from matrix elements. Following compression, an entanglement-based qubit reordering minimizes quantum mutual information between distant qubit pairs, formulated and solved as a quadratic assignment problem, strategically arranging qubits to improve the efficiency of subsequent circuit construction. Heuristic circuits are then built layer-by-layer from the reordered MPS, generating either sequential (SMPD) or brick wall (BMPD) architectures. The SMPD approach offers flexibility through left-, right-, and mixed-canonical MPS forms, each dictating a unique arrangement of quantum gates, with enhancements including isometric gate decompositions reducing the number of CNOT gates required for two-qubit unitaries from three to two and the removal of redundant gates. To further refine the prepared state, a variational optimisation procedure is implemented, initialising the process with the circuits generated by the heuristic methods, addressing the issue of barren plateaus often encountered in variational quantum algorithms. Both the Evenbly-Vidal and Riemannian optimisation algorithms are employed to maximise fidelity with the target MPS, leveraging the warm-start provided by the heuristic initialisation, allowing for iterative refinement and approximating the target MPS with a scalable quantum circuit. This new work fundamentally reshapes the approach, moving beyond reliance on purely deterministic or purely variational methods, intelligently combining their strengths by using heuristic circuits to ‘warm start’ a variational optimisation process, achieving a significant leap in both fidelity and scalability. What distinguishes this framework is its practicality, demonstrably preparing high-fidelity states across systems of 19 to 50 qubits, a scale edging closer to the requirements of genuinely useful quantum applications. The incorporation of entanglement-based qubit reordering and low-level circuit optimisations further underscores a commitment to real-world implementation, reducing circuit complexity by a notable margin. However, the trade-offs between fidelity, gate count, and circuit depth remain a critical consideration, with optimised brick wall circuits excelling in minimising depth while staircase-like circuits offer lower gate counts, forcing developers to make informed choices based on specific hardware constraints. Moreover, the inherent limitations of representing states with finite bond dimensions and the potential for truncation errors require careful monitoring and mitigation, with future work likely focusing on dynamically adjusting bond dimensions and exploring more sophisticated error mitigation strategies, potentially unlocking applications in materials science, machine learning, and beyond.
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🗞 Scalable Preparation of Matrix Product States with Sequential and Brick Wall Quantum Circuits
🧠 ArXiv: https://arxiv.org/abs/2602.12042