Catalá and Colleagues Design Physics-Informed VQC for Phase Detection in Correlated Matter

Hugo Catalá and colleagues at the University of Valencia present a new Physics-Informed Variational Quantum Classifier (VQC) for identifying quantum phases within strongly correlated matter. The VQC addresses a key need for characterising these phases, which is vital for advancing quantum sensing technologies. Their quantum architecture, built upon the Trotterised time-evolution of an effective Hamiltonian, uniquely links learnable parameters to physical quantities, enabling efficient discovery of the optimal interferometric protocol for distinguishing between Bose-Einstein Condensate and Bardeen-Cooper-Schrieffer regimes. Validated on the QRed superconducting quantum processor, the VQC maintains accurate phase ordering despite hardware limitations and offers a scalable solution with linear gate complexity, circumventing the challenges of classical simulation.

Quantum classifier resolves many-body system limitations with linear scalability

The Supercomputing Centre (BSC-CNS) has achieved a Physics-Informed Variational Quantum Classifier (VQC) with linear gate complexity, O(N), a sharp improvement over classical simulations hampered by exponential memory requirements. Strongly correlated systems, where interactions between particles are significant, present a formidable challenge to computational modelling. Traditional methods, such as Density Functional Theory and Quantum Monte Carlo, become computationally intractable as the number of interacting particles (N) increases, due to the exponential scaling of the Hilbert space. This VQC circumvents that limitation, enabling analysis of many-body systems previously inaccessible to computation. The core innovation lies in leveraging the principles of quantum mechanics to perform classification tasks, effectively utilising the inherent parallelism of quantum systems. The team validated their VQC on the QRed superconducting quantum processor, successfully detecting the transition between a Fermi polaron and a molecular bound state, and accurately distinguishing between Bose-Einstein Condensate and Bardeen-Cooper-Schrieffer regimes despite hardware imperfections. These regimes represent fundamentally different states of matter, characterised by distinct collective behaviours of the constituent particles.

Just two learnable parameters, the Trotter step size and effective background interaction strength, allowed the VQC to distinguish between different quantum phases. The Trotter decomposition is a crucial technique in quantum computation, approximating the time evolution operator by breaking it down into a series of simpler, single-qubit gates. The Trotter step size controls the accuracy of this approximation; smaller step sizes yield higher accuracy but require more gates. The effective background interaction strength represents the strength of the interactions between the particles in the system. This parameterisation represents a reduction of over two orders of magnitude in parameters compared to a classical Feed Forward Neural Network, which required 337 trainable weights to achieve equivalent classification accuracy. This significant reduction in parameters not only simplifies the model but also reduces the risk of overfitting, a common problem in machine learning where the model learns the training data too well and fails to generalise to new data. Benchmarking against classical methods revealed the VQC’s capacity to generalise across the parameter space with a minimal dataset of 100 samples, avoiding the overfitting common in classical models. Analysis of five representative points across the phase diagram, utilising between four and ten qubits, showed the VQC successfully mapped the underlying phase dynamics. Results on the QRed processor yielded values between 0.082 and 0.900 for the noiseless simulator, and between 0.107 and 0.875 for the hardware, providing insight into the durability of the approach and highlighting the potential for application in noisy intermediate-scale quantum (NISQ) devices. Ramsey interferometry is a sensitive technique used to measure the energy difference between quantum states, and the VQC effectively learns to optimise the parameters of this interferometry for accurate phase identification.

Identifying material phases using quantum machine learning bypasses simulation limitations

Increasing focus is placed on utilising quantum systems for sensing applications, demanding strong methods for characterising the complex phases of matter within these devices. Quantum sensors, leveraging phenomena like superposition and entanglement, promise unprecedented sensitivity and precision in measurements of physical quantities such as magnetic fields, electric fields, and temperature. However, realising the full potential of these sensors requires a deep understanding of the underlying quantum phases of the materials they are built from. While successful phase ordering was demonstrated, the extent to which these results generalise to larger, more complex quantum processors remains an open question, introducing a vital tension when relying on the QRed processor. The QRed processor, while a valuable platform for initial validation, has a limited number of qubits and is susceptible to noise, which could affect the performance of the VQC on larger, more complex systems. Further research is needed to assess the scalability and robustness of the VQC on different quantum hardware platforms. Nevertheless, the team’s physics-informed approach to quantum machine learning offers a pathway towards more interpretable and efficient algorithms, sidestepping the computational demands of simulating many interacting quantum particles on conventional computers. By embedding prior knowledge of the physical system into the design of the quantum circuit, the VQC can learn more effectively and require fewer training samples.

This advance provides a valuable benchmark for future development of quantum sensors and their application to materials science. A new method for identifying quantum phases has been established, directly linking quantum simulation with machine learning to overcome traditional computational limitations. By designing a quantum circuit mirroring the physical processes within a material, the classifier learns optimal measurement settings, offering a potentially powerful tool for materials characterisation and quantum sensing. The ability to accurately identify quantum phases is crucial for understanding the properties of materials and designing new materials with tailored functionalities. This work opens up exciting possibilities for accelerating materials discovery and developing advanced quantum technologies. The VQC’s linear scalability and robustness to noise make it a promising candidate for deployment on future, larger-scale quantum computers, paving the way for a new era of quantum-enhanced materials science.

The researchers successfully demonstrated a Physics-Informed Variational Quantum Classifier capable of distinguishing between different quantum phases of matter. This is important because characterising these phases is a key step towards developing more sensitive quantum sensors. Using the QRed superconducting quantum processor, the VQC accurately identified the topological phase transition between a Fermi polaron and a molecular bound state, even with inherent hardware noise. The classifier’s design, based on the physics of the system, also exhibits linear scalability, meaning it avoids the computational limitations of classical simulations and may be applicable to more complex systems.