Researchers are continually seeking ways to overcome the limitations of current quantum computers, particularly the challenge of performing complex calculations with limited resources. Smik Patel, Praveen Jayakumar, and Tao Zeng, alongside Artur F. Izmaylov and colleagues from the University of Toronto and York University, present a new approach called Quantum Seniority-based Subspace Expansion, or Q-SENSE, which streamlines quantum calculations by cleverly balancing the demands on the quantum computer and classical processing. This method constructs solutions by combining simpler quantum operations and classical computations, effectively reducing the complexity of the quantum circuits required, a major hurdle for near-term devices. Q-SENSE uniquely exploits inherent symmetries within the problem to minimise the number of measurements needed, offering a potentially scalable and resource-efficient pathway towards achieving quantum advantage, both with today’s hardware and in the future as more powerful quantum computers emerge.
SANOE Algorithm Reduces Qubit Requirements for Molecules
This research introduces the Seniority-Adaptive Non-Orthogonal Quantum Eigensolver (SANOE), a new quantum algorithm designed to efficiently calculate the ground state energy of molecules. Accurately simulating molecular electronic structure is computationally demanding, and SANOE addresses limitations of traditional algorithms by employing a seniority-based approach, categorizing electron pairs to allow for a more compact wavefunction representation. The algorithm focuses on the most important electron pairs to reduce computational complexity and utilizes a non-orthogonal ansatz, offering a more flexible wavefunction with fewer parameters and potentially shallower quantum circuits. Researchers also developed techniques to reduce the number of measurements needed to estimate the ground state energy, improving efficiency. Through theoretical development and numerical simulations, the team demonstrated that SANOE achieves accurate results with fewer qubits compared to traditional methods, confirming its potential for near-term implementation and scalability to larger molecular systems.
Quantum Subspace Expansion for Molecular Simulation
Researchers developed Quantum SENiority-based Subspace Expansion (Q-SENSE), a hybrid quantum-classical algorithm designed to overcome limitations in current methods for simulating molecular electronic structure. This innovative approach interpolates between the Variational Quantum Eigensolver (VQE) and Configuration Interaction (CI) techniques, constructing Hamiltonian matrix elements on a quantum computer and solving the resulting eigenvalue problem classically, reducing the depth of quantum circuits needed for near-term hardware. The method represents a quantum state as a combination of shallower circuits, determining coefficients by solving a mathematical problem on a classical computer. Unlike earlier subspace expansion methods, Q-SENSE specifically targets minimizing demands on quantum hardware. The team leveraged symmetry principles to construct orthogonal basis states, significantly reducing the number of measurements needed, and minimized the condition number of the overlap matrix for further efficiency.
Expanding Wavefunctions with Quantum Subspace Expansion
Researchers have developed Quantum SENiority-based Subspace Expansion (Q-SENSE), offering a promising route towards achieving quantum advantage on near-term and early fault-tolerant quantum computers. This hybrid quantum-classical method addresses a key limitation of Variational Quantum Eigensolver (VQE) approaches by exchanging circuit complexity for the computational cost of determining additional matrix elements, systematically expanding the wavefunction approximation with increasing seniority, a measure of electron correlation. The core innovation lies in building unitaries to ensure the resulting basis states are eigenstates of the seniority operator, guaranteeing orthogonality between different seniority sectors and allowing for free optimization of parameters. Furthermore, Q-SENSE leverages this property to utilize compressed qubit encodings, potentially reducing the number of qubits required for computation. Experiments demonstrate that Q-SENSE systematically includes higher seniority sectors, providing a more accurate representation of strongly correlated systems while maintaining computational efficiency, and offers adaptability to different quantum hardware capabilities.
Q-SENSE Bridges Quantum and Classical Accuracy
The research introduces Q-SENSE, a new framework for calculating molecular electronic structure that combines quantum and classical computation. This method addresses limitations of existing algorithms on near-term quantum hardware by exchanging circuit complexity for the need to compute additional basis functions, effectively interpolating between Variational Quantum Eigensolver (VQE) and Configuration Interaction (CI) methods. By leveraging symmetry principles and constructing orthogonal basis states, Q-SENSE reduces the number of necessary measurements and avoids numerical instabilities. Results demonstrate that Q-SENSE achieves chemical accuracy for both weakly and strongly correlated systems, including challenging bond dissociation scenarios, with fewer basis states than traditional methods like CISD. The method offers two variants, VO and PT, each with complementary trade-offs between circuit complexity and basis set size, both significantly reducing measurement costs compared to standard VQE, and is compatible with current quantum hardware, with calculations completed within minutes on existing superconducting processors.
👉 More information
🗞 Quantum Seniority-based Subspace Expansion: Linear Combinations of Short-Circuit Unitary Transformations for Efficient Quantum Measurements
🧠ArXiv: https://arxiv.org/abs/2509.01061