Quantum algorithms require accurate representations of electronic states on a quantum device, yet the approximation of electronic wavefunctions for strongly correlated systems remains a profound theoretical challenge, with existing methods struggling to balance the competing demands of chemical accuracy and gate efficiency. Moreover, a critical limitation of most of the state-of-the-art methods developed to date lies in their substantial reliance on extensive pre-circuit measurements, which introduce significant overheads and contribute to inefficiencies in practical implementation. To address these interconnected challenges and establish a harmonious synergy between them, we propose an algorithmic framework that focuses on efficiently capturing the molecular strong correlation through an ordered set of computationally less demanding rank-one and seniority-zero paired excitations, yielding a parameterized Ansatz with shallow gate depth. Furthermore, to achieve minimal pre-circuit measurement overhead, we implement a selective pruning of excitations through a hybrid approach that combines chemically informed system-specific operator selection with parallel rank-one excitation driven uni-parameter circuit optimization guided energy-sorting strategy. With the incorporation of qubit-based excitations via particle-preserving exchange circuits, we demonstrate a further reduction in quantum complexities, enhancing the overall resource efficiency of the approach. With a range of challenging applications on strongly correlated systems, we demonstrate that our dynamic Ansatz not only significantly enhances computational efficiency but also delivers exceptional accuracy, robustness, and resilience to the noisy environments inherent in near-term quantum hardware.
Quantum algorithms require accurate representations of electronic states on a quantum device, yet the approximation of electronic wavefunctions for strongly correlated systems remains a profound theoretical challenge, with existing methods struggling to balance the competing demands of chemical accuracy and gate efficiency. Moreover, a critical limitation of most of the state-of-the-art methods developed to date lies in their substantial reliance on extensive pre-circuit measurements, which introduce significant overheads and contribute to inefficiencies in practical implementation. To address these interconnected challenges and establish a harmonious synergy between them, we propose an algorithmic framework that focuses on efficiently capturing the molecular strong correlation through an ordered set of computationally less demanding rank-one and seniority-zero paired excitations, yielding a parameterized Ansatz with shallow gate depth. Furthermore, to achieve minimal pre-circuit measurement overhead, we implement a selective pruning of excitations through a hybrid approach that combines chemically informed system-specific operator selection with parallel rank-one excitation driven uni-parameter circuit optimization guided energy-sorting strategy. With the incorporation of qubit-based excitations via particle-preserving exchange circuits, we demonstrate a further reduction in quantum complexities, enhancing the overall resource efficiency of the approach. With a range of challenging applications on strongly correlated systems, we demonstrate that our dynamic Ansatz not only significantly enhances computational efficiency but also delivers exceptional accuracy, robustness, and resilience to the noisy environments inherent in near-term quantum hardware.
Quantum algorithms require accurate representations of electronic states on a quantum device, yet the approximation of electronic wave functions for strongly correlated systems remains a profound theoretical challenge, with existing methods struggling to balance the competing demands of chemical accuracy and gate efficiency. Moreover, a critical limitation of the most of the state-of-the-art methods developed to date lies in their substantial reliance on extensive pre-circuit measurements, which introduce significant overheads and contribute to inefficiencies in practical implementation. To address these interconnected challenges and establish a harmonious synergy between them, we propose an algorithmic framework that focuses on efficiently capturing the molecular strong correlation through an ordered set of computationally less demanding rank-one and seniority-zero excitations, yielding a parameterized ansatz with shallow gate depth. Furthermore, to achieve minimal pre-circuit measurement overhead, we implement a selective pruning of excitations through a hybrid approach that combines intuition-based selection with shallow-depth, rank-one excitations driven uni-parameter circuit optimization strategy. With the incorporation of qubit-based excitations via particle-preserving exchange circuits, we demonstrate a further reduction in quantum complexities, enhancing the overall resource efficiency of the approach. With a range of challenging applications on strongly correlated systems, we demonstrate that our dynamic ansatz not only significantly enhances computational efficiency but also delivers exceptional accuracy, robustness, and resilience to the noisy environments inherent in near-term quantum hardware.
Determining the exponentially scaled ground state wavefunction and the associated molecular properties remains one of the central challenges in quantum chemistry. Hybrid quantum-classical algorithms implemented on quantum computers offer a promising route toward addressing this problem. However, despite several successful demonstrations on small molecular systems, accurate simulations of large and chemically realistic molecules remain difficult due to the limited capability of noisy intermediate scale quantum (NISQ) hardware. To bypass the limitations of NISQ devices, while simultaneously retaining the accuracy of the ground state energy estimations, we propose a dynamic ansatz construction strategy based on operator commutativity and energy driven screening within density matrix embedding theory (DMET) framework. The partitioning of the full system allows us to dynamically construct the ansatz over individual embedded subsystems, allowing each embedding problem be solved individually to a desired accuracy. The embedding Hamiltonian is updated in a self-consistent manner with dynamically formulated wavefunction, and their coupled optimization leads to accurate and efficient description of the overall system. To assess the performance of this approach, we apply it to several molecular systems and chemical processes with up to 144 qubits. These simulations require at most 20 qubits at a time and demonstrate improved accuracy and significantly reduced quantum gate requirements compared with conventional ansatze. We further investigate the impact of various fragmentation strategies and demonstrate the adaptability of our approach at each step of the DMET self-consistency cycle that leads to significantly improved accuracy for strongly correlated system.
Determining the exponentially scaled ground state wavefunction and the associated molecular properties remains one of the central challenges in quantum chemistry. Hybrid quantum-classical algorithms implemented on quantum computers offer a promising route toward addressing this problem. However, despite several successful demonstrations on small molecular systems, accurate simulations of large and chemically realistic molecules remain difficult due to the limited capability of noisy intermediate-scale quantum (NISQ) hardware. To bypass the limitations of NISQ devices, while simultaneously retaining the accuracy of the ground state energy estimations, we propose a dynamic ansatz construction strategy based on operator commutativity and energy driven screening within the density matrix embedding theory (DMET) framework. The partitioning of the full system allows us to dynamically construct the ansatz over individual embedded subsystems, allowing each embedding problem to be solved individually to a desired accuracy. The embedding Hamiltonian is updated in a self-consistent manner with the dynamically formulated wavefunction, and their coupled optimization leads to an accurate and efficient description of the overall system. To assess the performance of this approach, we apply it to several molecular systems, including C10 (100 qubits), conformers of l-glucose (144 qubits), and the reactant, intermediate, and product structures of the methyl vinyl ketone and cyclopentadiene Diels-Alder reaction (124 qubits). These simulations require at most 20 qubits at a time and demonstrate improved accuracy and significantly reduced quantum gate requirements compared with conventional ansatze. We further investigate the impact of various fragmentation strategies and demonstrate the adaptability of our approach at each step of the DMET self-consistency cycle that leads to significantly improved accuracy for strongly correlated systems. These results highlight the emerging feasibility of addressing large-scale chemical problems of industrial relevance on near-term quantum devices.
The ability of quantum computers to overcome the exponential memory scaling of many-body problems is expected to transform quantum chemistry. Quantum algorithms require accurate representations of electronic states on a quantum device, but current approximations struggle to combine chemical accuracy and gate-efficiency while preserving physical symmetries, and rely on measurement-intensive adaptive methods that tailor the wave function ansatz to each molecule. In this contribution, we present a symmetry-preserving and gate-efficient ansatz that provides chemically accurate molecular energies with a well-defined circuit structure. Our approach exploits local qubit connectivity, orbital optimisation, and connections with generalised valence bond theory to maximise the accuracy that is obtained with shallow quantum circuits. Numerical simulations for molecules with weak and strong electron correlation, including benzene, water, and the singlet-triplet gap in tetramethyleneethane, demonstrate that chemically accurate energies are achieved with as much as 84% fewer two-qubit gates compared to state-of-the-art adaptive ansatz techniques.
The ability of quantum computers to overcome the exponential memory scaling of many-body problems is expected to transform quantum chemistry. Quantum algorithms require accurate representations of electronic states on a quantum device, but current approximations struggle to combine chemical accuracy and gate efficiency while preserving physical symmetries, and rely on measurement-intensive adaptive methods that tailor the wave function to each molecule. In this contribution, we present a symmetry-preserving and gate-efficient that provides chemically accurate molecular energies with a well-defined circuit structure. Our approach exploits local qubit connectivity, orbital optimization, and connections with generalized valence bond theory to maximize the accuracy that is obtained with shallow quantum circuits. Numerical simulations for molecules with weak and strong electron correlation, including benzene, water, and the singlet-triplet gap in tetramethyleneethane, demonstrate that chemically accurate energies are achieved with as much as 84% fewer two-qubit gates compared to state-of-the-art adaptive techniques. Published by the American Physical Society 2024
Computer simulation is central to understanding the behaviour of matter. Yet, more than a century after the development of quantum theory, first-principles simulation of chemistry remains a daunting challenge, owing to the exponential growth in memory required to represent interacting quantum particles such as electrons in molecules. Quantum computing offers, in principle, a fundamentally more efficient paradigm for simulating quantum systems, with quantum chemistry often cited as a flagship application. However, many quantum algorithms face intrinsic limitations, and any genuine quantum advantage must surpass the strong baseline set by decades of progress in classical algorithms and hardware. While classical methods often suffice for simulating weakly correlated systems, systems with many strongly correlated electrons remain a challenge for both classical and quantum approaches. In this thesis, we develop quantum algorithms for solving the time-independent Schrödinger equation, with a focus on molecular systems with strongly correlated electrons. We introduce a framework for identifying a compact set of states that parametrise the many-body wavefunction by capturing the correlation due to spin coupling between localised electrons. This representation requires very few variational parameters but incurs a very high memory cost on classical computers. To overcome this, we design quantum circuits that efficiently prepare such states by exploiting their symmetry, encoding the dominant entanglement structure of electronic wavefunctions into the initial qubit states. Through theoretical analysis and classical simulations of quantum computers, we show that this substantially reduces the quantum resources required to accurately compute ground- and excitedstate properties. Finally, we develop an approach for approximating the optimal ansatz within the variational quantum eigensolver, an algorithm designed for near-term quantum devices. Our method constructs wavefunctions from products of symmetrypreserving unitary operators and couples discrete and continuous optimisation to yield highly compact representations of strongly correlated electrons using shallow quantum circuits. Together, these results establish complementary directions for embedding problemspecific structure into quantum simulation algorithms, advancing the practical simulation of strongly correlated electrons.