Unitary Cluster Jastrow Ansatz Parameter Initialization Improves Energy Accuracy for Quantum Algorithms with up to 65 Qubits

Variational algorithms represent a promising path towards utilising quantum computers to solve complex problems, and the unitary cluster Jastrow ansatz, along with its local variant, offers a particularly efficient approach. Wan-Hsuan Lin from the University of California, Los Angeles, Fangchun Liang from The Cleveland Clinic, and Mario Motta from IBM Quantum, alongside their colleagues, now demonstrate significant improvements to the initial setup of these algorithms. The team addresses the loss of accuracy that occurs when simplifying the calculations to suit the limitations of current quantum hardware, developing methods to better approximate the results of a classical coupled cluster calculation. By employing compressed double factorisation and approximate tensor network simulation, they enhance both the accuracy and efficiency of these variational algorithms, validating their approach through simulations of up to 52 qubits and experiments on superconducting processors with up to 65 qubits. This work represents a crucial step towards realising the potential of near-term quantum computers for tackling challenging computational problems.

Variational Algorithms for Molecular Electronic Structure

Scientists are developing advanced algorithms to accurately and efficiently calculate the electronic structure of molecules, particularly those with complex electron interactions that challenge traditional computational methods. This research focuses on variational quantum algorithms (VQAs), which are designed to run on emerging quantum computers and promise solutions beyond the reach of classical computers. The team addresses limitations in existing methods by improving both accuracy and scalability for increasingly complex molecular systems. A central achievement is the development of Sample-Based Quantum Diagonalization (SBQD), an algorithm that efficiently approximates the ground state energy of a molecule using a quantum computer.

To further refine calculations, researchers utilize active space models, which focus computational effort on the most important electrons and orbitals. They also employ Matrix Product States (MPS) as a classical pre-optimization technique, improving the performance of the VQA by preparing the quantum circuit before execution. Additional classical algorithms, including Semistochastic Heat-Bath Configuration Interaction (SHB-CI) and Tailored Coupled Cluster (TCC), generate accurate initial estimates for the quantum circuit and incorporate higher-order correlation effects. The research leverages a suite of software tools, including ffsim, a fast fermionic simulator, and Qiskit Addon (SQD), an extension for implementing SBQD.

Classical calculations rely on PySCF, a Python-based quantum chemistry package, and Quimb, a library for quantum information and many-body calculations. The team also utilizes Dice, a tool for correlated wavefunction calculations, alongside standard scientific computing libraries like SciPy, JAX, and NumPy. All software is openly available through GitHub, fostering collaboration and reproducibility. These advancements improve the accuracy and efficiency of VQAs, enabling calculations on larger and more complex molecules, including those with strong electron correlation. The techniques are applicable to calculating key molecular properties, such as energies, geometries, and vibrational frequencies. This work emphasizes a hybrid quantum-classical approach, combining the strengths of both types of computers, and prioritizes practicality for implementation on near-term quantum hardware.

Compressed Factorization Improves Coupled Cluster Initialization

Scientists have developed innovative methods to enhance the initialization of parameters within the unitary cluster Jastrow (UCJ) and local UCJ (LUCJ) ansatzes, promising improvements for variational quantum algorithms. Recognizing that truncating repetitions or discarding interactions in these ansatzes degrades accuracy on near-term quantum processors, the study pioneered two complementary techniques to recover the fidelity of coupled cluster, singles and doubles (CCSD) approximations. The first method employs compressed double factorization of CCSD amplitudes, applicable to both expectation value- and sample-based algorithms, to refine the initial parameter estimates. This factorization effectively compresses the data, allowing for a more accurate representation of the original CCSD amplitudes despite the limitations imposed by quantum hardware.

To further improve performance, particularly for sample-based algorithms, researchers harnessed approximate tensor network simulation. This technique functions as a surrogate optimization method, enhancing the quality of samples generated by the ansatz circuit and mitigating the impact of noisy quantum computations. The team implemented this simulation to create more reliable data, effectively circumventing the challenges associated with limited quantum resources and improving the overall accuracy of the algorithm. Validation involved rigorous testing using exact state vector simulation on quantum systems of up to 52 qubits, complemented by experiments on superconducting quantum processors utilizing up to 65 qubits. Results consistently indicate that the combined use of compressed double factorization and approximate tensor network simulation significantly improves the performance of both expectation value- and sample-based quantum algorithms, paving the way for more accurate and efficient quantum simulations of complex systems. The team contributed an implementation of the compressed double factorization to the open-source software library ffsim, furthering the accessibility of these advancements to the wider research community.

Improved Variational Algorithms With Optimized Initialization

Scientists have achieved significant improvements in variational quantum algorithms through enhancements to parameter initialization techniques for the unitary cluster Jastrow (UCJ) ansatz and its local variant, LUCJ. Researchers developed two complementary methods to enhance the accuracy of the LUCJ ansatz, which balances physical motivation with hardware efficiency. The first method, applicable to both expectation value- and sample-based algorithms, employs compressed double factorization to refine the initial parameters derived from coupled cluster, singles and doubles (CCSD) calculations. This technique effectively recovers the accuracy of the CCSD approximation, even when the number of repetitions within the ansatz is truncated, a common necessity for reducing computational demands.

The second method, designed for sample-based algorithms, utilizes approximate tensor network simulation to generate higher-quality samples for the ansatz circuit, improving the reliability of the results through a surrogate optimization approach. Validation involved rigorous testing using exact state vector simulations on systems of up to 52 qubits, as well as experiments performed on superconducting quantum processors containing up to 65 qubits. Results demonstrate that these improvements significantly enhance the performance of both expectation value- and sample-based quantum algorithms. Specifically, the compressed double factorization method improves the initial parameter accuracy, while the tensor network simulation refines the quality of samples generated by the circuit. This combined approach delivers a substantial advancement in the ability to perform complex quantum calculations on available hardware.

Improved Variational Quantum Chemistry Parameter Initialisation

Scientists have made advancements in variational quantum algorithms for chemistry, specifically focusing on improving the performance of the unitary cluster Jastrow (UCJ) and local UCJ (LUCJ) ansatzes. Researchers developed two complementary methods to enhance parameter initialization. The first method utilizes compressed double factorization to more closely approximate the amplitudes derived from coupled cluster calculations, a standard technique in quantum chemistry. The second method employs approximate tensor network simulation to further optimize parameters, particularly for algorithms that rely on sampling quantum states.

Validation involved both precise classical simulations and experiments performed on superconducting quantum processors, encompassing systems of up to 65 qubits. Results demonstrate that compressed double factorization consistently improves upon simpler truncation methods across various molecular systems, and can even surpass the accuracy of the untruncated ansatz by generating a more diverse set of quantum configurations. Furthermore, the tensor network optimization provided additional gains, especially when the initial approximations used in the calculations were less accurate. The team acknowledges that the number of valid bitstrings sampled can be limited by the electron-to-orbital ratio of the system, and that this is an area for continued investigation. These combined advancements offer a practical pathway to enhance the performance of variational quantum algorithms on currently available quantum processors, enabling more accurate quantum chemistry calculations.