Researchers Map Nuclei Using Fewer Qubits with Quantum Algorithm

Chandan Sarma and Paul Stevenson at University of Surrey have developed a qubit-efficient variational algorithm, comparing three distinct qubit-mapping strategies within the Variational Quantum Eigensolver (VQE) approach. Their algorithm, focused on the nuclei ¹⁰B and ¹²C, shows that a Slater determinant to qubit mapping achieves the most accurate results on quantum hardware, with a 0.21% error for the ground state of ¹⁰B following error mitigation. The algorithm offers a pathway to scaling VQE algorithms for increasingly complex nuclei, potentially advancing our understanding of nuclear physics through quantum computation.

Boron-10 and carbon-12 ground state energies calculated with unprecedented quantum precision

Error rates in calculating the ground state of the ¹⁰B nucleus have fallen to 0.21 per cent, a substantial improvement over previous results of 3.37 and 8.88 per cent achieved with alternative quantum computing strategies. Previously unattainable due to the limitations of classical computational power, this level of precision was attained using a Slater determinant to qubit mapping within the Variational Quantum Eigensolver approach. Simulating the behaviour of even relatively simple atomic nuclei demands immense processing resources, stemming from the many-body problem inherent in quantum chromodynamics and the strong nuclear force. The shell model, a quantum mechanical model describing the structure of the atomic nucleus, provides a framework for these calculations, but its computational cost scales exponentially with the number of nucleons (protons and neutrons).

At the University of Surrey, the team extended this qubit-efficient mapping to successfully model the ground state of ¹²C, showing a 6.82 per cent deviation from the exact result and paving the way for calculations on increasingly complex nuclei. The nucleus of carbon-12 served as a test case, verifying the accuracy of this quantum computing approach and demonstrating its potential beyond boron-10. A Variational Quantum Eigensolver, a hybrid quantum-classical algorithm, was employed by the team, utilising the Slater determinant mapping to represent nuclear particles as qubits. This strategy required fewer qubits than alternative methods, enabling simulations on current quantum hardware such as IBM’s ‘ibm_fez’ processor and a simulator named ‘FakeFez’. Fidelity evaluations confirmed the quantum wavefunctions closely matched those predicted by the conventional nuclear shell model, suggesting the quantum calculations accurately capture the essential physics. The VQE algorithm works by iteratively optimising a trial wavefunction, encoded as a quantum circuit, to minimise the energy expectation value. This minimisation is performed using a classical optimiser that adjusts the parameters of the quantum circuit based on measurements performed on the quantum computer. Substantial error correction will be needed to tackle the complexities of heavier nuclei and enable practical applications, despite the 0.21 per cent error rate achieved for boron-10 being a major step. Current quantum devices are susceptible to decoherence and gate errors, which introduce noise into the calculations and limit the accuracy of the results.

Compressed Slater determinants enable feasible quantum nuclear structure modelling

Calculating the structure of atomic nuclei has long been a challenge, demanding ever greater computational resources as scientists strive for more accurate models. The team’s success with boron-10 and carbon-12 highlights the importance of qubit efficiency in quantum nuclear structure modelling, while other groups explore entirely different approaches to encoding nuclear data. Reducing qubit requirements is vital given current limitations in quantum hardware size and stability. The number of qubits required to represent a nuclear system grows rapidly with the number of nucleons, making it difficult to simulate even moderately sized nuclei with existing quantum computers. The Slater determinant mapping offers a particularly efficient way to represent the many-body wavefunction, as it directly corresponds to the antisymmetric nature of the nuclear wavefunction required by the Pauli exclusion principle.

Validating the approach, successful simulations were performed on both noisy simulators and actual quantum computers, achieving less than one percent error for boron-10. A comparison of three qubit-mappings for translating nuclear data into a format usable by quantum computers within the Variational Quantum Eigensolver approach was undertaken. These mappings included a direct mapping of the Hamiltonian matrix, a mapping based on second quantisation, and the compressed Slater determinant mapping. The Hamiltonian matrix represents the energy operator of the nuclear system, while the second quantisation approach expresses the Hamiltonian in terms of creation and annihilation operators for nucleons. Applying these mappings to mid-$p$-shell nuclei, ¹⁰B and ¹²C, revealed that a compressed Slater determinant mapping offers a promising balance between accuracy and qubit efficiency, key for scaling up quantum calculations. The mid-$p$-shell nuclei are particularly interesting because they exhibit a complex interplay between single-particle and collective behaviour. Demonstrating the potential of this method to overcome limitations inherent in classical computation, a 0.21 per cent error in determining the ground state of ¹⁰B opens avenues for exploring more complex nuclear systems. Future research will focus on extending this approach to heavier nuclei and incorporating more sophisticated error mitigation techniques to further improve the accuracy of the calculations. This could lead to a deeper understanding of nuclear structure, nuclear reactions, and the origin of the elements.

The significance of this work extends beyond simply achieving a lower error rate. It demonstrates the feasibility of using quantum computers to tackle problems in nuclear physics that are currently intractable for classical computers. The ability to accurately calculate the ground state energies of nuclei is crucial for understanding their stability, decay modes, and role in astrophysical processes. Furthermore, the development of qubit-efficient algorithms is essential for making quantum computing a practical tool for scientific discovery. The team’s work provides a valuable benchmark for future research in this field and paves the way for exploring even more complex nuclear systems with quantum computers.

Researchers demonstrated that a compressed Slater determinant mapping strategy successfully calculated the ground state energy of the ¹⁰B nucleus with an error of 0.21 per cent using quantum hardware. This finding suggests that quantum computing offers a potential route to solving complex problems in nuclear physics currently beyond the reach of conventional methods. The study also extended this approach to ¹²C and evaluated the resulting wavefunctions, indicating the method’s scalability. Future work will explore applying this technique to heavier nuclei and refining error mitigation strategies to enhance accuracy.