Dr Isaac Hobday
About
My research project
Quantum Computing for Nuclear PhysicsMy project aims to develop quantum computing algorithms to perform calculations associated with many-body nuclear systems. As the number of particles in a many-body nuclear system increases, the size of the associated Hamiltonian increases exponentially. This creates a problem for classical computers where large problems become essentially unsolvable. Quantum computing can address this issue due to the exponential nature of quantum bits, where additional qubits increase the size of the Hilbert space exponentially. Current quantum computers have large amounts of noise and are prone to large error rates, limiting the types of algorithms that can be performed on quantum hardware. Hybrid algorithms provide some form of solution, where small quantum circuits with low circuit depth are able to be run with sufficiently low error rates to produce meaningful results in tandem with a classical computer. These hybrid algorithms allow for some calculations to be performed on many-body nuclear systems, including ground-state energy and nuclear excited state spectra calculations.
Supervisors
My project aims to develop quantum computing algorithms to perform calculations associated with many-body nuclear systems. As the number of particles in a many-body nuclear system increases, the size of the associated Hamiltonian increases exponentially. This creates a problem for classical computers where large problems become essentially unsolvable. Quantum computing can address this issue due to the exponential nature of quantum bits, where additional qubits increase the size of the Hilbert space exponentially. Current quantum computers have large amounts of noise and are prone to large error rates, limiting the types of algorithms that can be performed on quantum hardware. Hybrid algorithms provide some form of solution, where small quantum circuits with low circuit depth are able to be run with sufficiently low error rates to produce meaningful results in tandem with a classical computer. These hybrid algorithms allow for some calculations to be performed on many-body nuclear systems, including ground-state energy and nuclear excited state spectra calculations.
Publications
Quantum computing can potentially provide advantages for specific computational tasks. The simulation of fermionic systems is one such task that lends itself well to quantum computation, with applications in nuclear physics and electronic systems. Here we present work in which we use a variance minimization method to find the full spectrum of energy eigenvalues of the Lipkin-Meshkov-Glick model, an exactly solvable nuclear shell model type system. We perform these calculations using both quantum simulators and real quantum hardware accessed via IBM cloud-based quantum computers. Using these IBM quantum computers we are able to obtain all eigenvalues for the cases of three and seven fermions (nucleons) in the Lipkin-Meshkov-Glick model. We further show a simulated result for a realistic calculation of 6 Li with a shell model interaction which performs equivalently to the Lipkin-Meshkov-Glick model.
Quantum computing opens up new possibilities for the simulation of many-body nuclear systems. As the number of particles in a many-body system increases, the size of the space if the associated Hamiltonian increases exponentially. This presents a challenge when performing calculations on large systems when using classical computing methods. By using a quantum computer, one may be able to overcome this difficulty thanks to the exponential way the Hilbert space of a quantum computer grows with the number of quantum bits (qubits). Our aim is to develop quantum computing algorithms which can reproduce and predict nuclear structure such as level schemes and level densities. As a sample Hamiltonian, we use the Lipkin-Meshkov-Glick model. We use an efficient encoding of the Hamiltonian onto many-qubit systems, and have developed an algorithm allowing the full excitation spectrum of a nucleus to be determined with a variational algorithm capable of implementation on today’s quantum computers with a limited number of qubits. Our algorithm uses the variance of the Hamiltonian,⟨H⟩2 − ⟨H⟩2, as a cost function for the widely-used variational quantum eigensolver (VQE). In this work we present a variance based method of finding the excited state spectrum of a small nuclear system using a quantum computer, using a reduced-qubit encoding method.