Projection algorithm for state preparation on quantum computers

Abstract

We present an efficient method to prepare states of a many-body system on quantum hardware, first isolating individual quantum numbers and then using time evolution to isolate the energy. Our method in its simplest form requires only one additional auxiliary qubit. The total time evolved for an accurate solution is proportional to the ratio of the spectrum range of the trial state to the gap to the lowest excited state, and the accuracy increases exponentially with the time evolved. Isolating the quantum numbers is efficient because of the known eigenvalues, and increases the gap thus shortening the propagation time required. The success rate of the algorithm, or the probability of producing the desired state, is a simple function of measurement times and phases and is dominated by the square overlap of the original state to the desired state. We present examples from the nuclear shell model and the Heisenberg model. We compare this algorithm to previous algorithms for short evolution times and discuss potential further improvements.

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• Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions
• Nuclear shell-model simulation in digital quantum computers
• Optimal scheduling in probabilistic imaginary-time evolution on a quantum computer
• Solving reaction dynamics with quantum computing algorithms
• Toward hybrid quantum simulations with qubits and qumodes on trapped-ion platforms
• Deep Quantum Circuit Simulations of Low-Energy Nuclear States
• First-quantized adiabatic time evolution for the ground state of a many-electron system and the optimal nuclear configuration
• Quantum techniques for eigenvalue problems
• Semicoherent Symmetric Quantum Processes: Theory and Applications
• Identification of a natural fieldlike entanglement resource in trapped-ion chains
• Toward scalable quantum computations of atomic nuclei
• Simplified projection on total spin zero for state preparation on quantum computers
• A penalty-free quantum algorithm to find energy eigenstates
• Quantum Algorithms for State Preparation and Data Classification based on Stabilizer Codes
• Accelerated spin-adapted ground state preparation with non-variational quantum algorithms