Variational Quantum Annealing With Auxiliary Hamiltonian
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Solution Overview
Problem
Current quantum annealing systems face challenges in achieving precise approximations of the ground state within the coherent operating window of superconducting devices, particularly due to limitations in coherence time and energy landscape modification.
Innovation Solution
A variational protocol for quantum annealing that utilizes a total Hamiltonian composed of an initial, problem, and auxiliary Hamiltonian, each with independent schedule functions. This protocol employs a piece-wise cubic interpolator to optimize the schedule functions, allowing for precise control of the energy landscape and extended coherence time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the annealing time is extended to achieve precise ground state approximation, then the precision improves, but the process exceeds the coherence time of the quantum device
Solution Approach 1:
The protocol applies preliminary actions by introducing an auxiliary Hamiltonian with local fields before the main annealing process. This auxiliary component pre-modifies the energy landscape to create more favorable conditions for the subsequent annealing evolution, enabling faster convergence to the ground state within the coherence time window.
Solution Approach 2:
The protocol employs parameter changes by dynamically adjusting the local field parameters in the auxiliary Hamiltonian throughout the annealing process. These time-dependent parameter modifications allow the system to adapt the energy landscape evolution rate, optimizing the balance between convergence speed and ground state precision within the limited coherence time.
2Productivity
If the energy landscape is modified to speed up convergence, then the annealing time decreases, but the ground state precision deteriorates
Solution Approach 1:
The protocol applies local quality by introducing local fields specifically at each qubit location through the auxiliary Hamiltonian. These localized modifications to the energy landscape provide targeted assistance where needed, enabling faster convergence without introducing global distortions that would compromise the overall ground state precision.
Solution Approach 2:
The auxiliary Hamiltonian acts as an intermediary that mediates between the initial transverse field Hamiltonian and the final problem Hamiltonian. It provides a controlled bridge that accelerates the transition while maintaining fidelity to the target ground state, reconciling the conflict between speed and precision.
3Measurement precision
If the quantum system evolves for longer time to achieve better ground state approximation, then the precision improves, but the system loses coherence
Solution Approach 1:
The protocol prepares the system in advance by applying the auxiliary Hamiltonian with local fields that pre-structure the energy landscape. This preliminary action creates a more favorable evolution path that requires less time to reach the ground state, thereby maintaining quantum coherence throughout the process.
Solution Approach 2:
The protocol maintains continuous useful action by ensuring that the auxiliary Hamiltonian's local fields are continuously optimized throughout the annealing process. This continuous optimization ensures that the quantum evolution remains productive and coherent, avoiding idle periods or inefficient transitions that would waste coherence time.
Data Source
Figure 1(a)~1(b)
Figure 2~3(d)
Figure 4(a)~5(d)
AI summary
The invention relates to a computer-implemented method, to a computer program and to a computer device as described herein. Specifically, the computer-implemented method for solving an optimization problem using a quantum annealer comprises a) providing a total Hamiltonian that consists of - an initial Hamiltonian - final Hamiltonian, encoding the solution to the problem being solved in its ground state, and - an auxiliary Hamiltonian, describing local fields over each of a set of given qubits, wherein each of the Hamiltonians has an independent schedule function, and b) performing a time evolution of the total Hamiltonian to obtain the solution to the optimization problem.