Quantum Annealing Schedules With Inhomogeneous Driving Fields
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Solution Overview
Problem
Existing quantum annealing technologies face challenges in controlling the dynamics of disordered quantum systems, leading to smeared phase transitions and exponentially long annealing times due to Griffiths effects, which violate adiabaticity conditions and result in domain walls and topological defects.
Innovation Solution
Implementing inhomogeneous quantum annealing schedules with spatially-induced gaps between low and high energy states, using multi-critical-fronts to synchronize local phase transitions in space and time, ensuring effective control over quantum phase transitions in disordered systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If homogeneous quantum annealing schedules are used, then the system evolves according to standard adiabatic quantum annealing, but the annealing time becomes exponentially long due to Griffiths effects and smeared phase transitions in disordered systems
Solution Approach 1:
The patent applies local quality by introducing spatially varying transverse field strengths across different regions of the quantum system. Each region experiences a locally optimized annealing schedule that accounts for its specific disorder characteristics, allowing faster evolution through critical regions while maintaining adiabaticity where needed. This local optimization resolves the contradiction by enabling region-specific speedups without compromising overall solution quality.
Solution Approach 2:
The patent implements dynamics by making the transverse field schedule time-dependent and adaptive. The field strength evolves dynamically according to a protocol that accelerates through regions where the instantaneous gap is large while slowing down near critical points. This dynamic adjustment allows the system to achieve both fast annealing and high solution quality by adapting the evolution rate to the instantaneous state of the system.
2Loss of time
If the transverse field changes rapidly, then annealing time is reduced, but adiabaticity conditions are violated leading to domain walls and topological defects
Solution Approach 1:
The patent employs periodic action through a multi-stage annealing protocol that alternates between acceleration phases and pause phases. During acceleration phases, the transverse field changes rapidly to reduce annealing time. During pause phases, the evolution slows down to maintain adiabaticity and allow the system to relax into the ground state. This periodic modulation resolves the contradiction by balancing speed and stability across different time intervals.
Solution Approach 2:
The patent applies preliminary action by preparing the system with an initial transverse field configuration that anticipates upcoming critical regions. Before the system encounters a region with small instantaneous gap, the annealing schedule pre-slowing occurs, allowing the system to maintain adiabaticity in advance. This preliminary adjustment prevents domain wall formation without requiring the entire annealing process to be slow.
3Productivity
If inhomogeneous transverse field schedules are applied, then effective gaps are created between energy states reducing annealing time, but the system complexity increases
Solution Approach 1:
The patent applies segmentation by dividing the quantum system into multiple regions or stages, each with its own optimized transverse field schedule. This segmentation allows the complex control problem to be broken down into simpler sub-problems that can be independently optimized and then combined. The overall inhomogeneous schedule emerges from the composition of these simpler regional schedules, resolving the contradiction between efficiency and complexity.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach ensures efficient and accurate solution approximation by creating controlled gaps between energy states, reducing annealing time scales and improving the quality of solutions in disordered quantum systems.
Implementation Method 1
The amplitudes of all candidate states change according to the time-dependent strength of a transverse field, which causes quantum tunneling between states.
Implementation Method 2
In adiabatic quantum annealing, the system stays close to the ground state of the instantaneous Hamiltonian if the rate of change of the transverse-field is slow enough.
Implementation Method 3
The system evolves following the time-dependent Schrödinger equation. The amplitudes of all candidate states change according to the time-dependent strength of a transverse field
Data Source
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AI summary
Methods and apparatus for performing quantum annealing using a quantum system. In one aspect, a method includes controlling the quantum system such that a total Hamiltonian characterizing the quantum system evolves from an initial quantum Hamiltonian to a problem quantum Hamiltonian, wherein controlling the quantum system comprises applying an inhomogeneous driving field to the quantum system to drive the quantum system across a quantum phase transition.