Gibbs-State Quantum Optimization for Barren Plateau Mitigation
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Solution Overview
Problem
Existing quantum optimization techniques for combinatorial optimization problems are susceptible to barren plateaus, where the cost function's gradient becomes extremely flat, making it difficult to find the global minimum, and there is a lack of efficient methods for determining suitable initial variational parameters, leading to inefficient processing and slow convergence.
Innovation Solution
Preparing a Gibbs state of a quantum system that represents the combinatorial optimization problem, using the Gibbs state to determine initial parameters for variational quantum circuits, which biases the optimization algorithm towards lower-energy configurations, thereby mitigating barren plateaus and improving convergence speed.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional quantum optimization techniques are used, then the optimization process can be performed, but the algorithm is susceptible to barren plateaus where the cost function's gradient becomes extremely flat, making it difficult to find the global minimum
Solution Approach 1:
The patent applies preliminary action by preparing a Gibbs state before the main optimization process. The Gibbs state is prepared by initializing a quantum system, applying a variational quantum circuit to create a thermal state, and using classical optimization to minimize free energy. This pre-computation of the Gibbs state provides a biased initial distribution that favors lower-energy configurations, thereby mitigating barren plateaus when the main optimization algorithm begins.
2Productivity
If conventional quantum optimization techniques are used, then the optimization process can be performed, but there is a lack of efficient methods for determining suitable initial variational parameters, leading to inefficient processing and slow convergence
Solution Approach 1:
The patent uses preliminary action to pre-compute the Gibbs state with optimized variational parameters before the main optimization algorithm runs. By minimizing the free energy of the quantum system during the Gibbs state preparation, the method efficiently determines suitable initial parameters that bias the system toward optimal solutions, thereby reducing the time needed for convergence in the subsequent optimization process.
Solution Approach 2:
The patent applies parameter changes by transitioning from arbitrary initial parameters to parameters that define a Gibbs state with minimized free energy. The variational parameters are optimized to create a thermal state distribution that reflects the underlying energy structure of the optimization problem, enabling faster convergence by starting closer to the optimal solution space.
Data Source
AI summary
Systems and techniques that facilitate Gibbs state-based quantum optimization for combinatorial optimization problems are provided. For example, one or more embodiments described herein can comprise a system, which can comprise a memory that can store computer executable components. The system can also comprise a processor, operably coupled to the memory that can execute at least one of the computer executable components that can prepare a Gibbs state of a quantum system that represents a combinatorial optimization problem, wherein the Gibbs state is a quantum state that minimizes free energy of the quantum system. The at least one of the computer executable components can further initialize a quantum optimization algorithm using a set of parameters that define the Gibbs state to solve the combinatorial optimization problem, wherein solving the combinatorial optimization problem comprises determining a ground state of a Hamiltonian of the quantum system.