Hybrid Quantum-Classical Algorithm for Discrete Quadratic Models
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Solution Overview
Problem
Current methods for solving problems with arbitrary variables, such as protein design and integer problems, are inefficient due to the need for conversion to quadratic unconstrained binary optimization (QUBO) or Ising Hamiltonian problems, which require significant overhead and lead to long computational times, especially for complex cases.
Innovation Solution
A hybrid computing system using Gibbs sampling and Cross-Boltzmann updates is employed to efficiently map arbitrary variable problems to binary quadratic models, allowing for direct solution on a quantum processor, with a classical processor generating candidate values and constructing Hamiltonians to guide the quantum computation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If arbitrary variable problems are converted to QUBO or Ising Hamiltonian problems for quantum processing, then the problem can be solved on a quantum processor, but the conversion requires significant overhead and leads to long computational times
Solution Approach 1:
The patent segments the arbitrary variable problem into discrete components by introducing binary variables that represent specific states or ranges of the arbitrary variables. This segmentation allows the problem to be decomposed into smaller binary quadratic optimization subproblems that can be efficiently processed by quantum annealers, avoiding the need for complex full-problem conversions while maintaining solution accuracy.
Solution Approach 2:
The patent transforms the problem parameters by reparameterizing arbitrary variables in terms of binary variables with specific mathematical relationships. This parameter transformation enables the arbitrary variable problem to be expressed in the binary quadratic form required by quantum processors, while the clever choice of parameterization minimizes the number of binary variables needed, thereby reducing computational overhead.
2Adaptability or versatility
If arbitrary variable problems are mapped to binary quadratic models, then quantum processing can be applied, but the mapping process increases device complexity
Solution Approach 1:
The patent performs preliminary analysis and preparation by identifying suitable binary variable representations for arbitrary variables before the main optimization process. This preliminary action includes determining the appropriate binary encoding schemes and pre-computing any necessary transformation matrices, which simplifies the subsequent quantum processing step and reduces the complexity of the overall mapping process.
Solution Approach 2:
The patent introduces binary variables as intermediary elements that bridge the gap between arbitrary variables and the binary quadratic model required by quantum processors. These intermediary binary variables serve as a compact representation that captures the essential relationships of the original problem while conforming to the constraints of quantum annealing, thereby reducing the overall complexity of the mapping.
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 significantly reduces computational time by efficiently solving arbitrary variable problems, including protein design and integer problems, by leveraging the power of quantum processors while maintaining the efficiency of classical preprocessing.
Implementation Method 1
Quantum annealing may use quantum effects, such as quantum tunneling, as a source of delocalization to reach an energy minimum.
Implementation Method 2
A quantum computer is a system that makes direct use of at least one quantum-mechanical phenomenon, such as, superposition, tunneling, and entanglement, to perform operations on data.
Implementation Method 3
A quantum computer is a system that makes direct use of at least one quantum-mechanical phenomenon, such as, superposition, tunneling, and entanglement, to perform operations on data.
Data Source
AI summary
Methods for solving discrete quadratic models are described. The methods compute an energy of each state of each variable based on its interaction with other variables, exponential weights, and normalized probabilities proportional to the exponential weights. The energy of each variable is computed as a function of the magnitude of each variable and a current state of all other variables, exponential weights, the feasible region for each variable, and normalized probabilities, proportional to the exponential weights and respecting constraints. Methods executed via a hybrid computing system obtain two candidate values for each variable; constructs a Hamiltonian that uses a binary value to determine which candidate values each variable should take, then constructs a binary quadratic model based on the Hamiltonian. Samples from the binary quadratic model are obtained via a quantum processor. The methods can be applied to solve resource scheduling optimization problems and/or for side-chain optimization for proteins.