Diabatic Quantum Hamiltonian Evolution for NP-Hard Problem Solving
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Solution Overview
Problem
Current quantum computing methods face challenges in efficiently solving computational problems, particularly NP-hard problems, due to exponential scaling of runtime and the inability to provide exact solutions, leading to the need for improved methods and devices.
Innovation Solution
A quantum system comprising a plurality of qubits is used, where the computational problem is encoded into a problem Hamiltonian with adjustable parameters, and the initial Hamiltonian is evolved into a final Hamiltonian via an intermediate Hamiltonian, allowing for faster solution determination through diabatic processes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If adiabatic quantum processes are used to solve computational problems, then exact solutions can be obtained, but the runtime scales exponentially with problem size
Solution Approach 1:
The patent changes the fundamental parameter of quantum evolution from adiabatic to diabatic. By using diabatic evolution with an intermediate Hamiltonian that is a linear combination of initial and final Hamiltonians, the system can transition between energy states more rapidly without requiring exponential time, thus reducing runtime while maintaining solution accuracy through controlled parameter transformations
Solution Approach 2:
The patent introduces an intermediate Hamiltonian as a mediator between the initial and final Hamiltonians. This intermediate Hamiltonian, defined as a linear combination of the initial and final Hamiltonians with appropriate coefficients, enables a controlled transition pathway that avoids direct exponential scaling while preserving the ability to encode and solve computational problems accurately
2Productivity
If quantum systems are used to solve NP-hard problems, then computational speedup can be achieved, but the architecture becomes complex and difficult to scale
Solution Approach 1:
The patent segments the Hamiltonian evolution process into distinct components: an initial Hamiltonian, a final Hamiltonian containing the problem encoding, and an intermediate Hamiltonian. This segmentation allows each component to be designed and optimized independently, simplifying the overall architecture while maintaining the ability to achieve computational speedup for NP-hard problems
Solution Approach 2:
The patent creates a universal quantum architecture where the same basic framework can solve different computational problems by simply changing the problem encoding in the final Hamiltonian. The intermediate Hamiltonian formulation provides a universal transition mechanism that works across different problem types, reducing architectural complexity while maintaining productivity benefits
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 enables faster computation of solutions to computational problems, including NP-hard problems, by evolving the initial Hamiltonian into a final Hamiltonian using a diabatic process, thereby overcoming the limitations of adiabatic quantum processes and achieving scalable architecture for various problem sizes.
Implementation Method 1
evolving an initial Hamiltonian of the quantum system at an initial time into a final Hamiltonian of the quantum system at a final time via an intermediate Hamiltonian of the quantum system at an intermediate time
Data Source
AI summary
A method of computing a solution to a computational problem using a quantum system comprising a plurality of qubits includes encoding the computational problem into a single-body problem Hamiltonian comprising a plurality of adjustable parameters, and encoding comprises determining a problem-encoding configuration for the plurality of adjustable parameters. The method includes evolving an initial Hamiltonian at an initial time into a final Hamiltonian at a final time via an intermediate Hamiltonian at an intermediate time, the intermediate Hamiltonian a linear combination of the initial Hamiltonian, the final Hamiltonian and a first short-range Hamiltonian, the final Hamiltonian a sum of the problem Hamiltonian and a second short-range Hamiltonian, the plurality of adjustable parameters of the problem Hamiltonian in the problem-encoding configuration, the second short-range Hamiltonian a d-body Hamiltonian; measuring a portion of the plurality of qubits to obtain a read-out; and determining a solution to the computational problem from the read-out.