Quantum Control Protocol Hamiltonian for Arbitrary State Transformation
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Solution Overview
Problem
Current quantum control methods face challenges in efficiently transforming between arbitrary quantum states, especially under time-dependent drift Hamiltonians, due to limitations in control Hamiltonian forms and constraints from external fields, which can lead to suboptimal fidelity and increased decoherence.
Innovation Solution
A computer-implemented method determines a control protocol Hamiltonian by iteratively solving for either a protocol time or a finite energy resource, using a time-dependent Hermitian drift Hamiltonian, initial, and final states, to construct a control protocol Hamiltonian in both interaction and Schrödinger pictures, ensuring unit fidelity and minimal decoherence impact.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If traditional optimal quantum control theory is used with fixed form control Hamiltonian, then manufacturing precision of state transformation is improved, but device complexity and difficulty of solving boundary-value problems increase
Solution Approach 1:
The patent transforms the quantum control problem from a boundary-value problem to an initial-value problem by changing the mathematical parameters and formulation approach. This allows standard numerical integration methods to be used instead of complex boundary-value solvers, reducing computational complexity while maintaining transformation fidelity.
Solution Approach 2:
The patent extracts and separates the control Hamiltonian design from the state transformation problem, formulating it as a distinct optimization task with clear objective functions. This separation allows independent optimization of control parameters without solving coupled boundary conditions.
2Loss of time
If time-optimal quantum control is used to reduce evolution time, then loss of time and decoherence impact are reduced, but control protocol complexity and energy requirements increase
Solution Approach 1:
The patent implements dynamic control protocols where the control Hamiltonian parameters are continuously optimized during the evolution process. This allows adaptive adjustment of control strength and timing to achieve time-optimal transformations while managing complexity through systematic optimization rather than fixed complex sequences.
Solution Approach 2:
The patent employs techniques to rush through the quantum evolution by applying maximum permissible control fields to accelerate state transformation. This skips through intermediate states more quickly, reducing exposure to decoherence while the optimization framework manages the resulting control complexity.
3Adaptability or versatility
If control Hamiltonian form is relaxed to achieve arbitrary state transformation, then adaptability is improved, but difficulty of solving boundary-value problems and implementation feasibility worsen
Solution Approach 1:
The patent performs preliminary optimization of the control Hamiltonian parameters before implementing the actual state transformation. By pre-calculating optimal control sequences using the formulated objective functions, the system prepares feasible control protocols in advance, making arbitrary state transformations adaptable while avoiding intractable boundary-value problems during execution.
Data Source
AI summary
A computer implemented method and a computer to determine a control protocol Hamiltonian for a quantum process is provided. Quantum systems driven according to the control protocol Hamiltonian are provided.