Quantum Job Shop Scheduling with Compact Noise-Resistant Encoding
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Solution Overview
Problem
Existing quantum computing methods for job shop scheduling problems, particularly the flexible job shop problem, face challenges due to the need for extensive quantum resources and susceptibility to thermal noise, making them impractical for real-world applications.
Innovation Solution
A method for encoding job shop scheduling problems using a number system representation that preserves the order of operations, employing a variational quantum algorithm like Filter-VQE, which reduces the number of qubits required and minimizes the influence of thermal noise, allowing for efficient optimization of schedules.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If quantum annealing or QAOA is used to solve job shop scheduling problems, then parallel examination of many configurations is achieved, but the number of qubits required becomes prohibitively large for real-world applications
Solution Approach 1:
The patent segments the scheduling problem by separating operation sequencing from machine assignment. The sequencing is encoded using a compact number system representation that requires fewer qubits, while machine assignment is handled through a different mechanism, reducing the overall quantum resource requirements.
Solution Approach 2:
The patent transitions from traditional binary encoding to a number system representation that captures operation sequences more efficiently. This dimensional change in encoding allows representing n! possible sequences using only O(n) qubits instead of O(n²) qubits required by binary encoding.
2Device complexity
If more qubits are used to encode operation schedules, then scheduling problem complexity is handled, but susceptibility to thermal noise and faulty qubits increases
Solution Approach 1:
The patent changes the encoding parameter from binary variables to a number system representation that inherently preserves operation order. This parameter change reduces the state space that needs to be explored and minimizes the number of qubits exposed to thermal noise and faults.
3Ease of manufacture
If traditional binary encoding is used for quantum algorithms, then problem formulation is straightforward, but the number of variables and qubits required becomes unmanageable for practical applications
Solution Approach 1:
The patent extracts the operation ordering constraint from the general scheduling problem and handles it separately through the number system representation. This extraction allows the remaining scheduling optimization to be performed with fewer variables and qubits.
Data Source
Figure 1
AI summary
The described method is a method for determining an operations schedule that attributes each individual operation of two or more jobs to two or more machines, wherein the operations schedule is subject to an optimization towards an optimum of a key performance indicator indicating the performance of the operations schedule, wherein an operations schedule is initially encoded (S1, S2, S3, S4, S5) into a quantum register of a quantum computer (QC) and the optimization is performed (S6) using a variational quantum algorithm on the quantum computer (QC) acting on the quantum register and wherein an optimized operations schedule is provided (S7) by the quantum computer (QC).