Nested Quantum Annealing Correction for Error Resilience
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Solution Overview
Problem
Quantum annealing devices face significant challenges with decoherence, noise, and control errors, limiting their scalability and accuracy in solving optimization problems, and existing error correction schemes are not easily generalizable to arbitrary optimization problems.
Innovation Solution
The nested quantum annealing correction (NQAC) scheme involves embedding a logical qubit into a larger number of physical qubits with a nesting level that controls hardware resources, using a nested Hamiltonian and minor embedding to represent couplings as inter-chain couplings, and employing a decoding procedure to recover the logical state, effectively reducing the effective temperature and enhancing error correction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If error correction is implemented using more physical qubits, then reliability is improved, but device complexity increases
Solution Approach 1:
The patent implements nested quantum annealing correction by embedding logical qubits into larger numbers of physical qubits through hierarchical nesting. Each logical qubit is encoded into C encoded qubits, which are further embedded into physical qubit chains of length L. This nested structure allows systematic improvement of error correction by increasing the nesting level C, providing a scalable framework where reliability can be enhanced by adding more physical resources in a structured manner.
Solution Approach 2:
The error correction scheme segments the quantum system into distinct logical layers: logical qubits are separated from encoded qubits, which are separated from physical qubits. This segmentation allows independent optimization of each layer and enables modular error correction where the logical problem structure is preserved while adding error protection at the physical layer through ferromagnetically coupled chains.
2Object-affected harmful factors
If more hardware resources are used to reduce effective temperature, then thermal errors are reduced, but device complexity increases
Solution Approach 1:
The nested encoding structure allows the system to effectively reduce temperature by increasing the nesting level C. The effective temperature reduction scales with the nesting level, enabling thermal error suppression through hierarchical encoding without requiring proportional increases in physical infrastructure. The nested structure amplifies the energy gap between logical states, effectively lowering the impact of thermal excitations.
3Reliability
If nested encoding with higher nesting level is used, then error correction performance is improved, but the number of physical qubits required increases
Solution Approach 1:
The patent provides dynamic scalability in error correction performance. The nesting level C can be adjusted according to available physical resources and error correction requirements. The system allows flexible trade-offs between error correction performance and physical qubit usage by dynamically selecting the appropriate nesting level, enabling adaptation to different hardware configurations and problem sizes.
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
NQAC improves the accuracy and scalability of quantum annealers by reducing thermal and control errors, allowing for the use of more physical resources to lower the effective temperature, and outperforms classical repetition codes with the same number of physical qubits.
Implementation Method 1
Quantum annealing (QA) attempts to exploit quantum fluctuations to solve computational problems faster than it is possible with classical computers
Implementation Method 2
replacing each qubit in the nested Hamiltonian by a ferromagnetically coupled chain of qubits, such that all couplings in the nested Hamiltonian are represented by inter-chain couplings
Data Source
AI summary
Systems and methods of processing using a quantum processor are described. A method includes obtaining a problem Hamiltonian and defining a nested Hamiltonian with a plurality of logical qubits by embedding a logical KN representing the problem Hamiltonian into a larger KC×N, where N represents a number of the logical qubits and C represents a nesting level defining the amount of hardware resources for the nest Hamiltonian. The method also includes encoding the nested Hamiltonian into the plurality of physical qubits of the quantum processor; and performing a quantum annealing process with the quantum processor after the encoding.