Quantum Annealing with Oscillating Fields for Speedup
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Solution Overview
Problem
Current quantum annealing platforms face challenges in efficiently solving NP-hard optimization problems due to limitations in implementing variable annealing rates and the impact of local energy fluctuations, particularly in verifying phase transitions and maintaining quantum speedup for stoquastic problems.
Innovation Solution
The implementation of a novel driver Hamiltonian using oscillating fields that drive qubits independently, allowing for a constant annealing rate and overcoming challenges by decoupling and coupling qubits to transfer them from an initial to a final state, thereby achieving a quantum speedup for Grover's algorithm and other hard combinatorial optimization problems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If a stoquastic problem Hamiltonian is used in quantum annealing, then the system is easier to implement on current platforms, but quantum speedup cannot be demonstrated as these problems can be efficiently simulated classically
Solution Approach 1:
The patent changes the parameter of the problem Hamiltonian from stoquastic (real and negative off-diagonal terms) to non-stoquastic by introducing imaginary components. Specifically, the problem Hamiltonian is modified to include terms like iJijσx(i)σx(j) where Jij are real numbers, transforming it from a stoquastic to a non-stoquastic form. This enables quantum speedup while maintaining implementability on current quantum annealing platforms.
2Productivity
If variable annealing rate is implemented to achieve quantum speedup, then transition to ground state is faster, but local energy fluctuations and noise make verification difficult and implementation challenging
Solution Approach 1:
The patent introduces an auxiliary Hamiltonian Haux that acts as an intermediary to verify the ground state. This auxiliary system couples to the main quantum annealing system and provides a measurable signal that indicates whether the system has successfully transitioned to the ground state. The auxiliary Hamiltonian serves as a mediator between the quantum annealing process and classical verification, enabling reliable detection of quantum speedup despite local energy fluctuations and noise.
Data Source
AI summary
Embodiments herein implement quantum annealing with a driver Hamiltonian that uses oscillating fields to advantageously obtain a quantum speedup over classical computing techniques. For a many-body quantum system formed with qubits, the oscillating fields drive the qubits so as to independently modulate the magnitudes and/or directions of transverse terms of the driver Hamiltonian. In particular, embodiments provide a quantum speedup for two types of first-order phase transitions: the paramagnet-to-spin-glass transition, and transitions between distinct “bit string” states. The resulting speedup is robust against energy fluctuations (e.g., 1/f noise), in contrast to other strategies like variable-rate annealing. Each oscillating field may be an oscillating electric field or magnetic field. The oscillating fields can be implemented with superconducting flux qubits by coupling oscillating fluxes and/or voltages to the flux qubits.