Hybrid Quantum-Classical Transition Amplitude Computation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current methods for computing transition amplitudes, such as SSVQE and MCVQE, face challenges in achieving accurate results for excited states, particularly in molecules like LiH, diazene, and azobenzine, with Variational Quantum Deflation (VQD) showing better performance but lacking a clear method for computing transition amplitudes effectively.
Innovation Solution
A hybrid system comprising a classical computer and a quantum computer executes quantum measurements on specific quantum state pairs to compute transition amplitudes using Equation (1), with the classical computer processing measurement results to obtain accurate transition amplitude values.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Extent of automation
If Variational Quantum Eigensolvers (VQE) or its extensions (SSVQE, MCVQE) are used to compute transition amplitudes, then quantum computational capability is utilized, but measurement precision and accuracy for excited states deteriorate
Solution Approach 1:
The patent segments the transition amplitude computation into multiple independent measurement components (|<ψ1|Pi|ψ2>|^2, |<ψ1|Uij,+|ψ2>|^2, |<ψ1|Uij,−|ψ2>|^2, |<ψ1|Pj|ψ2>|^2, |<ψ1|PiPj|ψ2>|^2) that are measured separately using VQE and then combined classically. This segmentation allows each measurement to be optimized independently while maintaining overall accuracy.
Solution Approach 2:
The patent transitions from purely quantum computation to a hybrid quantum-classical approach by moving the final synthesis and calculation of transition amplitudes to the classical dimension. This allows leveraging quantum measurement capabilities while using classical computation for precise mathematical combination of results.
2Measurement precision
If VQD is used to improve excited state computation, then computation accuracy improves, but the method for computing transition amplitudes becomes unclear and incomplete
Solution Approach 1:
The patent introduces classical computation as an intermediary between quantum measurements and final transition amplitude results. The classical computer receives measurement results from the quantum computer and performs the necessary mathematical operations to compute transition amplitudes, bridging the gap between quantum capabilities and clear computational methodology.
3Extent of automation
If quantum measurements are performed on quantum state pairs using VQE, then quantum computational power is utilized, but the number of measurements and computational complexity increase
Solution Approach 1:
The patent divides the complex transition amplitude computation into multiple simpler measurement tasks, each involving specific quantum operators (Pi, Pj, Uij,+, Uij,−). This segmentation reduces the complexity of individual quantum circuits while the overall process remains comprehensive.
Solution Approach 2:
The patent performs measurements for multiple operator combinations beyond what might be strictly necessary for a single transition amplitude, computing additional terms that can be reused for multiple different transition amplitude calculations, thereby amortizing the measurement complexity.
Data Source
AI summary
A quantum computer executes quantum measurement of <ψ1|Pi|ψ2>, <ψ1|Uij,+|ψ2>, <ψ1|Uij,−|ψ2>, <ψ1|Pj|ψ2>, and <ψ1|PiPj|ψ2< below based on a quantum state pair configured by a first quantum state ψ1 and a second quantum state ψ2, and outputs measurement results of the quantum measurement. A classical computer computes a transition amplitude |<ψ1|A|ψ2>|2 based on measurement results for <ψ1|Pi|ψ2>, <ψ1|Uij,+|ψ2>, <ψ1|Uij,−|ψ2>, <ψ1|Pj|ψ2>, and <ψ1|PiPj|ψ2>, wherein A is a physical quantity for computation of transition amplitude, i and j are indices for identifying a and P, a is a real number, P is a tensor product of a Pauli matrix, U is a unitary gate, and <ψ1|ψ2>=0.