Quantum Circuit Simulation via Polynomial Conversion
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Solution Overview
Problem
Current classical simulation methods for unitary coupled-cluster (UCC) quantum circuits face challenges due to the exponential operation required, leading to high computation complexity and difficulty in efficiently simulating these circuits on classical computers.
Innovation Solution
The method involves converting the UCC factor into a polynomial form, where the exponential part is expressed as a linear term and a quadratic term of the anti-hermitian excitation operator G, allowing for efficient quantum simulation without the need for quantum gate decomposition.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the UCC factor is simulated using exponential operation on classical computers, then the quantum circuit can be faithfully simulated, but the computation complexity becomes extremely high and simulation becomes difficult
Solution Approach 1:
The patent transforms the exponential operation e^θG into a polynomial operation by changing the mathematical parameter representation. Specifically, it uses the Taylor expansion to approximate the exponential function as a polynomial: e^θG ≈ I + θG + (θ^2/2)G^2 + ..., converting the computationally expensive exponential operation into a series of simpler polynomial operations that can be efficiently implemented on classical computers while maintaining simulation accuracy.
2Ease of manufacture
If the UCC factor is decomposed into quantum gates for classical simulation, then the quantum circuit can be realized, but the operation complexity increases significantly
Solution Approach 1:
The patent extracts the essential computational core of the UCC factor (the polynomial operation on the wave function) and separates it from the quantum gate decomposition process. By directly computing the polynomial e^θGψ without decomposing it into individual quantum gates, the method removes the unnecessary complexity of gate-level simulation while preserving the fundamental quantum chemical computation capability.
3Measurement precision
If exponential operation is used for UCC factors, then the quantum circuit can be accurately represented, but the simulation efficiency on classical computers decreases
Solution Approach 1:
The patent changes the mathematical parameter representation from exponential form to polynomial form using Taylor expansion. This parameter transformation maintains the precision of quantum state representation while dramatically improving simulation efficiency, as polynomial operations are computationally less intensive than exponential operations on classical computing hardware.
Data Source
AI summary
The present disclosure discloses a method and apparatus for simulating a quantum circuit, a computer device, a storage medium, and a program product. The method includes: acquiring a polynomial by converting a unitary coupled-cluster (UCC) factor, wherein: an exponential part of the UCC factor comprises an anti-hermitian excitation operator G, and the polynomial comprises a linear term of the G and a quadratic term of the G; acquiring N UCC factors for constructing the UCC quantum circuit, N being an integer greater than 1; acquiring a wave function for representing a quantum state of an object; and obtaining a result wave function by performing operation in the form of the polynomial for each UCC factor in the N UCC factors on the wave function, wherein the result wave function represents the quantum state of the object after quantum simulation with the UCC quantum circuit.