Interaction-Picture Magnus Expansion for Lower-Depth Quantum Simulation
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Solution Overview
Problem
Quantum simulation is prone to errors and requires high circuit depths and gate counts, exceeding the capabilities of current quantum hardware, leading to scalability and resource limitations.
Innovation Solution
Decompose a time-independent Hamiltonian into a first and second Hamiltonian, and employ a Magnus expansion in an interaction picture to approximate time evolution, using a truncated Magnus expansion with a Pauli decomposition to reduce circuit depth and gate count.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If quantum simulation is performed using conventional methods, then simulation capability is achieved, but error rates increase and hardware requirements exceed current capabilities
Solution Approach 1:
The patent transforms the time-dependent Hamiltonian simulation problem into a time-independent Hamiltonian simulation problem by using the Magnus expansion. This parameter transformation allows the use of more stable simulation methods while reducing the complexity of time-dependent control, thereby improving reliability without proportionally increasing hardware requirements
Solution Approach 2:
The Magnus expansion serves as an intermediary mathematical tool that bridges the gap between time-dependent and time-independent Hamiltonian simulations. By introducing this expansion as an intermediate step, the patent enables accurate time evolution simulation while maintaining simpler hardware requirements associated with time-independent methods
2Measurement precision
If circuit depth and gate count are increased to improve simulation accuracy, then simulation precision improves, but quantum hardware resource requirements increase
Solution Approach 1:
By changing the parameter representation from time-dependent to time-independent Hamiltonian through Magnus expansion, the patent achieves high simulation precision while reducing the number of quantum gates and circuit depth required, thus decreasing quantum hardware resource consumption
3Adaptability or versatility
If time-dependent Hamiltonian simulation is used, then dynamic quantum system evolution is captured, but error rates increase
Solution Approach 1:
The Magnus expansion acts as a mediator that preserves the dynamic evolution characteristics of time-dependent Hamiltonians while transforming them into an equivalent time-independent form. This intermediary transformation maintains adaptability for simulating dynamic quantum systems while significantly reducing error rates associated with direct time-dependent simulation methods
Data Source
AI summary
Systems and techniques that facilitate quantum simulation by using a Magnus expansion in an interaction picture are provided. One or more embodiments described herein can comprise a system, which can comprise a memory that can store computer executable components. The system can also comprise a processor, operably coupled to the memory that can execute the computer executable components stored in memory. The computer executable components can comprise a quantum circuit generation component that generates a quantum circuit that represents a quantum model of a quantum system, wherein generating of the quantum circuit can comprise decomposing a time-independent Hamiltonian that describes the quantum system into a first Hamiltonian and a second Hamiltonian. Generating of the quantum circuit can further comprise employing a Magnus expansion in an interaction picture of the first Hamiltonian to approximate a time evolution of the quantum system under a time-dependent Hamiltonian.