Quantum Subspace Expansion for Accurate Active-Space Simulation
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Solution Overview
Problem
Simulating complex quantum systems using classical techniques is untenable due to exponential resource scaling, and existing quantum computing methods focused on active spaces neglect important physical effects, leading to inaccurate results, especially for near- or intermediate-term quantum computers.
Innovation Solution
Implement quantum simulation techniques that extend beyond the active space without requiring additional qubits or gate complexity by leveraging quantum subspace expansion and orbital relaxation, using classical pre-computation and post-processing to reintroduce virtual space contributions and improve simulation accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If quantum simulation focuses on active space only, then quantum resource requirements are reduced, but simulation accuracy deteriorates due to neglecting virtual space contributions
Solution Approach 1:
The patent segments the full quantum system into active space and virtual space components. The active space is simulated directly on quantum computers with limited resources, while the virtual space contributions are handled through classical pre-computation and post-processing, allowing accurate representation without requiring quantum resources proportional to the full system size
Solution Approach 2:
The patent introduces an intermediary classical computing component that bridges the quantum active space simulation and the full system representation. Classical algorithms pre-compute and post-process the virtual space contributions, acting as a mediator that translates quantum simulation results into accurate full-system predictions without requiring direct quantum simulation of the entire system
2Device complexity
If classical techniques are used to simulate complex quantum systems, then computational resources scale exponentially, but implementation simplicity is maintained
Solution Approach 1:
The patent divides the computational task into segments suitable for different computing paradigms: the electronically correlated active space is simulated using quantum computers, while the computationally intensive virtual space contributions are pre-computed using classical techniques. This segmentation allows each component to be handled by the most appropriate computational approach
Solution Approach 2:
The patent performs preliminary classical pre-computation of virtual space contributions before the quantum simulation. By pre-computing these terms classically, the patent reduces the burden on quantum resources during the actual quantum simulation, making the overall approach more efficient
Data Source
AI summary
Methods, systems and apparatus for simulating physical systems. In one aspect, a method includes the actions of selecting a first set of basis functions for the simulation, wherein the first set of basis functions comprises an active and a virtual set of orbitals; defining a set of expansion operators for the simulation, wherein expansion operators in the set of expansion operators approximate fermionic excitations in an active space spanned by the active set of orbitals and a virtual space spanned by the virtual set of orbitals; performing multiple quantum computations to determine a matrix representation of a Hamiltonian characterizing the system in a second set of basis functions, computing, using the determined matrix representation of the Hamiltonian, eigenvalues and eigenvectors of the Hamiltonian; and determining properties of the physical system using the computed eigenvalues and eigenvectors.