Quantum Simulation Accuracy Through Active–Virtual Space Expansion
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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 require additional qubits and increased gate complexity to capture important physical effects, leading to inaccurate simulation results, especially on 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 computations to determine matrix elements and overlap matrices, and performing post-processing to improve simulation accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If quantum simulation methods use additional qubits and increased gate complexity to capture important physical effects, then simulation accuracy is improved, but device complexity and resource requirements increase
Solution Approach 1:
The patent segments the quantum system into active space and virtual space components. By dividing the Hamiltonian into these segments and treating them differently (using quantum resources for active space and classical computation for virtual space), the method achieves accurate simulation without requiring quantum resources to scale with the full system size, thus reducing gate complexity while maintaining simulation accuracy.
Solution Approach 2:
The patent introduces an intermediary classical computation step that bridges the quantum and classical domains. Classical computers compute matrix elements and perform diagonalization, acting as intermediaries that handle computationally intensive tasks without requiring additional quantum resources. This intermediary approach allows accurate simulation results without increasing quantum device complexity.
2Measurement precision
If quantum simulation methods use additional qubits and increased gate complexity to capture important physical effects, then simulation accuracy is improved, but quantum computing resources increase
Solution Approach 1:
The method segments the computational task into quantum and classical portions. By representing the Hamiltonian in a segmented basis set (active space orbitals and virtual orbitals) and computing matrix elements selectively, the patent reduces the number of qubits needed while maintaining simulation accuracy through classical computation of virtual space contributions.
Solution Approach 2:
The patent uses classical computation to copy and process information that would otherwise require additional quantum resources. By classically computing matrix elements and performing diagonalization, the method creates accurate simulation results without requiring proportional increases in quantum computing resources such as qubits and gates.
3Device complexity
If classical techniques are used to simulate quantum systems, then device complexity is reduced, but manufacturing precision and simulation accuracy become untenable due to exponential resource scaling
Solution Approach 1:
The patent segments the simulation task to match the complementary strengths of quantum and classical computers. Quantum computers handle the active space where quantum effects are essential, while classical computers handle the virtual space and diagonalization. This segmentation enables accurate simulation results with manageable computational resources by avoiding the exponential scaling problem of purely classical methods.
Solution Approach 2:
The patent creates a hybrid quantum-classical simulation framework that combines the capabilities of both computing paradigms. This universal approach leverages quantum computation for inherently quantum tasks and classical computation for linear algebra operations, achieving both accuracy and efficiency that neither approach could achieve alone.
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.