Quantum Computation Mapping for Constrained Electronic States
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Solution Overview
Problem
Existing quantum variational eigensolvers (VQEs) face challenges in enforcing constraints such as particle number, spin multiplicity, and spatial symmetries, leading to incorrect results and inefficient use of computational resources due to errors in state preparation and readout, and methods like penalty terms exacerbate these issues.
Innovation Solution
A method involving a linear bijective mapping between a subspace of constrained states and an unconstrained Hilbert space is used, allowing quantum computations to be performed efficiently by excluding states outside the subspace, thereby reducing the need for quantum resources and minimizing errors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If penalty terms are added to enforce constraints in VQE, then constraint satisfaction improves, but computational complexity and resource usage increase
Solution Approach 1:
The patent extracts and removes the harmful penalty terms from the Hamiltonian, replacing them with a direct constraint enforcement mechanism through Ansatz design. This eliminates the computational overhead of evaluating penalty terms while maintaining constraint satisfaction through the structure of the quantum circuit itself.
Solution Approach 2:
The patent applies constraints preliminarily through the Ansatz design before the optimization process begins. By embedding constraint satisfaction into the structure of the Ansatz (e.g., using particle number conserving operators, spin-adapted configurations), the system ensures constraints are satisfied from the start without requiring additional penalty terms during optimization.
2Adaptability or versatility
If VQE searches in full Fock space without constraints, then solution space coverage improves, but convergence to correct constrained solution deteriorates
Solution Approach 1:
The patent segments the full Fock space into constrained subspaces through the Ansatz design. By constructing the Ansatz to operate within specific subspaces (e.g., fixed particle number, specific spin multiplicity), the method maintains adequate solution space coverage within each subspace while ensuring convergence to physically valid solutions.
Solution Approach 2:
The patent applies different Ansatz structures to different regions of the solution space based on local constraint requirements. Each Ansatz is tailored to satisfy specific constraints (particle number, spin, spatial symmetry) appropriate to the particular subspace being searched, optimizing both coverage and convergence for each region.
3Ease of operation
If quantum computer prepares states without constraint enforcement, then state preparation flexibility improves, but state preparation errors increase
Solution Approach 1:
The patent applies constraints preliminarily through the Ansatz design before the optimization process begins. By embedding constraint satisfaction into the structure of the Ansatz (e.g., using particle number conserving operators, spin-adapted configurations), the system ensures constraints are satisfied from the start without requiring additional penalty terms during optimization.
4Productivity
If VQE uses constrained subspace search, then computational resource usage reduces, but algorithm complexity increases
Solution Approach 1:
The patent changes the parameterization of the quantum state through different Ansatz designs that inherently satisfy constraints. By using parameters that naturally enforce constraints (e.g., occupation numbers, spin-coupling parameters), the method reduces the effective search space and computational resources needed while avoiding the complexity of penalty term optimization.
Data Source
AI summary
A computer-implemented for representing a plurality of states conforming to a set of one or more constraints of an electronic structure when performing a quantum computation using a hybrid computer system comprising a quantum computer and a classical computer, the method comprising: using the classical computer to: identify a subspace of states conforming to a set of one or more constraints of an electronic structure; perform a linear bijective mapping between a plurality of states of the subspace and an unconstrained Hilbert space, the bijective mapping equalising the dimension of the unconstrained Hilbert space to the dimension of the subspace; and generate a representation of the electronic structure problem Hamiltonian in the unconstrained Hilbert space; and using the quantum computer to: generate a representation of the unconstrained Hilbert space comprising a plurality of qubits in the register of the quantum computer.