Simulating Quantum Systems with Quantum Computation

This patent application details a quantum simulation method using a hybrid classical/quantum computing system. The method simulates quantum systems by dividing them into fragments, each processed by a separate, unentangled quantum processor unit (QPU). A classical processor unit manages the overall simulation, coordinating the QPUs and updating parameters based on their results. Density matrix embedding theory (DMET) is employed, with variational quantum eigensolvers (VQEs) on the QPUs calculating reduced density matrices. The method aims to improve the accuracy and speed of simulating complex quantum systems.

Quantum Systems with Quantum Computation (US20210406421A1)

Main Themes:

• This patent application describes a novel method for simulating large quantum systems using quantum computation, specifically leveraging multiple unentangled Quantum Processor Units (QPUs) within a hybrid classical-quantum computing architecture.

• The proposed method utilizes Density Matrix Embedding Theory (DMET) to break down the complex system into smaller fragments. Each fragment is then simulated on a separate QPU using a Variational Quantum Eigensolver (VQE).

• This approach is particularly advantageous for simulating strongly correlated systems, where traditional classical methods struggle. It potentially allows for studying larger systems and capturing long-range correlation functions with higher accuracy.

Key Ideas and Facts:

1. DMET Fragmentation: The quantum system is partitioned into smaller fragments, allowing for parallelized computation on multiple QPUs.

• "For a large system Q, its wavefunction can be arbitrarily bi-partitioned into a fragment (or impurity) and bath (or environment)."

1. Hybrid Computation: A classical processor unit manages the overall simulation process, while individual QPUs are delegated to simulate the fragments.

• "In some instances, a hybrid computer system can simulate a quantum system whose Hamiltonian has a larger dimension than that which is provided by the number of qubits available to an individual quantum processor unit (QPU) in the hybrid computer system."

1. VQE as Embedded Solver: Each QPU utilizes a VQE algorithm to determine the ground state properties of its assigned fragment, generating reduced density matrices (RDMs).

• "The VQE can be used when solving for the 1-RDM and 2-RDM of the embedded Hamiltonian."

1. Iterative Refinement: The classical processor uses the RDMs from each fragment to update the embedding potentials in the approximate Hamiltonian, iteratively improving the overall simulation accuracy.

• "The first, second and third sub-processes can be repeated, for example, until particle conservation and the embedding potential do not change between iterations."

1. Scalability and Accuracy: By utilizing multiple QPUs in parallel, the method allows for simulating larger systems. Utilizing VQE within DMET potentially increases accuracy compared to classical methods for simulating certain systems.

• "DMET is applicable to very large scale problems be it either molecules or materials. Unlike DMFT that requires the frequency dependent two particle Green's function, DMET utilizes the 1-RDM of the embedded problem with high accuracy."

1. Applications: The patent application highlights potential applications in simulating a variety of quantum systems, including:

• Lattice models (e.g., the Hubbard model)

• Extended chemical systems

• Ground state and transition state molecules

• Correlated materials and molecules (e.g., metal-oxides, catalysts)

Important Quotes:

• DMET advantages: "The ability to study larger fragments at higher fidelity has many implications for accurate simulations of materials and chemistry."

• VQE suitability: "DMET's use of the 1-RDM of the embedded Hamiltonian makes VQE a suitable algorithm for this use case."

• Potential impact: "Further integration can lead to methodologies to study large quantum systems with higher resolution than what is currently possible with state of the art classical methods."

Overall, this patent application outlines a significant advancement in simulating complex quantum systems using the combined power of classical and quantum computing resources.

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