Sample-based Quantum Diagonalization: IBM Riken
The researchers from IBM, the Cleveland Clinic, and Riken presented a historic announcement at the annual IBM Think conference about a molecular modeling discovery that might significantly transform the field of materials science and drug development. Using Sample-based Quantum Diagonalization (SQD IBM), the scientists simulated a complicated protein with over 12,000 atoms, which was previously unattainable using quantum technology.
The same researchers modeled a 303-atom protein four months earlier, highlighting the fast scaling of the SQD technique with quantum-centric supercomputing.
The Challenge: The Exponential Wall of Chemistry
To discover novel catalysts and medications, scientists have spent decades trying to comprehend the atomic-level behaviors of molecules. Nonetheless, these systems’ mathematical intricacy is astounding. The Schrödinger energy eigenvalue equation, in which the eigenvalues stand for the system’s energy levels, controls a molecule’s electronic structure. A Hamiltonian matrix must be diagonalized to determine the ground state energy, which is the most stable, lowest-energy configuration.
The size of this matrix increases exponentially with the number of electrons in a system. Using a cc-PVDZ basis set, for example, even a relatively tiny nitrogen molecule (N2) yields a Hamiltonian with a dimension of 65,780×65,780. For 32-qubit computers, Hilbert space is too large: it has almost 4 billion basis vectors. The amount of memory and processing power needed to diagonalize such large matrices is simply too much for classical supercomputers.
The SQD Solution: Quantum-Classical combination
By fusing the special sampling capabilities of quantum computers with classical linear algebra, SQD provides a way forward. The basic principle of SQD is that it is frequently not required to diagonalize the entire matrix. The Hamiltonian is instead projected onto a considerably smaller, “useful” subspace using the technique.
The process works in a three-step cycle:
- Quantum Suggestion: A quantum computer creates “samples” or bitstrings by preparing a state using a particular circuit (like a variational ansatz). These samples are basically proposals for the location of ground state support, which is the most significant information in the Hilbert space.
- Classical Diagonalization: Using these recommended configurations, a classical computer projects the desired Hamiltonian into this much smaller subspace and determines the eigenvalues using conventional numerical techniques.
- Iterative Refinement: To improve subsequent samples, some characteristics of the resultant approximate ground state can be supplied back into the quantum hardware.
Why SQD Is Better Than Earlier Techniques
The most popular option for chemical simulations for many years was the Variational Quantum Eigensolver (VQE), however it has serious issues with pre-fault-tolerant hardware. According to IBM researchers, VQE has a significant measurement expense. To attain chemical precision, VQE may need millions of “shots” (measurements) and thousands of distinct circuits for a basic molecule.
SQD generally measures one circuit for a specific number of shots and has reduced expenses.Additionally, SQD always offers an upper bound on the ground state energy, but VQE findings might be distorted by noise to provide energies lower than the actual physical ground state. As a result, the findings are “noise-aware” and physically dependable.
The intrinsic noise tolerance of the SQD package is implemented using the qiskit-addon-sqd Python library. By setting their amplitudes to zero, the classical diagonalization method may successfully filter out “noisy” or non-physical samples produced by a quantum processor. To increase the quality of the final estimation and refine noisy data, the method additionally uses a self-consistent configuration recovery procedure that iteratively flips bits.
Materials Science’s Future
The 12,000-atom protein simulation’s effectiveness demonstrates that SQD is especially well-suited for concentrated or sparse wave functions, where a tiny percentage of basis states have the most weight. Because of this, it is a key component of “Quantum-Centric Supercomputing,” in which quantum and conventional technology cooperate rather than compete.
The scientific community now has a scalable way to investigate the secrets of molecular structures that were previously concealed by the “exponential wall” of classical computation as IBM continues to include these tools into the Qiskit ecosystem.
