# Quantum Algorithms for Scientific Computation

With the availability of near-term quantum devices and the breakthrough of quantum supremacy experiments, quantum computation has received an increasing amount of attention from a range of scientific disciplines in the past few years. There is currently intense research on using quantum computers to solve challenging computational problems in scientific and engineering computation. The tasks include solving linear systems, eigenvalue problems, least-squares problems, differential equations, as well as numerical optimization problems. Berkeley Lab researchers are working to improve asymptotic complexities for solving these tasks, providing provable performance guarantees, as well as variational quantum algorithms for near-term and early fault-tolerant quantum architectures.

## Projects

### Quantum Algorithms Team

Berkeley Lab's integrated team of scientists develops quantum algorithms for chemical sciences working closely with computer scientists, applied mathematicians, and quantum hardware developers.

### Quantum Information Science at NERSC

NERSC sees its role in the budding QIS field as a centralized resource for users who want to bridge the gap between classical computing and quantum computing for applications in chemistry, physics, materials science, drug discovery, and more. Many of the science problems NERSC users are currently focused on are quantum mechanical in nature; by combining classical and quantum resources, NERSC is looking to enhance and expand these research efforts both in the near term and beyond. Contacts: Katie Klymko, Nick Wright

### Quantum Numerical Linear Algebra

This project is developing efficient algorithms for solving eigenvalue problems, linear systems of equations, and block encodings of sparse matrices. **Contacts: Lin Lin, Chao Yang**

### Quantum Signal Processing

This project is developing an optimization-based algorithm for the robust solution of phase factors in quantum signal processing, which can be used in a variety of scientific computing applications. **Contact: Lin Lin**

### QCLAB

QCLAB is an object-oriented software library for creating and representing quantum circuits. QCLAB (also implemented in C++) can be used for rapid prototyping and testing of quantum algorithms and allows for fast algorithm development and discovery. QCLAB provides I/O through openQASM making it compatible with quantum hardware. **Contact: Roel Van Beeumen (Van Beeumen on the Web)**

### F3C

Fast Free Fermion Compiler (F3C or F3C++) is a software library for compiling time-evolution quantum circuits of spin Hamiltonians that can be mapped to free fermions. **Contact: Roel Van Beeumen (Van Beeumen on the Web)**

### FABLE

Fast Approximate BLock Encodings (FABLE) is a software library for synthesizing quantum circuits of approximate block-encodings of matrices. A block-encoding is the embedding of a matrix in the leading block of a larger unitary matrix. **Contact: Roel Van Beeumen (Van Beeumen on the Web)**

### Advancing Integrated Development Environments for Quantum Computing through Fundamental Research (AIDE-QC)

Scientists are developing and delivering open-source computing, programming, and simulation environment that supports the diversity of quantum computing research at the Department of Energy. AIDE-QC efforts focus on programming languages, compilers, verification, and debugging of quantum simulations. All of this is packaged in an integrated software development environment. **Contact: Bert de Jong** (de Jong on the Web)

### HEP Quantum Pattern Recognition (HEP.QPR)

As ever more powerful accelerators flood the detectors with billions of charged particle tracks per second, classical iterative pattern recognition algorithms are becoming the limiting factor in the discovery potential of many HEP experiments. Quantum Pattern Recognition (QPR) algorithms have the potential to provide orders of magnitude speed improvements and increased precision. The HEP. QPR pilot project aims to create a community of computer scientists and physicists dedicated to addressing the challenges of HEP pattern recognition and to start building a suite of promising QPR algorithms and tools. Contact: Heather Gray (Gray on the Web)

### Architecture for Quantum Time-dependent Circuits (ArQTiC)

ArQTiC is a domain-specific full-stack software package built for the dynamic simulations of materials on quantum computers. Its main contributions include providing a software library for high-level programming of such simulations on quantum computers, and providing post-processing capabilities that allow users to more efficiently analyze results from the quantum computer. Paired with the power to optimize and execute quantum circuits, ArQTiC opens the field of dynamic materials simulations on quantum computers to a broader community of scientists from a wider range of domain sciences, paving the way for accelerated progress towards physical quantum supremacy. **Contacts: Lindsay Bassman, Katie Klymko**

### Fundamental Algorithmic Research for Quantum Computing (FAR-QC)

The FAR-QC team is exploring and identifying scientific domains and problems for which quantum resources may offer significant advantages over classical counterparts, which is vital in realizing the potential of quantum computing. FAR-QC seeks to deliver quantum algorithms that offer provable asymptotic advantages over the best-known or best-possible classical counterparts. **Contact: Bert de Jong (Berkeley Lab Lead)**

### C2SEPEM: Center for Computational Study of Excited-State Phenomena in Energy Materials

C2SEPEM develops theories, methods, and general software to elucidate and predict excited-state phenomena in energy-related materials. Our software will use advanced algorithms and first-principles many-body perturbation theory that fully include but also go well beyond the interacting one- and two-particle Green’s function (GFs) to compute quasiparticle excitations and lifetimes, optical spectra, exciton-exciton interactions, trion formation, nonlinear optical processes, excited-state decay, time-dependent phenomena, and more. **Contact: Steven G. Louie (Louie on the Web)**

### CompCat-SciDAC: Advancing Catalysis Modeling, from Atomistic Chemistry to Whole System Simulation

Many catalytic processes are sufficiently complex, meaning experimental measurements cannot be used to accurately quantify various details of the reaction pathways and kinetics. Sophisticated computational models of chemical catalysis are therefore necessary to both understand and predict the outcomes of these reactions and to inform future catalyst development. This project investigates the myriad scientific difficulties posed by this system while developing computational tools which can also be transferred to the study of other catalytic systems of chemical and societal interest. **Contact: Martin Head-Gordon**