**Project Status:** Active

Welcome to the "Heterogeneous Digital-Analog Quantum Dynamics Simulations" (HDAQDS) project homepage.

We are a multidisciplinary team of computer scientists, applied mathematicians, scientific application domain experts, and quantum computing researchers. Our team is funded by DOE EXPRESS Quantum Algorithms Team (QAT) Research program to develop novel quantum simulations algorithms for scientific applications in Correlated Electron Systems, Nuclear Physics, and Quantum Field Theory. We take a ** heterogeneous **approach to quantum simulations and study quantum-classical algorithmic primitives in which classical computers are utilized as a part of the solution alongside with quantum hardware. We also combine quantum digital and analog simulation methods as a way to reduce simulation circuit depth and mitigate quantum errors. Our primary interest is in quantum dynamics simulations and ground state properties of strongly correlated many-body system.

### TEAM

Project Director: Pavel Lougovski (ORNL)

Ryan Bennink (ORNL)

Eugene Dumitrescu (ORNL)

Gaute Hagen (ORNL)

Travis Humble (ORNL)

Thomas Papenbrock (UT/ORNL)

Raphael Pooser (ORNL)

Nick Peters (ORNL)

Kody Law (UManchester/ORNL)

Thomas Maier (ORNL)

### RESEARCH

**Digital-analog quantum simulation algorithms**:

- We pursue a heterogeneous approach to quantum simulation algorithm design, whereby a quantum algorithm (QA) is designed to utilize individual algorithmic strengths of analog and digital simulations and to operate on a combination of quantum digital and analog hardware. We call this a hybrid digital-analog QA (DAQA). The centerpiece of DAQA is an idea of decomposing a quantum simulation into a product of restricted single and two-qubit gates interleaved with sparse analog unitaries. This heterogeneous simulation approach balances unitary decomposition complexity, and, hence, the length of a simulation, with natural features of the hardware implementation.

**Scientific Applications**:

*Correlated Electron Systems*: Our main focus is on developing DAQA for simulating Hubbard model. We are interested in determining under which conditions the DAQAs obtain linear complexity in log d, where d is the dimension of the quantum model. We are also investigating the scalability and noise tolerance of the developed DAQAs on various quantum hardware architectures (e.g., trapped ions, superconducting circuits, etc.).*Nuclear Physics*: We are developing shallow depth digital QAs and DAQAs for simulating ground states of various atomic nuclei. We are using Hamiltonians from the effective field theory. In particular, we are interested in the deuteron, triton and He8 systems and scaling of our algorithm to heavier nuclei such as oxygen.*Quantum Field Theory*: We are interested in quantum dynamics simulations of the Schwinger model on a lattice. The Schwinger model describes quantum electrodynamics in one space and one time dimension. It serves as a "prototype" for the strong interactions as it shares a number of features, such as confinement and spontaneous breaking of chiral symmetry, known to be important ingredients of the theory of strong interactions.

**Uncertainty verification for quantum simulations**:

- Bayesian algorithms for quantum state verification are a useful tool in the context of the quantum simulation algorithms. However, they are impractical for large quantum systems as they require exponentially many measurements to provide a complete state estimation. Instead we focus on developing methods for estimating averages of quantum observables of interest and for error model selection based on hierarchical Bayesian methods.

Last Updated: May 28, 2020 - 4:01 pm