### Quantum Algorithms, Mathematics and Compilation Tools for Chemical Sciences

Designing and delivering novel algorithms, compiling techniques, scheduling tools, and linear algebra approaches for chemical sciences

Mathematics and Computer Science Division # Quantum Computing

Offering the opportunity to revolutionize scientific computing

The quantum computing research group at Argonne National Laboratory leverages the traditional strengths of the laboratory in classical supercomputing. Scientists from the Argonne Leadership Computing Facility (ALCF), Computational Science division (CPS), and the Mathematics and Computer Science division (MCS) are studying hybrid quantum-classical architectures that combine the power of quantum processors and supercomputers. We also are developing highly scalable high-performance computing (HPC) quantum simulators to run large 50+ qubit quantum simulations on Argonne supercomputers.

Researchers, engineers, and students in our group have access to state-of-the-art quantum processors and simulators. We utilize the IBM Q System Hub, a universal quantum computing system with 20 superconducting qubits. Argonne also has an on-premise Atos QLM-35 quantum simulator, a state-of-the-art environment capable of simulating quantum algorithms using up to 35 qubits.

As a member of the Chicago Quantum Exchange, Argonne is participating in the design and construction of aunique experimental facility capable of teleporting quantum states; completion of a 30-mile quantum network connecting Argonne and Fermi is planned for 2020. Our group is collaborating with the project lead Professor David Awschalom (University of Chicago and Argonne) to investigate approaches for overcoming noise at the physical layer of the network and developing new applications of quantum networks.

We received DOE funding to participate in the Quantum Algorithms, Mathematics and Compilation Tools for Chemical Sciences project designing novel technologies that will enable near-term quantum computing devices to be used for scientific discovery. The Quantum Algorithms Team consists of researchers led by Lawrence Berkeley National Laboratory and includes UC Berkeley and Harvard University.

**Research Projects**

The Mathematics and Computer Science division at Argonne performs research on a number of complementary research projects in quantum information science with the following goals.

**Quantum Networks and Distributed Systems:**

- Build a quantum teleportation network between Argonne and Fermilab
- Demonstrate the use of quantum communication between small quantum processors to solve large computational problems
- Develop hybrid quantum-classical computing architectures that combine the power of supercomputing and emerging quantum technologies
- Develop distributed quantum computing architectures and quantum network protocols

**Quantum and Classical Algorithms:**

- Develop new variational classical/quantum algorithms with applications that support the mission of the Department of Energy
- Develop new parameter optimizers for variational algorithms
- Perform optimizations of quantum circuits (collaboration with Fred Chong at the University of Chicago)
- Design of new quantum materials using ALCF supercomputers (collaboration with Giulia Galli and David Awschalom at the University of Chicago)
- Develop numerical optimization algorithms for quantum computing problems

**Error Correction and Fault Tolerance:**

- Develop error models that allow accurate and efficient simulation of errors in quantum processors, quantum memory, and quantum network links
- Develop new, more efficient error-correcting codes tailored to the characteristics of quantum hardware
- Study entanglement purification techniques, their performance, and compare memory and classical communication requirements

**Quantum Simulators:**

- Develop a highly scalable HPC quantum simulator capable of simulating multiqubit quantum systems
- Implement fast data compression techniques that reduce computational cost of quantum simulations while maintaining precision (collaboration with Atos and Intel scientists)
- Perform Monte Carlo simulations of errors to investigate the effectiveness of error correction
- Perform quantum network simulations to evaluate scalability, correctness, and ability to support applications

**Where have we been publishing?**

Here are some recent papers we have published in peer-reviewed journals or presented at conferences.

- M. Otten, J. Larson, M. Min, S. M. Wild, M. Pelton, and S. K. Gray, “Origins and Optimization of Entanglement in Plasmonically Coupled Quantum Dots,” Physical Review A, vol. 94, no. 2, p. 15, 2016.
- M. Otten, R. A. Shah, N. F. Scherer, M. S. Min, M. Pelton, and S. K. Gray, “Entanglement of Two, Three and Four Plasmonically Coupled Quantum Dots,” Physical Review B, vol. 92, no. 12-15, 2015.
- A. Buluc, W. de Jong, J. Larson, L. Lin, S. Wild, “The Role of Applied Mathematics in Quantum Computing: Old Can Be New Again?” Whitepaper submitted to the 2017 DOE ASCR Applied Math Meeting, 2017.
- A. M. Gok, D. Tao, S. Di, V. Mironov, Y. Alexeev, F. Cappello, “PaSTRI: A Novel Data Compression Algorithm for Two-Electron Integrals in Quantum Chemistry,” poster presented at SC17.
- Martin Suchara, Yuri Alexeev, Frederic Chong, Hal Finkel, Henry Hoffmann, Jeffrey Larson, James Osborn, and Graeme Smith, “Hybrid Quantum-Classical Computing Architectures,” paper presented at Workshop: Post Moore’s Era Supercomputing (PMES) at SC18
- Xin-Chuan Wu, Sheng Di, Franck Cappello, Hal Finkel, Yuri Alexeev, and Frederic T. Chong, “Memory-Efficient Quantum Circuit Simulation by Using Lossy Data Compression,” paper presented at Workshop: Post Moore’s Era Supercomputing (PMES) at SC18
- Xin-Chuan Wu, Sheng Di, Franck Cappello, Hal Finkel, Yuri Alexeev, and Frederic T. Chong, “Amplitude-Aware Lossy Compression for Quantum Circuit Simulation,” paper presented at Workshop: 4
^{th}International Workshop on Data Reduction for Big Scientific Data (DRBSD-4) at SC18 - Xin-Chuan Wu, Sheng Di, Franck Cappello, Hal Finkel, Yuri Alexeev, and Frederic T. Chong, “Full State Quantum Circuits Simulation by Using Lossy Data Compression,” poster presented at SC18

Also of note is a new solver, available on github, for general simulation of quantum systems

- M. Otten, “QuaC: Open Quantum Systems in C,” a time-dependent open quantum systems solver, 2017.

**Seminars**

We’ve also been involved in several seminars and panels.

- S. Wild was session chair of Machine Learning and Quantum Computing at SC17.
- D. Maslov (NSF) gave an invited MCS seminar on “How to Program a Quantum Computer,” Sept. 14, 2017.
- S. Caldwell (Rigetti Quantum Computing) gave an invited MCS Seminar on “Toward Full-Stack Quantum Computing Built on Superconducting Qubits,” Sept. 12, 2017.
- A. M. Gok gave a seminar on “PaSTRI: A Novel Data Compression Algorithm for Two-Electron Integrals in Quantum Chemistry,” August 21, 2017.