Study and simulate: Quantum computers are supposed to calculate and solve problems that classic computers cannot handle or can handle much more slowly. In the last years, quantum systems based on superconductors and ion traps were installed at the Leibniz Supercomputing Center (LRZ). These are now being extensively tested and checked. Simulations play a major role here: “Concepts such as superposition, measurements and entanglement can be investigated,” says Mario Hernandez Vera, who earned his doctorate in physical chemistry and is now developing algorithms and applications in the LRZ team for Quantum Computing and Technologies (QCT). “We also use quantum simulations to evaluate our quantum hardware.” Without the simulations on classic (super) computers, the future technology could not be brought into the everyday lives of researchers: This means that the first applications can be created even before the new technology can be used. Simulations can also be used to compare and optimize the performance values of quantum systems or to develop innovative control methods. The QCT team not only simulates with the Quaptiva, a quantum simulator from Eviden, but also with the high performance computers (HPC) and the AI systems of the LRZ and hopefully soon also on the new SuperMUC-NG Phase 2 (SNG-2). Different software platforms and programs are also used.

*Why do-you simulate quantum computing algorithms and circuits?*

**Dr. Mario Hernandez Vera**: Simulating quantum circuits with classical computers offers an alternative approach to running quantum algorithms and studying them on quantum hardware. At LRZ simulations assist students and researchers in grasping the principles of quantum computing through numerical experiments. Consequently, complex concepts such as superposition, measurements, and entanglement can be explored. Additionally, our simulators are utilized for training at LRZ, where students and researchers are introduced to new architectures and algorithms. These tools enable as well experienced scientists to develop novel quantum algorithms, or error correction models. That’s also, what the QCT team at LRZ does – we use HPC simulations to evaluating the performance of our quantum hardware, to compare its technical metrics or to develop and proof workflows for the QPUs, for example the regulary necessary calibration of the systems. Our activities are primarily driven by our quantum computing user community, and for them we are launching the first novel services in this area. Currently our users are mainly from partner institutions of the Munich Quantum Valley and collaborators from our grant projects where we are jointly working, however we start getting collaboration and support requests from scientists and institutions outside our networks.

*How important are high performance computing simulations of quantum circuits or algorithms for the quantum computing integration at the LRZ? *

**Hernandez Vera**: The integration of quantum computing in HPC systems requires a complex infrastructure. Our main goal at QCT team is to allow users to connect safely and efficiently with the quantum computers. But we also provide tools such as numerical optimizers, external libraries and of course simulators that allow the users to be active even without or in preparation to the access of quantum systems. It’s a new technology, so the current number of quantum computers is limited at LRZ. By providing HPC simulations of quantum circuits, we can enable a larger number of users to explore quantum algorithms and to test and validate those algorithms before having access to quantum hardware. Moreover, the usage of the LRZ HPC computational resources allows the user to efficiently prototype larger circuits than those they could work with locally on their own PCs.

*Which systems can be used at LRZ for simulating quantum algorithms?*

**Hernandez Vera**: Our team is working on deploying software simulators on several platforms. At the moment we are preparing access to a portfolio of software simulators running on SuperMUC-NG Phase 1. Our team is testing quantum simulation software running also on LRZ’s AI systems, as well as on the new GPU-equipped SuperMUC-NG Phase 2. Moreover, we have special-purpose systems from Eviden, hardware simulators, which work with the Qaptiva package, with which you can simulate algorithms on systems up to 38 qubits.

*What are the differences in terms of performance for simulators running in different clusters? *

**Hernandez Vera**: Two different simulators typically exhibit varying performances when running the same quantum algorithm on identical hardware. This difference in performance is associated with several factors, such as programming language like C++, Python or Rust, compiler optimization, simulator design, and targeted hardware, for example Intel CPUs, NVIDIA or AMD GPUs. Some classical simulators may be well-tailored or even optimized for specific machines in our clusters. For instance, Qaptiva software performs effectively in the Eviden cluster and is user-friendly for newcomers. The Intel Quantum Simulator is more compatible with Intel CPUs and can be installed in SuperMUC-NG due to its MPI- and OpenMP capabilities, but it may require some previous HPC skills. Additionally, we have deployed and tested GPU-based simulators like CUDA Quantum from NVIDIA, which perform better on the LRZ AI systems.

*What role do software packages or platforms such as Quiskit, Cirq or Pennylane play in the simulation?*

**Hernandez Ver**a: These packages serve to translate a given problem, such as simulating the electronic structure of a real molecule, into the quantum circuit required to address it. The quantum circuit is then executed in the simulator provided by the respective package. While theoretically, identical quantum circuits can be implemented across each package, various factors such as documentation, user interface, or APIs may influence user preferences. Therefore, we strive to offer the most popular quantum software packages and simulators.

*How difficult is the simulation? How does it work? *

**Hernandez Vera**: It depends on the mathematical model you use in your simulation and the quantum algorithm you are implementing. Probably the simplest case is the ideal state vector simulation, in which noise and measurements are discarded. In this case, a series of quantum gates, which can be represented as matrices, are applied to a quantum state represented as a vector. The state vector changes after each gate operation. Once all operations have been applied, the resulting state vector contains information that can be used to extract useful data, such as expectation values linked to physical or chemical systems.

*What are the challenges to simulate quantum circuits?*

**Hernandez Vera**: Simulators can solve the same problem using different mathematical methods and algorithms. For example state vector or density matrix simulations rely basically on matrix multiplications to describe the execution of the quantum algorithm. A challenge with the above methods is that the size of the matrices and vectors grows exponentially with the number of qubits, which typically corresponds to the size of the problem being addressed. Other simulators use different methods such as tensor networks that allow compressing quantum information, saving computational resources, but facing another problem, namely, the simulation time may grow very fast with the size of the problem. Therefore, the simulation of quantum circuits is a hard computational task even for supercomputers. Besides realistic quantum simulations add other sources of complexities, such as the inclusion of models to account for noise and measurements of the quantum circuit.

*You work with “variational algorithms” – why and for what you use it?*

**Hernandez Vera**: The Variational Quantum Algorithm, for short VQA, is designed to solve optimization problems following a hybrid approach in which classical and quantum computing is involved. The quantum computer executes a parameterized quantum circuit that has the advantage of exploring a large space of solutions for a complex objective function, and whose parameters are improved iteratively by a classical optimizer. This algorithm has been proposed as a potential solution for effectively utilizing current quantum computers, known as NISQ- or Noisy Intermediate-Scale quantum computers, which still face challenges in scaling computational power while maintaining fault tolerance. Besides, VQA is well known among users because it can be applied to simulations of many physical problems.

*What is the Variational Quantum Eigensolver and why does one need it?*

**Hernandez Vera**: The Variational Quantum Eigensolver or VQE falls within the category of variational algorithms, notable for its utility in computing the ground energy of atoms, molecules, and other quantum systems. The determination of ground energy is vital for understanding real-world physical systems. Achieving high precision in computing this property poses a challenge for classical computers. However, it's worth noting that implementing VQE on actual quantum hardware can be challenging, especially as the complexity of the simulated physical problems increases, as one can expect in quantum chemistry problems.

*Quantum systems based on superconductors and ion traps are installed at the LRZ. Can different quantum technologies also be simulated?*

**Hernandez Vera**: Different quantum platforms vary in how they implement qubits and quantum gates in the hardware. Typically, users are not directly aware of these differences. Instead, they prepare quantum circuits that are mapped by a software development kit (SDK) to the specific native gates of the quantum hardware. This mapping also involves circuit optimization to enhance simulation speed. Certain simulators, such as those integrated into Qiskit and Pennylane packages, offer the capability to simulate specific types of hardware, including particular qubit connectivity and noise models. Thus, theoretically, one could explore through simulations whether a specific application runs more efficiently on a particular architecture. Users may even create a model describing a new architecture. Nevertheless, it's crucial to remember that all simulations are based on models. To discern differences in real hardware, one must refer to documentation provided by vendors and conduct benchmark studies of hardware performance.

##### More to read:

Quantensimulator Eviden: https://doku.lrz.de/atos-qlm-10745934.html