# QCE20 Workshop on

Quantum Simulation

## Date and Time

- Fri, Oct 16, 2020
- 10:45─16:45 Mountain Time (MDT) — UTC-6

## Organizers

- Yuri Alexeev, Argonne, National Laboratory (Lead)
- Matthew Otten, Argonne National Laboratory
- Salvatore Mandrà, NASA Ames

## Overview

The goal of the Quantum Simulation Workshop is to cover all aspects of the development and use of quantum simulators using various approaches applicable to a wide range of quantum platforms, with the focus on current and upcoming technologies and state-of-the-art algorithmic developments, such as parallelization of simulators to run on HPC systems. Additionally, the workshop will cover a wide range of applications of quantum simulators, including demonstrations of quantum advantage, development of quantum algorithms, and the design of new quantum systems. The Quantum Simulations Workshop will provide participants with both knowledge of how to design and implement state-of-the-art simulators, as well as how to utilize those simulators to make important progress in quantum information science.

## Agenda

- 10:45 – 11:15
*Kyungjoo Noh, AWS Center for Quantum Computing: Efficient classical simulation of noisy random quantum circuits in one dimension* - 11:15 – 11:45
*Brendon Lovett, University of St. Andrews: Modelling non-Markovian quantum systems using tensor networks* - 11:45 – 12:15
*Matt Otten, Argonne National Laboratory: Simulating Realistic Quantum Devices with QuaC*

- 13:00 – 13:30
*Raphael Pooser, Oak Ridge National Laboratory: Quantum simulators as application-inspired NISQ device benchmarks* - 13:30 – 14:00
*Dmitry Liakh***,**Oak Ridge National Laboratory: Tensor Network Quantum Virtual Machine for Quantum Circuit Simulations at Exascale - 14:00 – 14:30
*Johnnie Gray, California Institute of Technology: Tensor Network Quantum Circuit Simulation & Quimb*

- 15:15 – 15:45
*Cupjin Huang, Alibaba: Classical Simulation of Quantum Superiority Circuits: Classical Simulation of Quantum Superiority Circuits* - 15:45 – 16:15
*Salvatore Mandrà, NASA Ames: Quantum circuit simulations of NISQ devices with qFlex* - 16:15 – 16:45
*Danylo Lykov, Yuri Alexeev, Argonne National Laboratory: QTensor: Parallel quantum simulator using tensor networks*

## Abstracts

### Efficient classical simulation of noisy random quantum circuits in one dimension

Kyungjoo Noh, AWS Center for Quantum Computing

**Abstract:** Understanding the computational power of noisy intermediate-scale quantum (NISQ) devices is of both fundamental and practical importance to quantum information science. Here, we address the question of whether error-uncorrected noisy quantum computers can provide computational advantage over classical computers. Specifically, we study noisy random circuit sampling in one dimension (or 1D noisy RCS) as a simple model for exploring the effects of noise on the computational power of a noisy quantum device. In particular, we simulate the real-time dynamics of 1D noisy random quantum circuits via matrix product operators (MPOs) and characterize the computational power of the 1D noisy quantum system by using a metric we call MPO entanglement entropy. The latter metric is chosen because it determines the cost of classical MPO simulation. We numerically demonstrate that for the two-qubit gate error rates we considered, there exists a characteristic system size above which adding more qubits does not bring about an exponential growth of the cost of classical MPO simulation of 1D noisy systems. Specifically, we show that above the characteristic system size, there is an optimal circuit depth, independent of the system size, where the MPO entanglement entropy is maximized. Most importantly, the maximum achievable MPO entanglement entropy is bounded by a constant that depends only on the gate error rate, not on the system size. We also provide a heuristic analysis to get the scaling of the maximum achievable MPO entanglement entropy as a function of the gate error rate. The obtained scaling suggests that although the cost of MPO simulation does not increase exponentially in the system size above a certain characteristic system size, it does increase exponentially as the gate error rate decreases, possibly making classical simulation practically not feasible even with state-of-the-art supercomputers. https://arxiv.org/abs/2003.13163

### Modelling non-Markovian quantum systems using tensor networks

Brendon Lovett, University of St. Andrews

**Abstract:** In order to model realistic quantum devices it is necessary to simulate quantum systems strongly coupled to their environment. To date, most understanding of open quantum systems is restricted either to weak system-bath couplings, or to special cases where specific numerical techniques become effective. Here I present a general and yet exact numerical method to calculate the dynamics of an open quantum system coupled to a non-Markovian environment [1]. The method, the “Time-Evolving Matrix Product Operator” (TEMPO) is to express the equations of motion for such an open quantum system as a tensor network, which can be efficiently contracted, and whose structure allows for the environment effects to be dealt with separately from the system Hamiltonian. This so-called process tensor approach [2] enables the calculation of dynamics for different time-dependent system Hamiltonians while using the same object to capture the impact of the environment. In addition, this approach allows for the efficient calculation of multi-time system correlation functions, which I will show allows for the calculation of the dynamics of the environment [3].

[1] A. Strathearn, P. Kirton, D. Kilda, J. Keeling, and B. W. Lovett. Efficient non-Markovian quantum dynamics using time-evolving matrix product operators, Nature Communications 9 3322 (2018)

[2] M. P. Jørgensen and F. Pollock, Exploiting the Causal Tensor Network Structure of Quantum Processes to Efficiently Simulate Non-Markovian Path Integrals, Phys. Rev. Lett. 123 240602 (2019)

[3] D. Gribben, A. Strathearn, J. Iles-Smith, D. Kilda, A. Nazir, B. W. Lovett, and P. Kirton, Exact quantum dynamics in structured environments, Phys. Rev. Res. 2 013265 (2020)

### Simulating Realistic Quantum Devices with QuaC

Matt Otten, HRL Laboratories

Abstract: As quantum devices progress in scale and quality, understanding the effects of noise sources beyond single qubit Pauli errors, such as leakage errors in superconducting qubits, becomes critical. I will discuss the QuaC simulator, a high-performance Lindblad master equation solver designed to simulate the underlying physics of various quantum devices, including noise processes, pulse level control, and inter-system coupling.

### Quantum simulators as application-inspired NISQ device benchmarks

Raphael Pooser, Oak Ridge National Laboratory

**Abstract:** We will present several high level algorithms which have been distilled to essential benchmarks of current quantum computer hardware. We will also demonstrate error mitigation schemes which can be used to post process data and also to characterize a collection of qubits. These characterizations often probe low level chip components, and can be used to link high level application performance to low level characteristics such as pulse implementations. Finally, we will present a volumetric-style application which measures the computational power characterized by a quantum processor’s performance in variational applications.

### Tensor Network Quantum Virtual Machine for Quantum Circuit Simulations at Exascale

Dmitry Liakh, Oak Ridge National Laboratory

Abstract: Tensor Network Quantum Virtual Machine (TN-QVM) is a quantum circuit simulation backend used by the XACC framework that employs the tensor network representations of quantum circuits. In turn, the TN-QVM module offloads all computations to the recently developed math library ExaTN which can compose and process arbitrary tensor networks on regular workstations as well as HPC platforms, with or without GPU acceleration. With the new ExaTN backend, TN-QVM currently implements several strategies for quantum circuit simulation, including the direct contraction of the quantum circuit, an approximate ideal evolution via the tensor train (matrix product state) compression, and an approximate noisy evolution via the locally purified density operator formalism based on the tensor train ansatz. The ExaTN tensor processing backend employs the task-based execution model and can scale from workstations to the leadership HPC platforms, like Summit, enabling efficient simulation of rather large quantum circuits, both in terms of the number of qubits and the circuit depth.

### Tensor Network Quantum Circuit Simulation & Quimb

Johnnie Gray, California Institute of Technology

**Abstract:** Tensor networks naturally describe quantum circuits and offer state-of-the-art performance when it comes to exactly benchmarking large quantum chips. We describe the general method, how it differs from other tensor network and circuit simulation methods, including the introduction of hyper-indices and hyper-graph partitioning, and how to do this all in quimb.

### Classical Simulation of Quantum Superiority Circuits

Cupjin Huang, Alibaba Quantum Laboratory

**Abstract:** It is believed that random quantum circuits are difficult to simulate classically. These have been used to demonstrate quantum superiority: the execution of a computational task on a quantum computer that is infeasible for any classical computer. The task underlying the assertion of quantum superiority by Arute et al. (Nature, 574, 505 –510 (2019)) was initially estimated to require Summit, the world’s most powerful supercomputer today, approximately 10,000 years. The same task was performed on the Sycamore quantum processor in only 200 seconds.In this work, we present a tensor network-based classical simulation algorithm. Using a Summit-comparable cluster, we estimate that our simulator can perform this task in less than 20 days. This estimate is obtained under a strict interpretation of the superiority task where one generates samples from a distribution with negligible statistical distance to a mixture of the uniform distribution and the ideal distribution, with fidelity matching that of the quantum device. On moderately-sized instances, we reduce the runtime from years to minutes, running several times faster than Sycamore itself. These estimates are based on explicit simulations of parallel subtasks, and leave no room for hidden costs. The simulator’s key ingredient is identifying and optimizing the “stem” of the computation: a sequence of pairwise tensor contractions that dominates the computational cost. This orders-of-magnitude reduction in classical simulation time, together with proposals for further significant improvements, indicates that achieving quantum superiority may require a period of continuing quantum hardware developments without an unequivocal first demonstration.

### Quantum circuit simulations of NISQ devices with qFlex

Salvatore Mandra, NASA Ames

Abstract: Quantum supremacy is the task to perform a quantum calculation on a Noisy-Intermediate Scale Quantum (NISQ) device that cannot be performed on the latest and most powerful supercomputer by using the best known classical simulator. To this end, the Google team has designed a series of benchmarks, based on the sampling of Random Quantum Circuits (RQCs), to challenge classical supercomputers. In a programming-like language, the RQC sampling corresponds to the first “Hello, World!” program in the quantum computing era. In my talk I will present qFlex, a fast and flexible software to simulate large RQCs to both verify and benchmark NISQ devices. qFlex is designed to maximize the number of PFLOP/s, reaching a sustained average performance of 281 Pflop/s (true single precision) on Summit, corresponding to the 68% of the maximum achievable, with peaks of 381 Pflop/s (true single precision), corresponding to the 92% of the maximum achievable. qFlex is a NASA-Google-ORNL collaboration and it is publicity available at https://github.com/ngnrsaa/qFlex.

### QTensor: Parallel quantum simulator using tensor networks

Danylo Lykov and Yuri Alexeev, Argonne National Laboratory

**Abstract:** We will present a quantum circuit simulator designed to run in parallel on large supercomputers. It is based on the tensor network representation of quantum circuits. We proposed a novel parallelization strategy that is based on splitting partially contracted tensor expression. The simulator is very flexible and agnostic to both connectivity map of the quantum device and types of gates used in the circuit. The features of the simulator include:

- QAOA lightcone implementation
- Efficient batch amplitude calculations
- Advanced slice index search algorithm
- Feynman path approach to reduce memory requirement
- Native support of diagonalisation of sparse gates

The code is publicity available at https://github.com/danlkv/QTensor

## Contact Us

For more information about the Quantum Simulation workshop, contact Yuri Alexeev, yuri@alcf.anl.govA, Argonne, National Laboratory.