Quantum Simulation: The Future of Computing and Its Challenges in Simulating Open Quantum Systems

Quantum simulation, using quantum computers to simulate quantum systems, is a key area of research due to the computational challenges of simulating large quantum systems on classical computers. Quantum computers are more efficient, scaling polynomially with the number of quantum particles. Despite advancements in quantum hardware, more work is needed to reach fault-tolerant settings. The growing accessibility of Noisy Intermediate Scale Quantum (NISQ) computers has sparked interest in their use for simulating quantum systems. The research aims to simulate convex mixtures of single qubit Pauli channels on NISQ devices, focusing on Markovian and non-Markovian dynamics.

What is Quantum Simulation and Why is it Important?

Quantum simulation is the process of using quantum computers to simulate quantum systems. This is a significant area of research due to the computational challenges associated with simulating large, complex quantum systems on classical computers. The computational resources required for these simulations scale exponentially with the number of quantum particles, making them quickly intractable. However, quantum computers scale only polynomially with the number of quantum particles, making them a more efficient tool for these simulations.

Since the discovery of this advantage, quantum simulation has become one of the main motivations for developing quantum computers. Researchers have developed many algorithms to simulate quantum systems using quantum computers. However, these algorithms are best suited for fault-tolerant settings, where quantum computers provide a clear advantage over classical computers in the simulation of quantum systems.

Despite advancements in quantum hardware, much more work needs to be done to reach fault-tolerant settings. This, coupled with the growing accessibility of Noisy Intermediate Scale Quantum (NISQ) computers through cloud platforms such as the IBM Quantum Experience (IBM QE), has inspired interest in the use of NISQ devices for simulating quantum systems.

What are the Challenges and Opportunities with NISQ Devices?

In the NISQ settings, simulations are restricted by the size of the systems, various error rates, and noise sources. Despite these limitations, even currently available quantum computers provide versatile testbeds for various theories in quantum physics.

A majority of recent work has been devoted to the simulation of closed quantum systems in the NISQ era. However, there has been less work done in the simulation of open quantum systems in the NISQ era. Open quantum systems are systems that are allowed to interact with their environment, and to simulate them, we need to be able to simulate their evolution on a quantum computer.

How are Open Quantum Systems Simulated?

A master equation describes the dynamics of an open quantum system. The solution of this master equation is a dynamical map, also known as a quantum channel, which describes the evolution of an open quantum system. Under certain assumptions such as the Born-Markov approximation, the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) form of the master equation can be derived.

The GKSL form of the master equation describes Markovian dynamics, where all memory effects are neglected. Non-Markovian dynamics differ from Markovian dynamics in that it allows information to flow back into the system from the environment and does not neglect memory effects.

What is the Significance of Non-Markovian Dynamics?

There has been much interest in the study of the non-Markovian dynamics of an open quantum system. There are many different descriptions of non-Markovianity, however, in this work, the researchers make use of CP divisibility to characterize a channel as Markovian or non-Markovian.

The study of non-Markovianity in quantum physics is a highly nontrivial problem. However, understanding these dynamics is crucial for the accurate simulation of open quantum systems, particularly in the context of NISQ devices.

What is the Goal of this Research?

The goal of this research is to solve the more complicated problem of simulating convex mixtures of single qubit Pauli channels on NISQ devices. The researchers consider two specific cases: mixtures of Markovian channels that result in a non-Markovian channel (MMnM) and mixtures of non-Markovian channels that result in a Markovian channel (nMnMM).

The researchers show that efficient circuits which account for the topology of currently available devices and current levels of decoherence can be constructed by heuristic approaches that reduce the number of CNOT gates used in the circuit. They also present a strategy for regularizing the process matrix so that the process tomography yields a completely positive and trace-preserving (CPTP) channel.