Digital Simulation of Single Qubit Markovian Open Quantum Systems: A Tutorial
arXiv:2302.02953 · doi:10.12743/quanta.v12i1.226
Abstract
One of the first proposals for the use of quantum computers was the simulation of quantum systems. Over the past three decades, great strides have been made in the development of algorithms for simulating closed quantum systems and the more complex open quantum systems. In this tutorial, we introduce the methods used in the simulation of single qubit Markovian open quantum systems. It combines various existing notations into a common framework that can be extended to more complex open system simulation problems. The only currently available algorithm for the digital simulation of single qubit open quantum systems is discussed in detail. A modification to the implementation of the simpler channels is made that removes the need for classical random sampling, thus making the modified algorithm a strictly quantum algorithm. The modified algorithm makes use of quantum forking to implement the simpler channels that approximate the total channel. This circumvents the need for quantum circuits with a large number of C-NOT gates.
arXiv comment39 pages, 12 figures; formatting updated; minor corrections
References in corpus (17)
- Elementary gates for quantum computation
- Quantum Simulation
- Simulating Hamiltonian dynamics with a truncated Taylor series
- Toward the first quantum simulation with quantum speedup
- Hamiltonian simulation with nearly optimal dependence on all parameters
- A random compiler for fast Hamiltonian simulation
- Digital quantum simulation of open quantum systems using quantum imaginary time evolution
- Hamiltonian Simulation Using Linear Combinations of Unitary Operations
- Time-dependent Hamiltonian simulation with -norm scaling
- Universal simulation of Markovian quantum dynamics
- Universal simulation of Markovian open quantum systems
- Digital quantum simulation of many-body non-Markovian dynamics
- Two-Unitary Decomposition Algorithm and Open Quantum System Simulation
- Some Open Problems in Quantum Information Theory
- Simulation of single-qubit open quantum systems
- Efficient Quantum Algorithms for Simulating Lindblad Evolution
- Some Open Problems in Quantum Information Theory