Digital Simulation of Single Qubit Markovian Open Quantum Systems: A
Tutorial
- URL: http://arxiv.org/abs/2302.02953v2
- Date: Wed, 26 Apr 2023 15:01:58 GMT
- Title: Digital Simulation of Single Qubit Markovian Open Quantum Systems: A
Tutorial
- Authors: I J David, I Sinayskiy and F Petruccione
- Abstract summary: We introduce the methods used in the simulation of single qubit Markovian open quantum systems.
The only currently available algorithm for the digital simulation of single qubit open quantum systems is discussed in detail.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
Related papers
- Parallel Quantum Computing Simulations via Quantum Accelerator Platform Virtualization [44.99833362998488]
We present a model for parallelizing simulation of quantum circuit executions.
The model can take advantage of its backend-agnostic features, enabling parallel quantum circuit execution over any target backend.
arXiv Detail & Related papers (2024-06-05T17:16:07Z) - Simulation of Open Quantum Systems via Low-Depth Convex Unitary
Evolutions [0.0]
We propose a hybrid quantum-classical approach for simulating a class of open system dynamics called random-unitary channels.
We implement simulations of open quantum systems up to dozens of qubits and with large channel rank.
arXiv Detail & Related papers (2023-07-26T17:44:35Z) - Adaptive variational simulation for open quantum systems [0.25602836891933073]
We present an adaptive variational quantum algorithm for simulating open quantum system dynamics.
Our results demonstrate that near-future quantum processors are capable of simulating open quantum systems.
arXiv Detail & Related papers (2023-05-11T16:00:13Z) - Entanglement and coherence in Bernstein-Vazirani algorithm [58.720142291102135]
Bernstein-Vazirani algorithm allows one to determine a bit string encoded into an oracle.
We analyze in detail the quantum resources in the Bernstein-Vazirani algorithm.
We show that in the absence of entanglement, the performance of the algorithm is directly related to the amount of quantum coherence in the initial state.
arXiv Detail & Related papers (2022-05-26T20:32:36Z) - An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian
Simulation [55.41644538483948]
Current generation noisy intermediate-scale quantum (NISQ) computers are severely limited in chip size and error rates.
We derive localized circuit transformations to efficiently compress quantum circuits for simulation of certain spin Hamiltonians known as free fermions.
The proposed numerical circuit compression algorithm behaves backward stable and scales cubically in the number of spins enabling circuit synthesis beyond $mathcalO(103)$ spins.
arXiv Detail & Related papers (2021-08-06T19:38:03Z) - Synthesis of Quantum Circuits with an Island Genetic Algorithm [44.99833362998488]
Given a unitary matrix that performs certain operation, obtaining the equivalent quantum circuit is a non-trivial task.
Three problems are explored: the coin for the quantum walker, the Toffoli gate and the Fredkin gate.
The algorithm proposed proved to be efficient in decomposition of quantum circuits, and as a generic approach, it is limited only by the available computational power.
arXiv Detail & Related papers (2021-06-06T13:15:25Z) - A Grand Unification of Quantum Algorithms [0.0]
A number of quantum algorithms were recently tied together by a technique known as the quantum singular value transformation.
This paper provides a tutorial through these developments, first illustrating how quantum signal processing may be generalized to the quantum eigenvalue transform.
We then employ QSVT to construct intuitive quantum algorithms for search, phase estimation, and Hamiltonian simulation.
arXiv Detail & Related papers (2021-05-06T17:46:33Z) - Fast-Forwarding with NISQ Processors without Feedback Loop [0.0]
We present the Classical Quantum Fast Forwarding (CQFF) as an alternative diagonalisation based algorithm for quantum simulation.
CQFF removes the need for a classical-quantum feedback loop and controlled multi-qubit unitaries.
Our work provides a $104$ improvement over the previous record.
arXiv Detail & Related papers (2021-04-05T14:29:33Z) - Quantum walk processes in quantum devices [55.41644538483948]
We study how to represent quantum walk on a graph as a quantum circuit.
Our approach paves way for the efficient implementation of quantum walks algorithms on quantum computers.
arXiv Detail & Related papers (2020-12-28T18:04:16Z) - Optimal quantum simulation of open quantum systems [1.9551668880584971]
Digital quantum simulation on quantum systems require algorithms that can be implemented using finite quantum resources.
Recent studies have demonstrated digital quantum simulation of open quantum systems on Noisy Intermediate-Scale Quantum (NISQ) devices.
We develop quantum circuits for optimal simulation of Markovian and Non-Markovian open quantum systems.
arXiv Detail & Related papers (2020-12-14T14:00:36Z) - Electronic structure with direct diagonalization on a D-Wave quantum
annealer [62.997667081978825]
This work implements the general Quantum Annealer Eigensolver (QAE) algorithm to solve the molecular electronic Hamiltonian eigenvalue-eigenvector problem on a D-Wave 2000Q quantum annealer.
We demonstrate the use of D-Wave hardware for obtaining ground and electronically excited states across a variety of small molecular systems.
arXiv Detail & Related papers (2020-09-02T22:46:47Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.