Quantum stabilizer formalism for any composite system
- URL: http://arxiv.org/abs/2311.04255v4
- Date: Sun, 4 Aug 2024 11:33:02 GMT
- Title: Quantum stabilizer formalism for any composite system
- Abstract summary: We first introduce relevant background and necessary basic knowledge, then introduce the definition of quantum stabilizer and its application in quantum system evolution and measurement.
We try to extend the quantum stabilizer formalism to qubit-qutrit and qubit-ququart systems which not defined before, and further define quantum stabilizers of arbitrary composite systems.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: The quantum stabilizer formalism was originally introduced to describe quantum error correction codes more conveniently and now are also playing an important role in many other fields, e.g., quantum computing and quantum foundation. In this dissertation, we first introduce relevant background and necessary basic knowledge, then introduce the definition of quantum stabilizer and its application in quantum system evolution and measurement. Finally, we try to extend the quantum stabilizer formalism to qubit-qutrit and qubit-ququart systems which not defined before, and further define quantum stabilizers of arbitrary composite systems.
Related papers
- Complexity of quantum states in the stabilizer formalism [6.315323176162257]
We propose an information-theoretic quantifier for the complexity of quantum states within the stabilizer formalism of quantumvariable.<n>We establish the fundamental properties of this quantifier and demonstrate that state complexity is closely related to the nonstabilizerness of quantum states.
arXiv Detail & Related papers (2026-04-22T02:29:12Z) - Quantum Fisher Information With General Quantum Coherence in multi-dimensional quantum systems [8.494626739086195]
General Quantum Coherence (GQC) captures quantum nature of high-dimensional quantum states.<n>We observe a stringent square relationship between GQC and quantum Fisher information (QFI)
arXiv Detail & Related papers (2025-10-29T12:26:23Z) - Digital quantum simulation of many-body systems: Making the most of intermediate-scale, noisy quantum computers [51.56484100374058]
This thesis is centered around simulating quantum dynamics on quantum devices.<n>We present an overview of the most relevant quantum algorithms for quantum dynamics.<n>We identify relevant problems within quantum dynamics that could benefit from quantum simulation in the near future.
arXiv Detail & Related papers (2025-08-29T10:37:19Z) - Ergodic Theory of Inhomogeneous Quantum Processes [0.0]
This work presents a rigorous framework for understanding ergodicity and mixing in time-inhomogeneous quantum systems.<n>A key contribution is the development of a quantum Markov-Dobrushin approach to characterize mixing behavior.<n>Results contribute to the mathematical foundations of quantum dynamics and support the broader goal of advancing quantum information science.
arXiv Detail & Related papers (2025-06-14T00:04:59Z) - Quantum Homogenization as a Quantum Steady State Protocol on NISQ Hardware [42.52549987351643]
Quantum homogenization is a reservoir-based quantum state approximation protocol.
We extend the standard quantum homogenization protocol to the dynamically-equivalent ($mathttSWAP$)$alpha$ formulation.
We show that our proposed protocol yields a completely positive, trace preserving (CPTP) map under which the code subspace is correctable.
arXiv Detail & Related papers (2024-12-19T05:50:54Z) - Effect of the readout efficiency of quantum measurement on the system entanglement [44.99833362998488]
We quantify the entanglement for a particle on a 1d quantum random walk under inefficient monitoring.
We find that the system's maximal mean entanglement at the measurement-induced quantum-to-classical crossover is in different ways by the measurement strength and inefficiency.
arXiv Detail & Related papers (2024-02-29T18:10:05Z) - Construction of Antisymmetric Variational Quantum States with Real-Space
Representation [0.0]
A major difficulty in first quantization with a real-space basis is state preparation for many-body electronic systems.
We provide a design principle for constructing a variational quantum circuit to prepare an antisymmetric quantum state.
We implement the variational quantum eigensolver to obtain the ground state of a one-dimensional hydrogen molecular system.
arXiv Detail & Related papers (2023-06-14T11:11:31Z) - Unraveling the Mystery of Quantum Measurement with A New Space-Time Approach to Relativistic Quantum Mechanics [9.116661570248171]
Quantum measurement is a fundamental concept in the field of quantum mechanics.
Despite its significance, four fundamental issues continue to pose significant challenges to the broader application of quantum measurement.
We employ a new space-time approach to relativistic quantum mechanics to address these issues systematically.
arXiv Detail & Related papers (2023-06-01T13:25:08Z) - A vertical gate-defined double quantum dot in a strained germanium
double quantum well [48.7576911714538]
Gate-defined quantum dots in silicon-germanium heterostructures have become a compelling platform for quantum computation and simulation.
We demonstrate the operation of a gate-defined vertical double quantum dot in a strained germanium double quantum well.
We discuss challenges and opportunities and outline potential applications in quantum computing and quantum simulation.
arXiv Detail & Related papers (2023-05-23T13:42:36Z) - Quantum Semantic Communications for Resource-Efficient Quantum Networking [52.3355619190963]
This letter proposes a novel quantum semantic communications (QSC) framework exploiting advancements in quantum machine learning and quantum semantic representations.
The proposed framework achieves approximately 50-75% reduction in quantum communication resources needed, while achieving a higher quantum semantic fidelity.
arXiv Detail & Related papers (2022-05-05T03:49:19Z) - Efficient criteria of quantumness for a large system of qubits [58.720142291102135]
We discuss the dimensionless combinations of basic parameters of large, partially quantum coherent systems.
Based on analytical and numerical calculations, we suggest one such number for a system of qubits undergoing adiabatic evolution.
arXiv Detail & Related papers (2021-08-30T23:50:05Z) - Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator [41.74498230885008]
We demonstrate a programmable quantum simulator based on deterministically prepared two-dimensional arrays of neutral atoms.
We benchmark the system by creating and characterizing high-fidelity antiferromagnetically ordered states.
We then create and study several new quantum phases that arise from the interplay between interactions and coherent laser excitation.
arXiv Detail & Related papers (2020-12-22T19:00:04Z) - Direct Quantum Communications in the Presence of Realistic Noisy
Entanglement [69.25543534545538]
We propose a novel quantum communication scheme relying on realistic noisy pre-shared entanglement.
Our performance analysis shows that the proposed scheme offers competitive QBER, yield, and goodput.
arXiv Detail & Related papers (2020-12-22T13:06:12Z) - Quantum information spreading in a disordered quantum walk [50.591267188664666]
We design a quantum probing protocol using Quantum Walks to investigate the Quantum Information spreading pattern.
We focus on the coherent static and dynamic disorder to investigate anomalous and classical transport.
Our results show that a Quantum Walk can be considered as a readout device of information about defects and perturbations occurring in complex networks.
arXiv Detail & Related papers (2020-10-20T20:03:19Z) - Distribution of quantum coherence and quantum phase transition in the
Ising system [2.318473106845779]
Quantifying quantum coherence of a given system plays an important role in quantum information science.
We propose an analysis on the critical behavior of two types Ising systems when distribution of quantum coherence.
arXiv Detail & Related papers (2020-01-29T07:28:04Z) - Detecting dynamical quantum phase transition via out-of-time-order
correlations in a solid-state quantum simulator [12.059058714600607]
We develop and experimentally demonstrate that out-of-time-order correlators can be used to detect nonoequilibrium phase transitions in the transverse field Ising model.
Further applications of this protocol could enable studies other of exotic phenomena such as many body localization, and tests of the holographic duality between quantum and gravitational systems.
arXiv Detail & Related papers (2020-01-17T14:28:42Z)
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.