Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Torsion in Vector Calculus

Torsion in Vector Calculus

A toy train ascending a winding track that curves and tilts offers an intuitive view of torsion, a key geometric concept in the study of space curves. While curvature measures how sharply a path bends, torsion captures how the path twists out of the plane of bending. This twisting behavior is crucial in understanding three-dimensional motion and is precisely described using the Frenet–Serret framework.At each point along a space curve, the Frenet–Serret frame consists of three orthogonal unit...

Cartesian Form for Vector Formulation

Cartesian Form for Vector Formulation

The Cartesian form for vector formulation is a process to calculate the moment of force using the position and force vectors. The moment of force is defined as the cross-product of these vectors, making it a vector quantity. The Cartesian form of the position and force vectors involves unit vectors, which can be used to express the cross-product in determinant form.

Cartesian Vector Notation

Cartesian Vector Notation

Cartesian vector notation is a valuable tool in mechanical engineering for representing vectors in three-dimensional space, performing vector operations such as determining the gradient, divergence, and curl, and expressing physical quantities such as the displacement, velocity, acceleration, and force. By using Cartesian vector notation, engineers can more easily analyze and solve problems in various areas of mechanical engineering, including dynamics, kinematics, and fluid mechanics. This...

Vector Algebra: Method of Components

Vector Algebra: Method of Components

It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...

Couples: Scalar and Vector Formulation

Couples: Scalar and Vector Formulation

One might wonder how the captain of a large ship can navigate through the ocean with just a turn of the steering wheel. The answer lies in the concept of two parallel forces that are equal in magnitude and opposite sense, creating a couple moment.
A couple moment is a rotational force that tends to rotate the steering wheel. The wheel's rotation can either be in a clockwise or anticlockwise direction. The right-hand rule is a helpful method for determining the direction of a couple moment. To...

Curl and Divergence of Vector Fields

Curl and Divergence of Vector Fields

Curl and divergence describe two fundamental ways a vector field can behave. A vector field assigns both magnitude and direction to each point in space, such as the velocity of water flowing in a river. Leaves floating on the surface may reveal regions where the water swirls and other regions where it spreads outward or gathers inward. These motions correspond to curl and divergence.Curl measures the tendency of a vector field to rotate around a point. If leaves circle around a small whirlpool,...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Accurate Image Multi-Class Classification Neural Network Model with Quantum Entanglement Approach.

Sensors (Basel, Switzerland)·2023

See all related articles

Search research articles

Related Experiment Video

Updated: Jul 7, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Topological approaches to quantum tensor train compression via ZX-calculus and SVD.

Luis Gerardo Ayala Bertel¹, Srinjoy Ganguly²

¹Department of Mathematics, Faculty of Exact and Natural Sciences, University of Cartagena, Cartagena de Indias, Bolivar, Colombia. layalab@unicartagena.edu.co.

Scientific Reports

|July 5, 2026

Summary

This study introduces a hybrid tensor network compression method combining ZX-Calculus and SVD. This approach algebraically reduces complexity, offering significant computational speedups for symmetric systems.

Keywords:

Matrix product states (MPS)Quantics tensor trains (QTT)Quantum-inspired algorithms Singular value decomposition (SVD)Topological compression ZX-calculus

More Related Videos

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Related Experiment Videos

Last Updated: Jul 7, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Area of Science:

Quantum computing
High-dimensional linear algebra
Tensor network algorithms

Background:

Quantum-inspired algorithms like Quantics Tensor Trains (QTT) efficiently handle large vectors using Matrix Product States (MPS).
Tensor network compression traditionally relies on Singular Value Decomposition (SVD), which is numerically optimal but ignores exact algebraic structures.

Purpose of the Study:

To develop a hybrid compression protocol integrating ZX-Calculus with SVD for tensor networks.
To leverage algebraic correlations and symmetries for more efficient tensor network compression.

Main Methods:

Constructing an isomorphism between Rank-3 MPS tensors and ZX-diagrams.
Applying ZX-Calculus diagrammatic rewriting rules for topological preconditioning before SVD truncation.
Benchmarking against hardware-accelerated SVD on discretized functions and stabilizer states.

Main Results:

Topological Preconditioning algebraically collapses bond dimension (χ) and T-count without information loss.
ZX-driven algebraic erasure bypasses standard computational bottlenecks, achieving significant speedups.
Formalization of a structural complexity class [Formula: see text] for symmetric systems.

Conclusions:

The hybrid ZX-Calculus and SVD approach offers a powerful method for optimizing high-dimensional linear algebra.
This work advances the understanding of Categorical Quantum Mechanics and its applications in tensor network compression.
The proposed method provides a pathway to more efficient quantum-inspired algorithms by exploiting algebraic symmetries.