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ZX-calculus
Canada
เข้าร่วมเมื่อ 18 ก.พ. 2021
Presentations recorded at the weekly ZX-meetings
A SAT Scalpel for Lattice Surgery: Representation and Synthesis of Subroutines for Surface-Code FTQC
Speaker: Daniel Bochen Tan (Harvard University)
arXiv: arxiv.org/pdf/2404.18369
Abstract: Quantum error correction is necessary for largescale quantum computing. A promising quantum error correcting code is the surface code. For this code, fault-tolerant quantum computing (FTQC) can be performed via lattice surgery, i.e., splitting and merging patches of code. Given the frequent use of certain lattice-surgery subroutines (LaS), it becomes crucial to optimize their design in order to minimize the overall spacetime volume of FTQC. In this study, we define the variables to represent LaS and the constraints on these variables. Leveraging this formulation, we develop a synthesizer for LaS, LaSsynth, that encodes a LaS construction problem into a SAT instance, subsequently querying SAT solvers for a solution. Starting from a baseline design, we can gradually invoke the solver with shrinking spacetime volume to derive more compact designs. Due to our foundational formulation and the use of SAT solvers, LaSsynth can exhaustively explore the design space, yielding optimal designs in volume. For example, it achieves 8% and 18% volume reduction respectively over two states-of-the-art human designs for the 15-to-1 T-factory, a bottleneck in FTQC.
Joint-Work With: Murphy Yuezhen Niu and Craig Gidney
Presented at the ZX-calculus seminar on the 16th of December 2024.
arXiv: arxiv.org/pdf/2404.18369
Abstract: Quantum error correction is necessary for largescale quantum computing. A promising quantum error correcting code is the surface code. For this code, fault-tolerant quantum computing (FTQC) can be performed via lattice surgery, i.e., splitting and merging patches of code. Given the frequent use of certain lattice-surgery subroutines (LaS), it becomes crucial to optimize their design in order to minimize the overall spacetime volume of FTQC. In this study, we define the variables to represent LaS and the constraints on these variables. Leveraging this formulation, we develop a synthesizer for LaS, LaSsynth, that encodes a LaS construction problem into a SAT instance, subsequently querying SAT solvers for a solution. Starting from a baseline design, we can gradually invoke the solver with shrinking spacetime volume to derive more compact designs. Due to our foundational formulation and the use of SAT solvers, LaSsynth can exhaustively explore the design space, yielding optimal designs in volume. For example, it achieves 8% and 18% volume reduction respectively over two states-of-the-art human designs for the 15-to-1 T-factory, a bottleneck in FTQC.
Joint-Work With: Murphy Yuezhen Niu and Craig Gidney
Presented at the ZX-calculus seminar on the 16th of December 2024.
มุมมอง: 71
วีดีโอ
The Galois-Qudit ZH Calculus and Quantum Reed-Solomon Codes - Dichuan (David) Gao
มุมมอง 90วันที่ผ่านมา
arXiv: arxiv.org/pdf/2406.02219 Abstract: We propose a generalization of the graphical ZH calculus to qudits of prime-power dimensions, implementing Galois field arithmetic over its computational basis. This is an extension of a previous result by Roy et.al. which implemented arithmetic of prime-sized fields; and an alternative to a result by de Beaudrap and East which extended the ZH to implem...
Scalable Spider Nests (How to Graphically Grok Transversal Non-Clifford Gates) - Aleks Kissinger
มุมมอง 7314 วันที่ผ่านมา
arXiv: arxiv.org/pdf/2404.07828 Abstract: This is the second in a series of "graphical grokking" papers in which we study how stabiliser codes can be understood using the ZX-calculus. In this paper we show that certain complex rules involving ZX-diagrams, called spider nest identities, can be captured succinctly using the scalable ZX-calculus, and all such identities can be proved inductively f...
The Focked-up ZX Calculus: Picturing Continuous-Variable Quantum Computation - Razin A. Shaikh
มุมมอง 13128 วันที่ผ่านมา
arXiv: arxiv.org/pdf/2406.02905 Abstract: While the ZX and ZW calculi have been effective as graphical reasoning tools for finite-dimensional quantum computation, the possibilities for continuous-variable quantum computation (CVQC) in infinite-dimensional Hilbert space are only beginning to be explored. In this work, we formulate a graphical language for CVQC. Each diagram is an undirected grap...
The XYZ Ruby Code: Julio C. Magdalena de la Fuente and Josias Old
มุมมอง 115หลายเดือนก่อน
Making a Case for a Three-Colored Graphical Calculus for Quantum Error Correction in Spacetime arXiv: arxiv.org/pdf/2407.08566 Abstract: Analyzing and developing new quantum error-correcting schemes is one of the most prominent tasks in quantum computing research. In such efforts, introducing time dynamics explicitly in both analysis and design of error-correcting protocols constitutes an impor...
Towards Faster Quantum Circuit Simulation via Graph Decompositions, GNNs and Reinforcement Learning
มุมมอง 122หลายเดือนก่อน
Speaker: Alexander Koziell-Pipe Paper: openreview.net/pdf?id=54060pbCKY Abstract: In this work, we train a graph neural network with reinforcement learning to more efficiently simulate quantum circuits using the ZX-calculus. Our experiments show a marked improvement in simulation efficiency using the trained model over existing methods that do not incorporate AI. In this way, we demonstrate a m...
Catalysing Completeness and Universality - John van de Wetering
มุมมอง 84หลายเดือนก่อน
arXiv: arxiv.org/pdf/2404.09915 Abstract: A catalysis state is a quantum state that is used to make some desired operation possible or more efficient, while not being consumed in the process. Recent years have seen catalysis used in state-of-the-art protocols for implementing magic state distillation or small angle phase rotations. In this paper we will see that we can also use catalysis to pro...
Quantum Picturalism: Learning Quantum Theory in High School - Lia Yeh
มุมมอง 232หลายเดือนก่อน
arXiv: arxiv.org/pdf/2312.03653 Abstract: Quantum theory is often regarded as challenging to learn and teach, with advanced mathematical prerequisites ranging from complex numbers and probability theory to matrix multiplication, vector space algebra and symbolic manipulation within the Hilbert space formalism. It is traditionally considered an advanced undergraduate or graduate-level subject. I...
Qubit-Count Optimization Using ZX-Calculus - Vivien Vandaele
มุมมอง 1672 หลายเดือนก่อน
arXiv: arxiv.org/pdf/2407.10171 Abstract: We propose several methods for optimizing the number of qubits in a quantum circuit while preserving the number of non-Clifford gates. One of our approaches consists in reversing, as much as possible, the gadgetization of Hadamard gates, which is a procedure used by some T-count optimizers to circumvent Hadamard gates at the expense of additional qubits...
Minimal Complete ZW-Calculi for Qudit and Mixed Dimensional Systems - Renaud Vilmart
มุมมอง 862 หลายเดือนก่อน
arXiv: arxiv.org/pdf/2401.16225 Abstract: The ZW-calculus is a graphical language capable of representing 2-dimensional quantum systems (qubit) through its diagrams, and manipulating them through its equational theory. We extend the formalism to accommodate finite dimensional Hilbert spaces beyond qubit systems. First we define a qudit version of the language, where all systems have the same ar...
Genons, Double Covers and Fault-tolerant Clifford Gates - Simon Burton
มุมมอง 992 หลายเดือนก่อน
arXiv: arxiv.org/pdf/2406.09951 Abstract: A great deal of work has been done developing quantum codes with varying overhead and connectivity constraints. However, given the such an abundance of codes, there is a surprising shortage of fault-tolerant logical gates supported therein. We define a construction, such that given an input [[n,k,d]] code, yields a [[2n,2k,≥d]] symplectic double code wi...
Redefining Lexicographical Ordering: Optimizing Pauli String Decompositions for Quantum Compiling
มุมมอง 1382 หลายเดือนก่อน
Speaker: Qunsheng Huang (Technical University of Munich) arXiv: arxiv.org/pdf/2408.00354 Abstract: In quantum computing, the efficient optimization of Pauli string decompositions is a crucial aspect for the compilation of quantum circuits for many applications, such as chemistry simulations and quantum machine learning. In this paper, we propose a novel algorithm for the synthesis of trotterize...
ZX and Measurement-Based Quantum Computing
มุมมอง 1922 หลายเดือนก่อน
Speaker: Miriam Backens Slides: drive.google.com/file/d/1D1JhKOH2Cq01D7j1JVrQSAFS7MZ7F90p/view
ZX and Machine Learning
มุมมอง 2472 หลายเดือนก่อน
Speakers: Matthew Sutcliffe and Richie Yeung Slides: drive.google.com/file/d/1d1lxihKutoN8zztdHrFluJb07iq3DdGV/view
Measurement-Based Quantum Approximate Optimization - Tobias Stollenwerk
มุมมอง 1195 หลายเดือนก่อน
Measurement-Based Quantum Approximate Optimization - Tobias Stollenwerk
Constructing NP^{#P}-Complete Problems and #P-Hardness of Circuit Extraction in Phase-Free ZH
มุมมอง 825 หลายเดือนก่อน
Constructing NP^{#P}-Complete Problems and #P-Hardness of Circuit Extraction in Phase-Free ZH
Nonunitary Gates Using Measurements Only - Daniel Azses
มุมมอง 2196 หลายเดือนก่อน
Nonunitary Gates Using Measurements Only - Daniel Azses
Complete Graphical Language for Linear Optical Circuits with Finite-Photon-Number Sources&Detectors
มุมมอง 956 หลายเดือนก่อน
Complete Graphical Language for Linear Optical Circuits with Finite-Photon-Number Sources&Detectors
Multi-Controlled Phase Gate Synthesis with ZX-Calculus Applied to Neutral Atom Hardware
มุมมอง 1666 หลายเดือนก่อน
Multi-Controlled Phase Gate Synthesis with ZX-Calculus Applied to Neutral Atom Hardware
All Graph State Verification Protocols are Composably Secure - Léo Colisson
มุมมอง 896 หลายเดือนก่อน
All Graph State Verification Protocols are Composably Secure - Léo Colisson
Speeding Up Classical Simulation of Quantum Circuits with the ZX calculus - Matthew Sutcliffe
มุมมอง 2707 หลายเดือนก่อน
Speeding Up Classical Simulation of Quantum Circuits with the ZX calculus - Matthew Sutcliffe
Zero-Temperature Entanglement Membranes in Quantum Circuits - Grace M. Sommers
มุมมอง 1257 หลายเดือนก่อน
Zero-Temperature Entanglement Membranes in Quantum Circuits - Grace M. Sommers
Complete Equational Theories for Classical and Quantum Gaussian Relations - Robert Booth
มุมมอง 1557 หลายเดือนก่อน
Complete Equational Theories for Classical and Quantum Gaussian Relations - Robert Booth
Optimising T-Count is NP-Hard, but Optimising Parametrised Circuits is Easy - John van de Wetering
มุมมอง 1127 หลายเดือนก่อน
Optimising T-Count is NP-Hard, but Optimising Parametrised Circuits is Easy - John van de Wetering
Minimal Equational Theories for Quantum Circuits - Alexandre Clément
มุมมอง 788 หลายเดือนก่อน
Minimal Equational Theories for Quantum Circuits - Alexandre Clément
Teaching Small Transformers to Rewrite ZX Diagrams - Richie Yeung
มุมมอง 1349 หลายเดือนก่อน
Teaching Small Transformers to Rewrite ZX Diagrams - Richie Yeung
Really nice talk Daniel! Great work!
damn... I kinda think as a species we should have just like checked out man. we're doing too much. fuck your academic curiosity come join the rest of us on the grass staring at the sky
Best channel talk in this field my question can i apply all this in financial market
❤❤❤ thanks all of you
Merci contenues with this videos about real quant world pls how can i apply this in financial market
Harris Cynthia White Patricia Martin Sarah
Pls put more videos im waiting ❤❤ and pls can you do video about kan4tsf model pllllls
Syntax is dual to semantics -- languages, communication. If mathematics is a language then it is dual. "Always two there are" -- Yoda.
Thanks.
Thanks. 😊
Promo_SM
Wow. Today was the first day of my PhD on Quantum Generative AI. I learned ZXC from Stefano this summer, it was a heavy focus on my proposal. Opening TH-cam before bed and this being the first thing I saw is melting my mind. Thank you so much for sharing and the work you all are doing.
in the illustration at 12m14s showing the logical qubits they each have the same height / number of planes of connection betweern top and bottom. is this a necessary condition? i ask only because there might be some benefits to being able to exploit this property in ZX diagrams of reinterpreting wires as qubits to more computational effect if the logical qubits move about a circuit periodically and you have multiple distinct periods, so that over time you are able to measure states effectivel in a product of the periods.
Brilliant presentation. Got me interested in checking out ZX calculus. Found myself here because I'm working on spin networks.
"promosm"