Quantum Shift Register Circuits Mark M. Wilde arXiv:0903.3894 National Institute of Standards and Technology, Wednesday, June 10, 2009 To appear in Physical.

Slides:



Advertisements
Similar presentations
Entanglement Boosts Quantum Turbo Codes Mark M. Wilde School of Computer Science McGill University Seminar for the Quantum Computing Group at McGill Montreal,
Advertisements

Generating Random Stabilizer States in Matrix Multiplication Time: A Theorem in Search of an Application Scott Aaronson David Chen.
Quantum Computation and Quantum Information – Lecture 2
Quantum Circuit Decomposition
University of Queensland
Quantum Walks, Quantum Gates, and Quantum Computers Andrew Hines P.C.E. Stamp [Palm Beach, Gold Coast, Australia]
Logic Circuits Design presented by Amr Al-Awamry
Register Transfer Level
Types of Logic Circuits
Quantum Computing MAS 725 Hartmut Klauck NTU
Give qualifications of instructors: DAP
CS 151 Digital Systems Design Lecture 37 Register Transfer Level
Quantum Phase Estimation using Multivalued Logic.
EEE377 Lecture Notes1 EEE436 DIGITAL COMMUNICATION Coding En. Mohd Nazri Mahmud MPhil (Cambridge, UK) BEng (Essex, UK) Room 2.14.
An Arbitrary Two-qubit Computation in 23 Elementary Gates or Less Stephen S. Bullock and Igor L. Markov University of Michigan Departments of Mathematics.
BIST AND DATA COMPRESSION 1 JTAG COURSE spring 2006 Andrei Otcheretianski.
Quantum Counters Smita Krishnaswamy Igor L. Markov John P. Hayes.
Introduction to Quantum logic (2) Yong-woo Choi.
Quantum Computation and Quantum Information – Lecture 2 Part 1 of CS406 – Research Directions in Computing Dr. Rajagopal Nagarajan Assistant: Nick Papanikolaou.
ROM-based computations: quantum versus classical B.C. Travaglione, M.A.Nielsen, H.M. Wiseman, and A. Ambainis.
Quantum Convolutional Coding with Entanglement Assistance Mark M. Wilde Communication Sciences Institute, Ming Hsieh Department of Electrical Engineering,
Quantum Communication, Quantum Entanglement and All That Jazz Mark M. Wilde Communication Sciences Institute, Ming Hsieh Department of Electrical Engineering,
Quantum Algorithms for Neural Networks Daniel Shumow.
Alice and Bob’s Excellent Adventure
Outline Main result Quantum computation and quantum circuits Feynman’s sum over paths Polynomials QuPol program “Quantum Polynomials” Quantum polynomials.
1 Channel Coding (II) Cyclic Codes and Convolutional Codes.
Quantum Convolutional Coding for Distillation and Error Correction Mark M. Wilde Communication Sciences Institute, Ming Hsieh Department of Electrical.
1 hardware of quantum computer 1. quantum registers 2. quantum gates.
QUANTUM COMPUTING What is it ? Jean V. Bellissard Georgia Institute of Technology & Institut Universitaire de France.
Quantum Coding with Entanglement Mark M. Wilde Communication Sciences Institute, Ming Hsieh Department of Electrical Engineering, University of Southern.
Quantum Convolutional Coding Techniques Mark M. Wilde Communication Sciences Institute, Ming Hsieh Department of Electrical Engineering, University of.
Quantum Computing: An Overview for non-specialists Mikio Nakahara Department of Physics & Research Centre for Quantum Computing Kinki University, Japan.
Quantum Computing & Algorithms
IPQI-2010-Anu Venugopalan 1 qubits, quantum registers and gates Anu Venugopalan Guru Gobind Singh Indraprastha Univeristy Delhi _______________________________________________.
An Introduction to Quantum Computation Sandy Irani Department of Computer Science University of California, Irvine.
Logic Design (CE1111 ) Lecture 6 (Chapter 6) Registers &Counters Prepared by Dr. Lamiaa Elshenawy 1.
1 Convolutional Codes An (n,k,m) convolutional encoder will encode a k bit input block into an n-bit ouput block, which depends on the current input block.
1 An Introduction to Quantum Computing Sabeen Faridi Ph 70 October 23, 2007.
Lecture 1 Gunjeet kaur Dronacharya group of institutions.
Appendix C Basics of Logic Design. Appendix C — Logic Basic — 2 Logic Design Basics §4.2 Logic Design Conventions Objective: To understand how to build.
Quantum gates SALEEL AHAMMAD SALEEL. Introduction.
DIGITAL SYTEM DESIGN MINI PROJECT CONVOLUTION CODES
QUANTUM COMPUTING: Quantum computing is an attempt to unite Quantum mechanics and information science together to achieve next generation computation.
EKT 221 : Digital 2 Serial Transfers & Microoperations
Complexity-Theoretic Foundations of Quantum Supremacy Experiments
ELECTRONICS AND COMMUNICATION ENGINEERING
Introduction to Quantum Computing Lecture 1 of 2
EKT 221 : Digital 2 Serial Transfers & Microoperations
Seoul National University
MATH2999 Directed Studies in Mathematics Quantum Process on One Qubit System Name: Au Tung Kin UID:
Morgan Kaufmann Publishers The Processor
Morgan Kaufmann Publishers
Overview Instruction Codes Computer Registers Computer Instructions
Quantum Teleportation
Subject Name: Information Theory Coding Subject Code: 10EC55
Quantum Computing Dorca Lee.
Chap 4 Quantum Circuits: p
Introduction to Quantum logic (2)
OSU Quantum Information Seminar
DESIGN OF SEQUENTIAL CIRCUITS
Grover. Part 2 Anuj Dawar.
Quantum Computing: the Majorana Fermion Solution
“Definition” of Combinational
Quantum computation with classical bits
Improving Quantum Circuit Dependability
Quantum Computing Prabhas Chongstitvatana Faculty of Engineering
Quantum Computation – towards quantum circuits and algorithms
Outline Registers Counters 5/11/2019.
Quantum Computing Joseph Stelmach.
Presentation transcript:

Quantum Shift Register Circuits Mark M. Wilde arXiv: National Institute of Standards and Technology, Wednesday, June 10, 2009 To appear in Physical Review A (from a company in Northern Virginia)

Classical Shift Register Circuits Overview Examples with Classical CNOT gate Quantum Shift Register Circuits “Memory Consumption” Theorem Future Work

Shift Registers and Convolutional Coding techniques have application in cellulardeep space communication and Viterbi Algorithm is most popular technique for determining errors Applications of Shift Registers

Classical Shift Registers Store input stream sequentially Compute output streams from memory bits (D represents “delay”)

Mathematical Representation Input stream is a binary sequence Output stream is a binary sequence Convolve input stream with system function to get output stream: Can also represent input stream as a polynomial And same for output stream Multiply input with system function to get output polynomial:

Classical Shift Register Example Input : Input Polynomial: 1 Output : Output Polynomial : 1 + D

Another Example Input : Input Polynomial: 1 Output : Output Polynomial : D / (1 + D)

What is a quantum shift register? A quantum shift register circuit acts on a set of input qubits and memory qubits, outputs a set of output qubits and updated memory qubits, and feeds the memory back into the device for the next cycle (similar to the operation of a classical shift register).

Quantum Circuit Depiction

Lattice Depiction

Brief Intro to Stabilizer Formalism Unencoded StabilizerEncoded Stabilizer Laflamme et al., Physical Review Letters 77, (1996).

Binary Vector Representation

CNOT Gate Pauli Operator Transformation Binary Vector Transformation

CNOT gate with Memory How to describe input, output, and memory?

Recursive Equations

D-Transform Input Vector Output Vector Transformation

CNOT gate with more memory Transformation

Combo Shift Register Circuits Is it possible to simplify?

Simplified Shift Register Circuit “Commute last gate through memory”

Example of a Code Check matrix of a CSS quantum convolutional code Use Grassl-Roetteler algorithm to decompose as CNOT(3,2)(1+1/D) CNOT(1,2)(D) CNOT(1,3)(1+D)

Quantum Shift Register Circuit

“CSS Shift Register Memory” Theorem Given a description of a quantum convolutional code, how large of a quantum memory do we need to implement? Proof uses induction and exhaustively considers all the ways that CNOT gates can combine

General Shift Register Circuit General technique applies to arbitrary quantum convolutional codes

Experimental Implementations? Optical lattices of neutral atoms Linear-optical circuits Spin chains for state transfer

Current Directions Extend Memory Consumption Theorem to arbitrary quantum convolutional codes Study the Entanglement Structure of states that are input to a quantum shift register circuit ( Area Laws should apply here) THANK YOU!