On the effect of quantum interaction distance on quantum addition circuits

Byung Soo Choi, Rodney D Van Meter

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

We investigate the theoretical limits of the effect of the quantum interaction distance on the speed of exact quantum addition circuits. For this study, we exploit graph embedding for quantum circuit analysis. We study a logical mapping of qubits and gates of any Ω(log n)-depth quantum adder circuit for two n-qubit registers onto a practical architecture, which limits interaction distance to the nearest neighbors only and supports only one-and two-qubit logical gates. Unfortunately, on the chosen k-dimensional practical architecture, we prove that the depth lower bound of any exact quantum addition circuits is no longer Ω(log n), but Ω(i√n). This result, the first application of graph embedding to quantum circuits and devices, provides a new tool for compiler development, emphasizes the impact of quantum computer architecture on performance, and acts as a cautionary note when evaluating the time performance of quantum algorithms.

Original languageEnglish
Article number11
JournalACM Journal on Emerging Technologies in Computing Systems
Volume7
Issue number3
DOIs
Publication statusPublished - 2011 Aug

Fingerprint

Networks (circuits)
Quantum computers
Computer architecture
Adders
Electric network analysis

Keywords

  • Depth lower bound
  • Graph embedding
  • Interaction distance
  • Quantum adder
  • Quantum architecture

ASJC Scopus subject areas

  • Hardware and Architecture
  • Software
  • Electrical and Electronic Engineering

Cite this

On the effect of quantum interaction distance on quantum addition circuits. / Choi, Byung Soo; Van Meter, Rodney D.

In: ACM Journal on Emerging Technologies in Computing Systems, Vol. 7, No. 3, 11, 08.2011.

Research output: Contribution to journalArticle

@article{e725c64472144171aa765c8d33397b5e,
title = "On the effect of quantum interaction distance on quantum addition circuits",
abstract = "We investigate the theoretical limits of the effect of the quantum interaction distance on the speed of exact quantum addition circuits. For this study, we exploit graph embedding for quantum circuit analysis. We study a logical mapping of qubits and gates of any Ω(log n)-depth quantum adder circuit for two n-qubit registers onto a practical architecture, which limits interaction distance to the nearest neighbors only and supports only one-and two-qubit logical gates. Unfortunately, on the chosen k-dimensional practical architecture, we prove that the depth lower bound of any exact quantum addition circuits is no longer Ω(log n), but Ω(i√n). This result, the first application of graph embedding to quantum circuits and devices, provides a new tool for compiler development, emphasizes the impact of quantum computer architecture on performance, and acts as a cautionary note when evaluating the time performance of quantum algorithms.",
keywords = "Depth lower bound, Graph embedding, Interaction distance, Quantum adder, Quantum architecture",
author = "Choi, {Byung Soo} and {Van Meter}, {Rodney D}",
year = "2011",
month = "8",
doi = "10.1145/2000502.2000504",
language = "English",
volume = "7",
journal = "ACM Journal on Emerging Technologies in Computing Systems",
issn = "1550-4832",
publisher = "Association for Computing Machinery (ACM)",
number = "3",

}

TY - JOUR

T1 - On the effect of quantum interaction distance on quantum addition circuits

AU - Choi, Byung Soo

AU - Van Meter, Rodney D

PY - 2011/8

Y1 - 2011/8

N2 - We investigate the theoretical limits of the effect of the quantum interaction distance on the speed of exact quantum addition circuits. For this study, we exploit graph embedding for quantum circuit analysis. We study a logical mapping of qubits and gates of any Ω(log n)-depth quantum adder circuit for two n-qubit registers onto a practical architecture, which limits interaction distance to the nearest neighbors only and supports only one-and two-qubit logical gates. Unfortunately, on the chosen k-dimensional practical architecture, we prove that the depth lower bound of any exact quantum addition circuits is no longer Ω(log n), but Ω(i√n). This result, the first application of graph embedding to quantum circuits and devices, provides a new tool for compiler development, emphasizes the impact of quantum computer architecture on performance, and acts as a cautionary note when evaluating the time performance of quantum algorithms.

AB - We investigate the theoretical limits of the effect of the quantum interaction distance on the speed of exact quantum addition circuits. For this study, we exploit graph embedding for quantum circuit analysis. We study a logical mapping of qubits and gates of any Ω(log n)-depth quantum adder circuit for two n-qubit registers onto a practical architecture, which limits interaction distance to the nearest neighbors only and supports only one-and two-qubit logical gates. Unfortunately, on the chosen k-dimensional practical architecture, we prove that the depth lower bound of any exact quantum addition circuits is no longer Ω(log n), but Ω(i√n). This result, the first application of graph embedding to quantum circuits and devices, provides a new tool for compiler development, emphasizes the impact of quantum computer architecture on performance, and acts as a cautionary note when evaluating the time performance of quantum algorithms.

KW - Depth lower bound

KW - Graph embedding

KW - Interaction distance

KW - Quantum adder

KW - Quantum architecture

UR - http://www.scopus.com/inward/record.url?scp=80052003690&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052003690&partnerID=8YFLogxK

U2 - 10.1145/2000502.2000504

DO - 10.1145/2000502.2000504

M3 - Article

VL - 7

JO - ACM Journal on Emerging Technologies in Computing Systems

JF - ACM Journal on Emerging Technologies in Computing Systems

SN - 1550-4832

IS - 3

M1 - 11

ER -