skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Ancilla-driven quantum computation for qudits and continuous variables

Abstract

Although qubits are the leading candidate for the basic elements in a quantum computer, there are also a range of reasons to consider using higher-dimensional qudits or quantum continuous variables (QCVs). In this paper, we use a general “quantum variable” formalism to propose a method of quantum computation in which ancillas are used to mediate gates on a well-isolated “quantum memory” register and which may be applied to the setting of qubits, qudits (for d>2), or QCVs. More specifically, we present a model in which universal quantum computation may be implemented on a register using only repeated applications of a single fixed two-body ancilla-register interaction gate, ancillas prepared in a single state, and local measurements of these ancillas. In order to maintain determinism in the computation, adaptive measurements via a classical feed forward of measurement outcomes are used, with the method similar to that in measurement-based quantum computation (MBQC). We show that our model has the same hybrid quantum-classical processing advantages as MBQC, including the power to implement any Clifford circuit in essentially one layer of quantum computation. In some physical settings, high-quality measurements of the ancillas may be highly challenging or not possible, and hence we also present amore » globally unitary model which replaces the need for measurements of the ancillas with the requirement for ancillas to be prepared in states from a fixed orthonormal basis. In conclusion, we discuss settings in which these models may be of practical interest.« less

Authors:
 [1];  [2];  [2];  [3];  [4]
  1. Univ. of Leeds, Leeds (United Kingdom); Univ. of California, Berkeley, CA (United States); Sandia National Lab. (SNL-CA), Livermore, CA (United States)
  2. Univ. of St. Andrews, Fife (Scotland)
  3. Heriot-Watt Univ., Edinburgh (United Kingdom)
  4. Durham Univ., Durham (United Kingdom)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1411880
Report Number(s):
SAND-2017-6076J
Journal ID: ISSN 2469-9926; PLRAAN; 656114; TRN: US1800280
Grant/Contract Number:  
AC04-94AL85000
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review A
Additional Journal Information:
Journal Volume: 95; Journal Issue: 5; Journal ID: ISSN 2469-9926
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Proctor, Timothy, Giulian, Melissa, Korolkova, Natalia, Andersson, Erika, and Kendon, Viv. Ancilla-driven quantum computation for qudits and continuous variables. United States: N. p., 2017. Web. doi:10.1103/physreva.95.052317.
Proctor, Timothy, Giulian, Melissa, Korolkova, Natalia, Andersson, Erika, & Kendon, Viv. Ancilla-driven quantum computation for qudits and continuous variables. United States. doi:10.1103/physreva.95.052317.
Proctor, Timothy, Giulian, Melissa, Korolkova, Natalia, Andersson, Erika, and Kendon, Viv. Wed . "Ancilla-driven quantum computation for qudits and continuous variables". United States. doi:10.1103/physreva.95.052317. https://www.osti.gov/servlets/purl/1411880.
@article{osti_1411880,
title = {Ancilla-driven quantum computation for qudits and continuous variables},
author = {Proctor, Timothy and Giulian, Melissa and Korolkova, Natalia and Andersson, Erika and Kendon, Viv},
abstractNote = {Although qubits are the leading candidate for the basic elements in a quantum computer, there are also a range of reasons to consider using higher-dimensional qudits or quantum continuous variables (QCVs). In this paper, we use a general “quantum variable” formalism to propose a method of quantum computation in which ancillas are used to mediate gates on a well-isolated “quantum memory” register and which may be applied to the setting of qubits, qudits (for d>2), or QCVs. More specifically, we present a model in which universal quantum computation may be implemented on a register using only repeated applications of a single fixed two-body ancilla-register interaction gate, ancillas prepared in a single state, and local measurements of these ancillas. In order to maintain determinism in the computation, adaptive measurements via a classical feed forward of measurement outcomes are used, with the method similar to that in measurement-based quantum computation (MBQC). We show that our model has the same hybrid quantum-classical processing advantages as MBQC, including the power to implement any Clifford circuit in essentially one layer of quantum computation. In some physical settings, high-quality measurements of the ancillas may be highly challenging or not possible, and hence we also present a globally unitary model which replaces the need for measurements of the ancillas with the requirement for ancillas to be prepared in states from a fixed orthonormal basis. In conclusion, we discuss settings in which these models may be of practical interest.},
doi = {10.1103/physreva.95.052317},
journal = {Physical Review A},
number = 5,
volume = 95,
place = {United States},
year = {2017},
month = {5}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Qudit color codes and gauge color codes in all spatial dimensions
journal, August 2015


Quantum error correction of continuous-variable states against Gaussian noise
journal, August 2011


Gaussian quantum information
journal, May 2012

  • Weedbrook, Christian; Pirandola, Stefano; García-Patrón, Raúl
  • Reviews of Modern Physics, Vol. 84, Issue 2
  • DOI: 10.1103/RevModPhys.84.621

Enhanced Fault-Tolerant Quantum Computing in d -Level Systems
journal, December 2014


Quantum Computation over Continuous Variables
journal, February 1999


Atomic homodyne detection of continuous-variable entangled twin-atom states
journal, November 2011


Phase control of the Kerr nonlinearity in electromagnetically induced transparency media
journal, March 2008

  • Sun, Hui; Niu, Yueping; Jin, Shiqi
  • Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 41, Issue 6
  • DOI: 10.1088/0953-4075/41/6/065504

Quantum computation mediated by ancillary qudits and spin coherent states
journal, January 2015


Superconducting qubit–oscillator circuit beyond the ultrastrong-coupling regime
journal, October 2016

  • Yoshihara, Fumiki; Fuse, Tomoko; Ashhab, Sahel
  • Nature Physics, Vol. 13, Issue 1
  • DOI: 10.1038/nphys3906

Reversible state transfer between superconducting qubits and atomic ensembles
journal, April 2009


Stabilizer states and Clifford operations for systems of arbitrary dimensions and modular arithmetic
journal, April 2005


Quantum information with continuous variables
journal, June 2005


Coupling superconducting flux qubits at optimal point via dynamic decoupling with the quantum bus
journal, January 2009


Quantum computation based on d -level cluster state
journal, December 2003


Fast decoders for qudit topological codes
journal, June 2014


Quantum Key Distribution with Higher-Order Alphabets Using Spatially Encoded Qudits
journal, March 2006


Multivalued logic gates for quantum computation
journal, October 2000


Quantum Enhancement of the Zero-Area Sagnac Interferometer Topology for Gravitational Wave Detection
journal, June 2010


Quantum computation by communication
journal, February 2006


Squeezed light at 1550 nm with a quantum noise reduction of 123 dB
journal, January 2011

  • Mehmet, Moritz; Ast, Stefan; Eberle, Tobias
  • Optics Express, Vol. 19, Issue 25
  • DOI: 10.1364/OE.19.025763

Parallelizing quantum circuits
journal, June 2009


Quantum Storage of Orbital Angular Momentum Entanglement in an Atomic Ensemble
journal, February 2015


Enhanced cross-Kerr nonlinearity via electromagnetically induced transparency in a four-level tripod atomic system
journal, January 2009

  • Yang, Xudong; Li, Shujing; Zhang, Chunhong
  • Journal of the Optical Society of America B, Vol. 26, Issue 7
  • DOI: 10.1364/JOSAB.26.001423

Hybrid quantum computing with ancillas
journal, March 2016


Measurement-Based Quantum Computation with Trapped Ions
journal, November 2013


Universal Quantum Computation with Continuous-Variable Cluster States
journal, September 2006


Scaling and Better Approximating Quantum Fourier Transform by Higher Radices
journal, February 2007

  • Zilic, Zeljko; Radecka, Katarzyna
  • IEEE Transactions on Computers, Vol. 56, Issue 2
  • DOI: 10.1109/TC.2007.35

Multipath Entanglement of Two Photons
journal, April 2009


Minimal ancilla mediated quantum computation
journal, September 2014

  • Proctor, Timothy J.; Kendon, Viv
  • EPJ Quantum Technology, Vol. 1, Issue 1
  • DOI: 10.1140/epjqt13

Quantum memory using a hybrid circuit with flux qubits and nitrogen-vacancy centers
journal, July 2013


Ancilla-driven universal quantum computation
journal, August 2010


Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond
journal, October 2011

  • Zhu, Xiaobo; Saito, Shiro; Kemp, Alexander
  • Nature, Vol. 478, Issue 7368
  • DOI: 10.1038/nature10462

Observation of optical-fibre Kerr nonlinearity at the single-photon level
journal, January 2009

  • Matsuda, Nobuyuki; Shimizu, Ryosuke; Mitsumori, Yasuyoshi
  • Nature Photonics, Vol. 3, Issue 2
  • DOI: 10.1038/nphoton.2008.292

Almost Any Quantum Logic Gate is Universal
journal, July 1995


Gate sequence for continuous variable one-way quantum computation
journal, November 2013

  • Su, Xiaolong; Hao, Shuhong; Deng, Xiaowei
  • Nature Communications, Vol. 4, Issue 1
  • DOI: 10.1038/ncomms3828

Quantum Control in the Cs 6 S 1 / 2 Ground Manifold Using Radio-Frequency and Microwave Magnetic Fields
journal, October 2013


Magic-State Distillation in All Prime Dimensions Using Quantum Reed-Muller Codes
journal, December 2012


Efficient Synthesis of Universal Repeat-Until-Success Quantum Circuits
journal, February 2015


Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States
journal, March 2014


Large Kerr nonlinearities on cavity-atom polaritons
journal, January 2010


Experimental quantum tomography of photonic qudits via mutually unbiased basis
journal, January 2011


Ultra-large-scale continuous-variable cluster states multiplexed in the time domain
journal, November 2013


Optical-Fiber Source of Polarization-Entangled Photons in the 1550 nm Telecom Band
journal, February 2005


Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics
journal, September 2004

  • Wallraff, A.; Schuster, D. I.; Blais, A.
  • Nature, Vol. 431, Issue 7005
  • DOI: 10.1038/nature02851

High quantum-efficiency photon-number-resolving detector for photonic on-chip information processing
journal, January 2013

  • Calkins, Brice; Mennea, Paolo L.; Lita, Adriana E.
  • Optics Express, Vol. 21, Issue 19
  • DOI: 10.1364/OE.21.022657

Measurement-based quantum computation on cluster states
journal, August 2003


Kitaev's Z d -code threshold estimates
journal, June 2013


Accurate and Robust Unitary Transformations of a High-Dimensional Quantum System
journal, June 2015


Demonstration of Unconditional One-Way Quantum Computations for Continuous Variables
journal, June 2011


Sequential measurement-based quantum computing with memories
journal, June 2011


Quantum computing with continuous-variable clusters
journal, June 2009


Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities
journal, May 2011

  • Dada, Adetunmise C.; Leach, Jonathan; Buller, Gerald S.
  • Nature Physics, Vol. 7, Issue 9
  • DOI: 10.1038/nphys1996

Electromagnetically induced transparency with single atoms in a cavity
journal, May 2010

  • Mücke, Martin; Figueroa, Eden; Bochmann, Joerg
  • Nature, Vol. 465, Issue 7299
  • DOI: 10.1038/nature09093

Demonstrating elements of measurement-based quantum error correction
journal, October 2014


Quantum interference of a single spin excitation with a macroscopic atomic ensemble
journal, March 2014


Sequential Implementation of Global Quantum Operations
journal, October 2008


An ideal characterization of the Clifford operators
journal, July 2014


Hybrid Quantum Processors: Molecular Ensembles as Quantum Memory for Solid State Circuits
journal, July 2006


Fast geometric gate operation of superconducting charge qubits in circuit QED
journal, August 2011


Quantum encodings in spin systems and harmonic oscillators
journal, May 2002


The measurement calculus
journal, April 2007

  • Danos, Vincent; Kashefi, Elham; Panangaden, Prakash
  • Journal of the ACM, Vol. 54, Issue 2
  • DOI: 10.1145/1219092.1219096

Coupling Nitrogen-Vacancy Centers in Diamond to Superconducting Flux Qubits
journal, November 2010


Efficient Classical Simulation of Continuous Variable Quantum Information Processes
journal, February 2002


Repeat-Until-Success Linear Optics Distributed Quantum Computing
journal, July 2005


Universal quantum computation by the unitary control of ancilla qubits and using a fixed ancilla-register interaction
journal, October 2013


Quantum systems with finite Hilbert space
journal, February 2004


A One-Way Quantum Computer
journal, May 2001


Comparison of quantum and semiclassical radiation theories with application to the beam maser
journal, January 1963


Quantum memory for entangled continuous-variable states
journal, November 2010

  • Jensen, K.; Wasilewski, W.; Krauter, H.
  • Nature Physics, Vol. 7, Issue 1
  • DOI: 10.1038/nphys1819

Error thresholds for Abelian quantum double models: Increasing the bit-flip stability of topological quantum memory
journal, April 2015


Tomography of photon-number resolving continuous-output detectors
journal, October 2015


Encoding a qubit in an oscillator
journal, June 2001


Experimental measurement-based quantum computing beyond the cluster-state model
journal, January 2011


Emulation of a Quantum Spin with a Superconducting Phase Qudit
journal, August 2009


Efficient optical quantum information processing
journal, June 2005

  • Munro, W. J.; Nemoto, Kae; Spiller, T. P.
  • Journal of Optics B: Quantum and Semiclassical Optics, Vol. 7, Issue 7
  • DOI: 10.1088/1464-4266/7/7/002

Deterministic quantum teleportation between distant atomic objects
journal, June 2013

  • Krauter, H.; Salart, D.; Muschik, C. A.
  • Nature Physics, Vol. 9, Issue 7
  • DOI: 10.1038/nphys2631

Quantum fast Fourier transform using multilevel atoms
journal, November 2002


A note on quantum error correction with continuous variables
journal, November 2010


Twisted Graph States for Ancilla-driven Universal Quantum Computation
journal, August 2009


Resolving photon number states in a superconducting circuit
journal, February 2007

  • Schuster, D. I.; Houck, A. A.; Schreier, J. A.
  • Nature, Vol. 445, Issue 7127
  • DOI: 10.1038/nature05461

Analog Quantum Error Correction
journal, May 1998