Coherent manipulation of graph states composed of finite-energy Gottesman-Kitaev-Preskill-encoded qubits
Abstract
Graph states are a central resource in measurement-based quantum information processing. In the photonic qubit architecture based on Gottesman-Kitaev-Preskill (GKP) encoding, the generation of high-fidelity graph states composed of realistic, finite-energy approximate GKP-encoded qubits thus constitutes a key task. We consider the finite-energy approximation of GKP-qubit states given by a coherent superposition of shifted finite-squeezed vacuum states, where the displacements are Gaussian distributed. We present an exact description of graph states composed of such approximate GKP qubits as a coherent superposition of a Gaussian ensemble of randomly displaced ideal GKP-qubit graph states. Using standard Gaussian dynamics, we track the transformation of the covariance matrix and the mean-displacement vector elements of the Gaussian distribution of the ensemble under tools such as GKP-Steane error-correction and fusion operations that can be used to grow large high-fidelity GKP-qubit graph states. The covariance matrix elements capture the noise in the graph state due to the finite-energy approximation of GKP qubits, while the mean displacements relate to the possible absolute shift errors on the individual qubits arising conditionally from the homodyne measurements that are a part of these tools. Our work thus pins down an exact coherent error model for graph states generated from truly finite-energymore »
- Authors:
-
- Univ. of Arizona, Tucson, AZ (United States); Univ. of Pittsburgh, PA (United States)
- Univ. of Arizona, Tucson, AZ (United States); Birla Inst. of Technology and Science Pilani (India)
- Univ. of Arizona, Tucson, AZ (United States)
- Univ. of Chicago, IL (United States)
- Publication Date:
- Research Org.:
- Univ. of Arizona, Tucson, AZ (United States)
- Sponsoring Org.:
- USDOE; National Science Foundation (NSF); US Army Research Office (ARO); US Air Force Office of Scientific Research (AFOSR); Packard Foundation
- OSTI Identifier:
- 1982752
- Grant/Contract Number:
- AC05-00OR22725; 4000178321; 1941583; W911NF-18-1- 0020; W911NF-18-1-0212; W911NF-16-1- 0349; FA9550-19-1-0399; EFMA- 1640959; OMA-1936118; EEC-1941583; 2013-39273
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review A
- Additional Journal Information:
- Journal Volume: 105; Journal Issue: 5; Journal ID: ISSN 2469-9926
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Optics; Physics; Measurement-based quantum computing; Quantum error correction; Quantum information processing; Quantum information processing with continuous variables; Quantum repeaters
Citation Formats
Seshadreesan, Kaushik P., Dhara, Prajit, Patil, Ashlesha, Jiang, Liang, and Guha, Saikat. Coherent manipulation of graph states composed of finite-energy Gottesman-Kitaev-Preskill-encoded qubits. United States: N. p., 2022.
Web. doi:10.1103/physreva.105.052416.
Seshadreesan, Kaushik P., Dhara, Prajit, Patil, Ashlesha, Jiang, Liang, & Guha, Saikat. Coherent manipulation of graph states composed of finite-energy Gottesman-Kitaev-Preskill-encoded qubits. United States. https://doi.org/10.1103/physreva.105.052416
Seshadreesan, Kaushik P., Dhara, Prajit, Patil, Ashlesha, Jiang, Liang, and Guha, Saikat. Wed .
"Coherent manipulation of graph states composed of finite-energy Gottesman-Kitaev-Preskill-encoded qubits". United States. https://doi.org/10.1103/physreva.105.052416. https://www.osti.gov/servlets/purl/1982752.
@article{osti_1982752,
title = {Coherent manipulation of graph states composed of finite-energy Gottesman-Kitaev-Preskill-encoded qubits},
author = {Seshadreesan, Kaushik P. and Dhara, Prajit and Patil, Ashlesha and Jiang, Liang and Guha, Saikat},
abstractNote = {Graph states are a central resource in measurement-based quantum information processing. In the photonic qubit architecture based on Gottesman-Kitaev-Preskill (GKP) encoding, the generation of high-fidelity graph states composed of realistic, finite-energy approximate GKP-encoded qubits thus constitutes a key task. We consider the finite-energy approximation of GKP-qubit states given by a coherent superposition of shifted finite-squeezed vacuum states, where the displacements are Gaussian distributed. We present an exact description of graph states composed of such approximate GKP qubits as a coherent superposition of a Gaussian ensemble of randomly displaced ideal GKP-qubit graph states. Using standard Gaussian dynamics, we track the transformation of the covariance matrix and the mean-displacement vector elements of the Gaussian distribution of the ensemble under tools such as GKP-Steane error-correction and fusion operations that can be used to grow large high-fidelity GKP-qubit graph states. The covariance matrix elements capture the noise in the graph state due to the finite-energy approximation of GKP qubits, while the mean displacements relate to the possible absolute shift errors on the individual qubits arising conditionally from the homodyne measurements that are a part of these tools. Our work thus pins down an exact coherent error model for graph states generated from truly finite-energy GKP qubits, which can shed light on their error-correction properties.},
doi = {10.1103/physreva.105.052416},
journal = {Physical Review A},
number = 5,
volume = 105,
place = {United States},
year = {Wed May 11 00:00:00 EDT 2022},
month = {Wed May 11 00:00:00 EDT 2022}
}
Works referenced in this record:
Quantum computational advantage using photons
journal, December 2020
- Zhong, Han-Sen; Wang, Hui; Deng, Yu-Hao
- Science, Vol. 370, Issue 6523
All-optical long-distance quantum communication with Gottesman-Kitaev-Preskill qubits
journal, August 2021
- Fukui, Kosuke; Alexander, Rafael N.; van Loock, Peter
- Physical Review Research, Vol. 3, Issue 3
Quantum Optical Technologies for Metrology, Sensing, and Imaging
journal, June 2015
- Dowling, Jonathan P.; Seshadreesan, Kaushik P.
- Journal of Lightwave Technology, Vol. 33, Issue 12
Gaussian quantum information
journal, May 2012
- Weedbrook, Christian; Pirandola, Stefano; García-Patrón, Raúl
- Reviews of Modern Physics, Vol. 84, Issue 2
Quantum Computation over Continuous Variables
journal, February 1999
- Lloyd, Seth; Braunstein, Samuel L.
- Physical Review Letters, Vol. 82, Issue 8
High-Dimensional Frequency-Encoded Quantum Information Processing with Passive Photonics and Time-Resolving Detection
journal, May 2020
- Cui, Chaohan; Seshadreesan, Kaushik P.; Guha, Saikat
- Physical Review Letters, Vol. 124, Issue 19
Encoding qubits into oscillators with atomic ensembles and squeezed light
journal, May 2017
- Motes, Keith R.; Baragiola, Ben Q.; Gilchrist, Alexei
- Physical Review A, Vol. 95, Issue 5
Photonic quantum technologies
journal, December 2009
- O'Brien, Jeremy L.; Furusawa, Akira; Vučković, Jelena
- Nature Photonics, Vol. 3, Issue 12
Quantum Capacity Bounds of Gaussian Thermal Loss Channels and Achievable Rates With Gottesman-Kitaev-Preskill Codes
journal, April 2019
- Noh, Kyungjoo; Albert, Victor V.; Jiang, Liang
- IEEE Transactions on Information Theory, Vol. 65, Issue 4
Advances in photonic quantum sensing
journal, November 2018
- Pirandola, S.; Bardhan, B. R.; Gehring, T.
- Nature Photonics, Vol. 12, Issue 12
Resource-Efficient Linear Optical Quantum Computation
journal, June 2005
- Browne, Daniel E.; Rudolph, Terry
- Physical Review Letters, Vol. 95, Issue 1
Twisted photons: new quantum perspectives in high dimensions
journal, October 2017
- Erhard, Manuel; Fickler, Robert; Krenn, Mario
- Light: Science & Applications, Vol. 7, Issue 3
High-rate photon pairs and sequential Time-Bin entanglement with Si 3 N 4 microring resonators
journal, January 2019
- Samara, Farid; Martin, Anthony; Autebert, Claire
- Optics Express, Vol. 27, Issue 14
Invited Article: Generation of one-million-mode continuous-variable cluster state by unlimited time-domain multiplexing
journal, September 2016
- Yoshikawa, Jun-ichi; Yokoyama, Shota; Kaji, Toshiyuki
- APL Photonics, Vol. 1, Issue 6
Time-bin entangled photons from a quantum dot
journal, June 2014
- Jayakumar, Harishankar; Predojević, Ana; Kauten, Thomas
- Nature Communications, Vol. 5, Issue 1
Why I am optimistic about the silicon-photonic route to quantum computing
journal, March 2017
- Rudolph, Terry
- APL Photonics, Vol. 2, Issue 3
Temporal shaping of single photons enabled by entanglement
journal, October 2017
- Averchenko, Valentin; Sych, Denis; Schunk, Gerhard
- Physical Review A, Vol. 96, Issue 4
Quantum communication
journal, March 2007
- Gisin, Nicolas; Thew, Rob
- Nature Photonics, Vol. 1, Issue 3
Active Stabilization, Quantum Computation, and Quantum State Synthesis
journal, March 1997
- Steane, A. M.
- Physical Review Letters, Vol. 78, Issue 11
Universal Quantum Computation with Continuous-Variable Cluster States
journal, September 2006
- Menicucci, Nicolas C.; van Loock, Peter; Gu, Mile
- Physical Review Letters, Vol. 97, Issue 11
Photonic quantum information processing: a review
journal, November 2018
- Flamini, Fulvio; Spagnolo, Nicolò; Sciarrino, Fabio
- Reports on Progress in Physics, Vol. 82, Issue 1
Quantum computation with optical coherent states
journal, October 2003
- Ralph, T. C.; Gilchrist, A.; Milburn, G. J.
- Physical Review A, Vol. 68, Issue 4
Distilling Gaussian States with Gaussian Operations is Impossible
journal, September 2002
- Eisert, J.; Scheel, S.; Plenio, M. B.
- Physical Review Letters, Vol. 89, Issue 13
Loss Tolerance in One-Way Quantum Computation via Counterfactual Error Correction
journal, September 2006
- Varnava, Michael; Browne, Daniel E.; Rudolph, Terry
- Physical Review Letters, Vol. 97, Issue 12
Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States
journal, March 2014
- Menicucci, Nicolas C.
- Physical Review Letters, Vol. 112, Issue 12
Experimental Realization of Multipartite Entanglement of 60 Modes of a Quantum Optical Frequency Comb
journal, March 2014
- Chen, Moran; Menicucci, Nicolas C.; Pfister, Olivier
- Physical Review Letters, Vol. 112, Issue 12
Generation of time-domain-multiplexed two-dimensional cluster state
journal, October 2019
- Asavanant, Warit; Shiozawa, Yu; Yokoyama, Shota
- Science, Vol. 366, Issue 6463
Equivalence of approximate Gottesman-Kitaev-Preskill codes
journal, September 2020
- Matsuura, Takaya; Yamasaki, Hayata; Koashi, Masato
- Physical Review A, Vol. 102, Issue 3
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
Coherent state topological cluster state production
journal, November 2011
- Myers, C. R.; Ralph, T. C.
- New Journal of Physics, Vol. 13, Issue 11
Photon Temporal Modes: A Complete Framework for Quantum Information Science
journal, October 2015
- Brecht, B.; Reddy, Dileep V.; Silberhorn, C.
- Physical Review X, Vol. 5, Issue 4
Frequency-encoded photonic qubits for scalable quantum information processing
journal, December 2016
- Lukens, Joseph M.; Lougovski, Pavel
- Optica, Vol. 4, Issue 1
Conditional and unconditional Gaussian quantum dynamics
journal, January 2016
- Genoni, Marco G.; Lami, Ludovico; Serafini, Alessio
- Contemporary Physics, Vol. 57, Issue 3
Error analysis for encoding a qubit in an oscillator
journal, January 2006
- Glancy, S.; Knill, E.
- Physical Review A, Vol. 73, Issue 1
Quantum error correction of a qubit encoded in grid states of an oscillator
journal, August 2020
- Campagne-Ibarcq, P.; Eickbusch, A.; Touzard, S.
- Nature, Vol. 584, Issue 7821
High-Threshold Fault-Tolerant Quantum Computation with Analog Quantum Error Correction
journal, May 2018
- Fukui, Kosuke; Tomita, Akihisa; Okamoto, Atsushi
- Physical Review X, Vol. 8, Issue 2
Universal Quantum Computing with Measurement-Induced Continuous-Variable Gate Sequence in a Loop-Based Architecture
journal, September 2017
- Takeda, Shuntaro; Furusawa, Akira
- Physical Review Letters, Vol. 119, Issue 12
Emergence and control of complex behaviors in driven systems of interacting qubits with dissipation
journal, January 2021
- Andreev, A. V.; Balanov, A. G.; Fromhold, T. M.
- npj Quantum Information, Vol. 7, Issue 1
Rate-distance tradeoff and resource costs for all-optical quantum repeaters
journal, January 2017
- Pant, Mihir; Krovi, Hari; Englund, Dirk
- Physical Review A, Vol. 95, Issue 1
Experimental boson sampling
journal, May 2013
- Tillmann, Max; Dakić, Borivoje; Heilmann, René
- Nature Photonics, Vol. 7, Issue 7
Encoding a qubit in an oscillator
journal, June 2001
- Gottesman, Daniel; Kitaev, Alexei; Preskill, John
- Physical Review A, Vol. 64, Issue 1
Encoding a qubit into a cavity mode in circuit QED using phase estimation
journal, January 2016
- Terhal, B. M.; Weigand, D.
- Physical Review A, Vol. 93, Issue 1
Encoding a qubit in a trapped-ion mechanical oscillator
journal, February 2019
- Flühmann, C.; Nguyen, T. L.; Marinelli, M.
- Nature, Vol. 566, Issue 7745
Universal quantum computation with temporal-mode bilayer square lattices
journal, March 2018
- Alexander, Rafael N.; Yokoyama, Shota; Furusawa, Akira
- Physical Review A, Vol. 97, Issue 3
Performance and structure of single-mode bosonic codes
journal, March 2018
- Albert, Victor V.; Noh, Kyungjoo; Duivenvoorden, Kasper
- Physical Review A, Vol. 97, Issue 3
Broadband quadrature-squeezed vacuum and nonclassical photon number correlations from a nanophotonic device
journal, September 2020
- Vaidya, V. D.; Morrison, B.; Helt, L. G.
- Science Advances, Vol. 6, Issue 39
Wavelength-multiplexed quantum networks with ultrafast frequency combs
journal, December 2013
- Roslund, Jonathan; de Araújo, Renné Medeiros; Jiang, Shifeng
- Nature Photonics, Vol. 8, Issue 2
Photonic quantum information processing: A concise review
journal, December 2019
- Slussarenko, Sergei; Pryde, Geoff J.
- Applied Physics Reviews, Vol. 6, Issue 4
No-Go Theorem for Gaussian Quantum Error Correction
journal, March 2009
- Niset, Julien; Fiurášek, Jaromír; Cerf, Nicolas J.
- Physical Review Letters, Vol. 102, Issue 12
Error correction of a logical grid state qubit by dissipative pumping
journal, February 2022
- de Neeve, Brennan; Nguyen, Thanh-Long; Behrle, Tanja
- Nature Physics, Vol. 18, Issue 3