A Quadratic Speedup In The Optimization Of Noisy Quantum Optical Circuits

Robbe De Prins¹, Yuan Yao², Anuj Apte^3,4, and Filippo M. Miatto^2,3

¹Photonics Research Group, INTEC, Ghent University – imec, Sint-Pietersnieuwstraat 41, 9000 Ghent, Belgium
²Télécom Paris and Institut Polytechnique de Paris, LTCI, 20 Place Marguerite Perey, 91120 Palaiseau, France
³Xanadu, Toronto, ON, M5G 2C8, Canada
⁴Kadanoff Center for Theoretical Physics & Enrico Fermi Institute, Department of Physics, University of Chicago, Chicago, IL 60637

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

Linear optical quantum circuits with photon number resolving (PNR) detectors are used for both Gaussian Boson Sampling (GBS) and for the preparation of non-Gaussian states such as Gottesman-Kitaev-Preskill (GKP), cat and NOON states. They are crucial in many schemes of quantum computing and quantum metrology. Classically optimizing circuits with PNR detectors is challenging due to their exponentially large Hilbert space, and quadratically more challenging in the presence of decoherence as state vectors are replaced by density matrices. To tackle this problem, we introduce a family of algorithms that calculate detection probabilities, conditional states (as well as their gradients with respect to circuit parametrizations) with a complexity that is comparable to the noiseless case. As a consequence we can simulate and optimize circuits with twice the number of modes as we could before, using the same resources. More precisely, for an $M$-mode noisy circuit with detected modes $D$ and undetected modes $U$, the complexity of our algorithm is $O(M^2 prod_{i mskip2mu in mskip2mu U} C_i^2 prod_{i mskip2mu in mskip2mu D} C_i)$, rather than $O(M^2 prod_{mskip2mu i mskip2mu in mskip2mu D mskip3mu cup mskip3mu U} C_i^2)$, where $C_i$ is the Fock cutoff of mode $i$. As a particular case, our approach offers a full quadratic speedup for calculating detection probabilities, as in that case all modes are detected. Finally, these algorithms are implemented and ready to use in the open-source photonic optimization library MrMustard.

Featured image: This quantum photonic circuit prepares a non-Gaussian quantum state. Such states are crucial resources in the field of quantum computing.

Animated versions of some figures in the manuscript (GIFs) are included in the Supplementary Materials.

Popular summary

Quantum photonic circuits with photon-number-resolving detectors play a pivotal role in the advancement of quantum computing. These circuits have been physically realized to showcase that quantum computers have the potential to surpass classical computers. Similar circuits are being designed to generate complex quantum optical states like GKP states which serve as building blocks to make a practical and useful photonic quantum computer.
Scientists can rely on classical computers to simulate and optimize these circuits. However, such numerical simulations are fundamentally challenging, especially as the size of the circuit grows (if quantum circuits could be simulated efficiently, they wouldn’t be able to outperform classical computers in the first place). More precisely, as circuits grow larger, both the time needed for simulations and the required computer memory increase exponentially. There is little one can do to escape this.
This challenge becomes even greater when we move away from ideal circuits and we take into account that part of the light inevitably escapes from the circuit. Incorporating such realistic effects adds a quadratic increase in computational demands on top of the existing exponential growth. In this manuscript, we introduce a new family of algorithms that can take such real-world effects into account without adding the extra quadratic load. This allows us to simulate and optimize realistic circuits with the same effort as ideal ones.

► BibTeX data

@article{DePrins2023quadraticspeedupin, doi = {10.22331/q-2023-08-29-1097}, url = {https://doi.org/10.22331/q-2023-08-29-1097}, title = {A {Q}uadratic {S}peedup in the {O}ptimization of {N}oisy {Q}uantum {O}ptical {C}ircuits}, author = {De Prins, Robbe and Yao, Yuan and Apte, Anuj and Miatto, Filippo M.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {1097}, month = aug, year = {2023}<br /> }

► References

[1] Juan Miguel Arrazola and Thomas R. Bromley. Using Gaussian boson sampling to find dense subgraphs. Physical Review Letters, 121 (3), July 2018. 10.1103/physrevlett.121.030503.
https://doi.org/10.1103/physrevlett.121.030503

[2] Juan Miguel Arrazola, Thomas R. Bromley, and Patrick Rebentrost. Quantum approximate optimization with Gaussian boson sampling. Physical Review A, 98 (1), July 2018. 10.1103/physreva.98.012322.
https://doi.org/10.1103/physreva.98.012322

[3] Leonardo Banchi, Mark Fingerhuth, Tomas Babej, Christopher Ing, and Juan Miguel Arrazola. Molecular docking with Gaussian boson sampling. Science Advances, 6 (23), June 2020a. 10.1126/sciadv.aax1950.
https://doi.org/10.1126/sciadv.aax1950

[4] Leonardo Banchi, Nicolás Quesada, and Juan Miguel Arrazola. Training Gaussian boson sampling distributions. Physical Review A, 102 (1): 012417, 2020b. 10.1103/PhysRevA.102.012417.
https://doi.org/10.1103/PhysRevA.102.012417

[5] J. Eli Bourassa, Rafael N. Alexander, Michael Vasmer, Ashlesha Patil, Ilan Tzitrin, Takaya Matsuura, Daiqin Su, Ben Q. Baragiola, Saikat Guha, Guillaume Dauphinais, et al. Blueprint for a scalable photonic fault-tolerant quantum computer. Quantum, 5: 392, 2021. 10.22331/q-2021-02-04-392.
https://doi.org/10.22331/q-2021-02-04-392

[6] Kamil Brádler, Pierre-Luc Dallaire-Demers, Patrick Rebentrost, Daiqin Su, and Christian Weedbrook. Gaussian boson sampling for perfect matchings of arbitrary graphs. Physical Review A, 98 (3), September 2018. 10.1103/physreva.98.032310.
https://doi.org/10.1103/physreva.98.032310

[7] Kamil Brádler, Shmuel Friedland, Josh Izaac, Nathan Killoran, and Daiqin Su. Graph isomorphism and Gaussian boson sampling. Special Matrices, 9 (1): 166–196, January 2021. 10.1515/spma-2020-0132.
https://doi.org/10.1515/spma-2020-0132

[8] Thomas R. Bromley, Juan Miguel Arrazola, Soran Jahangiri, Josh Izaac, Nicolás Quesada, Alain D. Gran, Maria Schuld, Jeremy Swinarton, Zeid Zabaneh, and Nathan Killoran. Applications of near-term photonic quantum computers: software and algorithms. Quantum Science and Technology, 5 (3): 034010, 2020. 10.1088/2058-9565/ab8504.
https://doi.org/10.1088/2058-9565/ab8504

[9] Jacob F. F. Bulmer, Bryn A. Bell, Rachel S. Chadwick, Alex E. Jones, Diana Moise, Alessandro Rigazzi, Jan Thorbecke, Utz-Uwe Haus, Thomas Van Vaerenbergh, Raj B. Patel, et al. The boundary for quantum advantage in Gaussian boson sampling. Science advances, 8 (4): eabl9236, 2022. 10.1126/sciadv.abl9236.
https://doi.org/10.1126/sciadv.abl9236

[10] Kevin E. Cahill and Roy J. Glauber. Density operators and quasiprobability distributions. Physical Review, 177 (5): 1882, 1969. 10.1103/PhysRev.177.1882.
https://doi.org/10.1103/PhysRev.177.1882

[11] Kosuke Fukui, Shuntaro Takeda, Mamoru Endo, Warit Asavanant, Jun-ichi Yoshikawa, Peter van Loock, and Akira Furusawa. Efficient backcasting search for optical quantum state synthesis. Phys. Rev. Lett., 128: 240503, June 2022. 10.1103/PhysRevLett.128.240503.
https://doi.org/10.1103/PhysRevLett.128.240503

[12] Christopher C. Gerry and Peter L. Knight. Introductory quantum optics. Cambridge university press, 2005.

[13] Daniel Gottesman, Alexei Kitaev, and John Preskill. Encoding a qubit in an oscillator. Phys. Rev. A, 64: 012310, June 2001. 10.1103/PhysRevA.64.012310.
https://doi.org/10.1103/PhysRevA.64.012310

[14] Craig S. Hamilton, Regina Kruse, Linda Sansoni, Sonja Barkhofen, Christine Silberhorn, and Igor Jex. Gaussian boson sampling. Phys. Rev. Lett., 119: 170501, October 2017. 10.1103/PhysRevLett.119.170501.
https://doi.org/10.1103/PhysRevLett.119.170501

[15] Joonsuk Huh and Man-Hong Yung. Vibronic boson sampling: Generalized Gaussian boson sampling for molecular vibronic spectra at finite temperature. Scientific Reports, 7 (1), August 2017. 10.1038/s41598-017-07770-z.
https://doi.org/10.1038/s41598-017-07770-z

[16] Soran Jahangiri, Juan Miguel Arrazola, Nicolás Quesada, and Nathan Killoran. Point processes with Gaussian boson sampling. Physical Review E, 101 (2), February 2020. 10.1103/physreve.101.022134.
https://doi.org/10.1103/physreve.101.022134

[17] Regina Kruse, Craig S. Hamilton, Linda Sansoni, Sonja Barkhofen, Christine Silberhorn, and Igor Jex. Detailed study of Gaussian boson sampling. Phys. Rev. A, 100: 032326, September 2019. 10.1103/PhysRevA.100.032326.
https://doi.org/10.1103/PhysRevA.100.032326

[18] Filippo M. Miatto and Nicolás Quesada. Fast optimization of parametrized quantum optical circuits. Quantum, 4: 366, 2020. 10.22331/q-2020-11-30-366.
https://doi.org/10.22331/q-2020-11-30-366

[19] Changhun Oh, Minzhao Liu, Yuri Alexeev, Bill Fefferman, and Liang Jiang. Tensor network algorithm for simulating experimental Gaussian boson sampling. arXiv preprint arXiv:2306.03709, 2023. 10.48550/arXiv.2306.03709.
https://doi.org/10.48550/arXiv.2306.03709
arXiv:2306.03709

[20] Nicolás Quesada. Franck-Condon factors by counting perfect matchings of graphs with loops. The Journal of chemical physics, 150 (16): 164113, 2019. 10.1063/1.5086387.
https://doi.org/10.1063/1.5086387

[21] Nicolás Quesada, Luke G. Helt, Josh Izaac, Juan Miguel Arrazola, Reihaneh Shahrokhshahi, Casey R. Myers, and Krishna K. Sabapathy. Simulating realistic non-Gaussian state preparation. Phys. Rev. A, 100: 022341, August 2019. 10.1103/PhysRevA.100.022341.
https://doi.org/10.1103/PhysRevA.100.022341

[22] Krishna K. Sabapathy, Haoyu Qi, Josh Izaac, and Christian Weedbrook. Production of photonic universal quantum gates enhanced by machine learning. Phys. Rev. A, 100: 012326, July 2019. 10.1103/PhysRevA.100.012326.
https://doi.org/10.1103/PhysRevA.100.012326

[23] Maria Schuld, Ville Bergholm, Christian Gogolin, Josh Izaac, and Nathan Killoran. Evaluating analytic gradients on quantum hardware. Phys. Rev. A, 99 (3): 032331, 2019. 10.1103/PhysRevA.99.032331.
https://doi.org/10.1103/PhysRevA.99.032331

[24] Maria Schuld, Kamil Brádler, Robert Israel, Daiqin Su, and Brajesh Gupt. Measuring the similarity of graphs with a Gaussian boson sampler. Physical Review A, 101 (3), March 2020. 10.1103/physreva.101.032314.
https://doi.org/10.1103/physreva.101.032314

[25] Daiqin Su, Casey R. Myers, and Krishna K. Sabapathy. Conversion of Gaussian states to non-Gaussian states using photon-number-resolving detectors. Phys. Rev. A, 100: 052301, November 2019a. 10.1103/PhysRevA.100.052301.
https://doi.org/10.1103/PhysRevA.100.052301

[26] Daiqin Su, Casey R. Myers, and Krishna K. Sabapathy. Generation of photonic non-Gaussian states by measuring multimode Gaussian states. arXiv preprint arXiv:1902.02331, 2019b. 10.48550/arXiv.1902.02331.
https://doi.org/10.48550/arXiv.1902.02331
arXiv:1902.02331

[27] Kan Takase, Jun-ichi Yoshikawa, Warit Asavanant, Mamoru Endo, and Akira Furusawa. Generation of optical Schrödinger cat states by generalized photon subtraction. Phys. Rev. A, 103: 013710, January 2021. 10.1103/PhysRevA.103.013710.
https://doi.org/10.1103/PhysRevA.103.013710

[28] Kan Takase, Kosuke Fukui, Akito Kawasaki, Warit Asavanant, Mamoru Endo, Jun-ichi Yoshikawa, Peter van Loock, and Akira Furusawa. Gaussian breeding for encoding a qubit in propagating light. arXiv preprint arXiv:2212.05436, 2022. 10.48550/arXiv.2212.05436.
https://doi.org/10.48550/arXiv.2212.05436
arXiv:2212.05436

[29] Xanadu Quantum Technologies. MrMustard. https://github.com/XanaduAI/MrMustard, 2022.
https://github.com/XanaduAI/MrMustard

[30] Ilan Tzitrin, J. Eli Bourassa, Nicolas C. Menicucci, and Krishna K. Sabapathy. Progress towards practical qubit computation using approximate Gottesman-Kitaev-Preskill codes. Phys. Rev. A, 101: 032315, March 2020. 10.1103/PhysRevA.101.032315.
https://doi.org/10.1103/PhysRevA.101.032315

[31] Yuan Yao, Filippo M. Miatto, and Nicolás Quesada. The recursive representation of Gaussian quantum mechanics. arXiv preprint arXiv:2209.06069, 2022. 10.48550/arXiv.2209.06069.
https://doi.org/10.48550/arXiv.2209.06069
arXiv:2209.06069

Cited by

[1] Pranav Chandarana, Koushik Paul, Mikel Garcia-de-Andoin, Yue Ban, Mikel Sanz, and Xi Chen, “Photonic counterdiabatic quantum optimization algorithm”, arXiv:2307.14853, (2023).

The above citations are from SAO/NASA ADS (last updated successfully 2023-08-29 15:00:10). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch Crossref cited-by data during last attempt 2023-08-29 15:00:08: Could not fetch cited-by data for 10.22331/q-2023-08-29-1097 from Crossref. This is normal if the DOI was registered recently.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

SEO Powered Content & PR Distribution. Get Amplified Today.
PlatoData.Network Vertical Generative Ai. Empower Yourself. Access Here.
PlatoAiStream. Web3 Intelligence. Knowledge Amplified. Access Here.
PlatoESG. Automotive / EVs, Carbon, CleanTech, Energy, Environment, Solar, Waste Management. Access Here.
PlatoHealth. Biotech and Clinical Trials Intelligence. Access Here.
ChartPrime. Elevate your Trading Game with ChartPrime. Access Here.
BlockOffsets. Modernizing Environmental Offset Ownership. Access Here.
Source: https://quantum-journal.org/papers/q-2023-08-29-1097/

Generative Data Intelligence

A Quadratic Speedup in the Optimization of Noisy Quantum Optical Circuits

Abstract

Popular summary

► BibTeX data

► References

Cited by

Atlassian outsources office drudgery to GenAI agents

UK inertia on LLMs and copyright is ‘de facto endorsement’

Latest Intelligence

Is Ethereum Back? Record 267,000 New Users Spark Speculation

Metabirkin NFTs Making Their Way To A Stockholm Museum – CryptoInfoNet

Former DFS Regulator Secures $5.1 Million For Cryptocurrency Venture Fund Supported By Winklevoss Twins And Robert Leshner – CryptoInfoNet

CoinEx Emphasizes Financial Leadership at 15th National Finance Summit | BitPinas

Bitcoin Cash Analysis: BCH Faces Uphill Task at $462 | Live Bitcoin News

Ethereum Price Could Rally If It’s Able To Reclaims The 100 SMA

Chat with us