Here is a list of my publications, you can also consult my google scholar or arXiv pages.
2020 |
Barbara M Terhal; Jonathan Conrad; Christophe Vuillot Towards Scalable Bosonic Quantum Error Correction Unpublished 2020, (arXiv:2002.11008). @unpublished{Terhal2020, title = { Towards Scalable Bosonic Quantum Error Correction}, author = {Barbara M Terhal and Jonathan Conrad and Christophe Vuillot}, url = {https://arxiv.org/abs/2002.11008}, year = {2020}, date = {2020-02-25}, abstract = {We review some of the recent efforts in devising and engineering bosonic qubits for superconducting devices, with emphasis on the Gottesman-Kitaev-Preskill (GKP) qubit. We present some new results on decoding repeated GKP error correction using finitely-squeezed GKP ancilla qubits, exhibiting differences with previously studied stochastic error models. We discuss circuit-QED ways to realize CZ gates between GKP qubits and we discuss different scenario's for using GKP and regular qubits as building blocks in a scalable superconducting surface code architecture. }, note = {arXiv:2002.11008}, keywords = {}, pubstate = {published}, tppubtype = {unpublished} } We review some of the recent efforts in devising and engineering bosonic qubits for superconducting devices, with emphasis on the Gottesman-Kitaev-Preskill (GKP) qubit. We present some new results on decoding repeated GKP error correction using finitely-squeezed GKP ancilla qubits, exhibiting differences with previously studied stochastic error models. We discuss circuit-QED ways to realize CZ gates between GKP qubits and we discuss different scenario's for using GKP and regular qubits as building blocks in a scalable superconducting surface code architecture. |
C Vuillot Fault-tolerant quantum computation: Theory and practice PhD Thesis TU Delft, 2020, ISBN: 978-94-6384-097-2. @phdthesis{vuillot_fault-tolerant_2020, title = {Fault-tolerant quantum computation: Theory and practice}, author = {C Vuillot}, url = {https://site.vuillot.info/perso/wp-content/uploads/2020/01/dissertation_vuillot_final.pdf}, doi = {10.4233/uuid:7cb715f4-eaf0-4526-8552-9f97cc864383}, isbn = {978-94-6384-097-2}, year = {2020}, date = {2020-01-01}, urldate = {2020-01-02}, school = {TU Delft}, abstract = {Quantum computation is the modern version of Schrödinger’s cat experiment. It is backed up in principle by the theory and thinking about it can make people equally uncomfortable and excited. Besides, its practical realization seems so extremely challenging that some people even doubt it is possible. On the other hand, we are nowadays much closer to realizing quantum computation and in addition, it has much more implications than Schrödinger’s original cat experiment. One of the major difficulties in realizing quantum computation is the inevitable presence of noise in realistic quantum devices which makes the direct realization of quantum computers impossible. In order to protect quantum information and quantum processes against noise, quantum error correction and fault-tolerance have been devised. Although the gap between experiments and the requirements of fault-tolerance is still daunting, the field of quantum error correction and fault-tolerance extends and influences architectural decisions from the hardware to the ideal quantum programs that we want to run. That is why it has the potential to make or break the practicality of quantum computation and a lot of research effort goes into this field. In this thesis we investigate and improve several aspects of fault-tolerant schemes and quantum error correction. We implement an experiment which validates on a small device the usefulness of fault-tolerance for quantum computation. We investigate the advantages of harnessing quantum continuous degrees of freedom present in the lab to protect discrete quantum information in a scalable way. We establish a framework to analyze the fault-tolerant properties of code deformation techniques which are versatile techniques to process quantum information protected by an error correcting code. We also present some novel code deformation techniques with the potential to increase reliability. Finally we define a new class of quantum error correcting codes, quantum pin codes, with built in capabilities for fault-tolerant quantum gates. We give some practical constructions and show some protocols with interesting parameters. The roads towards universal and fault-tolerant quantum computation are still steep but research efforts are pushing in the right directions.}, keywords = {}, pubstate = {published}, tppubtype = {phdthesis} } Quantum computation is the modern version of Schrödinger’s cat experiment. It is backed up in principle by the theory and thinking about it can make people equally uncomfortable and excited. Besides, its practical realization seems so extremely challenging that some people even doubt it is possible. On the other hand, we are nowadays much closer to realizing quantum computation and in addition, it has much more implications than Schrödinger’s original cat experiment. One of the major difficulties in realizing quantum computation is the inevitable presence of noise in realistic quantum devices which makes the direct realization of quantum computers impossible. In order to protect quantum information and quantum processes against noise, quantum error correction and fault-tolerance have been devised. Although the gap between experiments and the requirements of fault-tolerance is still daunting, the field of quantum error correction and fault-tolerance extends and influences architectural decisions from the hardware to the ideal quantum programs that we want to run. That is why it has the potential to make or break the practicality of quantum computation and a lot of research effort goes into this field. In this thesis we investigate and improve several aspects of fault-tolerant schemes and quantum error correction. We implement an experiment which validates on a small device the usefulness of fault-tolerance for quantum computation. We investigate the advantages of harnessing quantum continuous degrees of freedom present in the lab to protect discrete quantum information in a scalable way. We establish a framework to analyze the fault-tolerant properties of code deformation techniques which are versatile techniques to process quantum information protected by an error correcting code. We also present some novel code deformation techniques with the potential to increase reliability. Finally we define a new class of quantum error correcting codes, quantum pin codes, with built in capabilities for fault-tolerant quantum gates. We give some practical constructions and show some protocols with interesting parameters. The roads towards universal and fault-tolerant quantum computation are still steep but research efforts are pushing in the right directions. |
2019 |
Christophe Vuillot; Lingling Lao; Ben Criger; Carmen García Almudéver; Koen Bertels; Barbara M Terhal Code deformation and lattice surgery are gauge fixing Journal Article New Journal of Physics, 21 (3), pp. 033028, 2019, ISSN: 1367-2630. @article{vuillot_code_2019, title = {Code deformation and lattice surgery are gauge fixing}, author = {Christophe Vuillot and Lingling Lao and Ben Criger and Carmen García Almudéver and Koen Bertels and Barbara M Terhal}, url = {https://site.vuillot.info/perso/wp-content/uploads/2019/12/code_deformation_is_gauge_fixing.pdf https://arxiv.org/abs/1810.10037}, doi = {10.1088/1367-2630/ab0199}, issn = {1367-2630}, year = {2019}, date = {2019-03-01}, urldate = {2019-04-28}, journal = {New Journal of Physics}, volume = {21}, number = {3}, pages = {033028}, abstract = {The large-scale execution of quantum algorithms requires basic quantum operations to be implemented fault-tolerantly. The most popular technique for accomplishing this, using the devices that can be realized in the near term, uses stabilizer codes which can be embedded in a planar layout. The set of fault-tolerant operations which can be executed in these systems using unitary gates is typically very limited. This has driven the development of measurement-based schemes for performing logical operations in these codes, known as lattice surgery and code deformation. In parallel, gauge fixing has emerged as a measurement-based method for performing universal gate sets in subsystem stabilizer codes. In this work, we show that lattice surgery and code deformation can be expressed as special cases of gauge fixing, permitting a simple and rigorous test for fault-tolerance together with simple guiding principles for the implementation of these operations. We demonstrate the accuracy of this method numerically with examples based on the surface code, some of which are novel.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The large-scale execution of quantum algorithms requires basic quantum operations to be implemented fault-tolerantly. The most popular technique for accomplishing this, using the devices that can be realized in the near term, uses stabilizer codes which can be embedded in a planar layout. The set of fault-tolerant operations which can be executed in these systems using unitary gates is typically very limited. This has driven the development of measurement-based schemes for performing logical operations in these codes, known as lattice surgery and code deformation. In parallel, gauge fixing has emerged as a measurement-based method for performing universal gate sets in subsystem stabilizer codes. In this work, we show that lattice surgery and code deformation can be expressed as special cases of gauge fixing, permitting a simple and rigorous test for fault-tolerance together with simple guiding principles for the implementation of these operations. We demonstrate the accuracy of this method numerically with examples based on the surface code, some of which are novel. |
Christophe Vuillot; Nikolas P Breuckmann Quantum Pin Codes Unpublished 2019, (arXiv: 1906.11394). @unpublished{vuillot_quantum_2019-1, title = {Quantum Pin Codes}, author = {Christophe Vuillot and Nikolas P Breuckmann}, url = {https://site.vuillot.info/perso/wp-content/uploads/2019/12/PinCodes_arxivv2.pdf http://arxiv.org/abs/1906.11394}, year = {2019}, date = {2019-01-01}, urldate = {2019-06-28}, journal = {arXiv:1906.11394 [quant-ph]}, abstract = {We introduce quantum pin codes: a class of quantum CSS codes. Quantum pin codes are a vast generalization of quantum color codes and Reed-Muller codes. A lot of the structure and properties of color codes carries over to pin codes. Pin codes have gauge operators, an unfolding procedure and their stabilizers form multi-orthogonal spaces. This last feature makes them interesting for devising magic-state distillation protocols. We study examples of these codes and their properties.}, note = {arXiv: 1906.11394}, keywords = {}, pubstate = {published}, tppubtype = {unpublished} } We introduce quantum pin codes: a class of quantum CSS codes. Quantum pin codes are a vast generalization of quantum color codes and Reed-Muller codes. A lot of the structure and properties of color codes carries over to pin codes. Pin codes have gauge operators, an unfolding procedure and their stabilizers form multi-orthogonal spaces. This last feature makes them interesting for devising magic-state distillation protocols. We study examples of these codes and their properties. |
Christophe Vuillot; Hamed Asasi; Yang Wang; Leonid P Pryadko; Barbara M Terhal Quantum error correction with the toric Gottesman-Kitaev-Preskill code Journal Article Physical Review A, 99 (3), pp. 032344, 2019. @article{vuillot_quantum_2019b, title = {Quantum error correction with the toric Gottesman-Kitaev-Preskill code}, author = {Christophe Vuillot and Hamed Asasi and Yang Wang and Leonid P Pryadko and Barbara M Terhal}, url = {https://site.vuillot.info/perso/wp-content/uploads/2019/12/Toric-GKP-code-arxiv-v2.pdf https://arxiv.org/abs/1810.00047}, doi = {10.1103/PhysRevA.99.032344}, year = {2019}, date = {2019-01-01}, urldate = {2019-04-28}, journal = {Physical Review A}, volume = {99}, number = {3}, pages = {032344}, abstract = {We examine the performance of the single-mode Gottesman-Kitaev-Preskill (GKP) code and its concatenation with the toric code for a noise model of Gaussian shifts, or displacement errors. We show how one can optimize the tracking of errors in repeated noisy error correction for the GKP code. We do this by examining the maximum-likelihood problem for this setting and its mapping onto a 1D Euclidean path-integral modeling a particle in a random cosine potential. We demonstrate the efficiency of a minimum-energy decoding strategy as a proxy for the path integral evaluation. In the second part of this paper, we analyze and numerically assess the concatenation of the GKP code with the toric code. When toric code measurements and GKP error correction measurements are perfect, we find that by using GKP error information the toric code threshold improves from 10% to 14%. When only the GKP error correction measurements are perfect we observe a threshold at 6%. In the more realistic setting when all error information is noisy, we show how to represent the maximum likelihood decoding problem for the toric-GKP code as a 3D compact QED model in the presence of a quenched random gauge field, an extension of the random-plaquette gauge model for the toric code. We present a decoder for this problem which shows the existence of a noise threshold at shift-error standard deviation σ0≈0.243 for toric code measurements, data errors and GKP ancilla errors. If the errors only come from having imperfect GKP states, then this corresponds to states with just four photons or more. Our last result is a no-go result for linear oscillator codes, encoding oscillators into oscillators. For the Gaussian displacement error model, we prove that encoding corresponds to squeezing the shift errors. This shows that linear oscillator codes are useless for quantum information protection against Gaussian shift errors.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We examine the performance of the single-mode Gottesman-Kitaev-Preskill (GKP) code and its concatenation with the toric code for a noise model of Gaussian shifts, or displacement errors. We show how one can optimize the tracking of errors in repeated noisy error correction for the GKP code. We do this by examining the maximum-likelihood problem for this setting and its mapping onto a 1D Euclidean path-integral modeling a particle in a random cosine potential. We demonstrate the efficiency of a minimum-energy decoding strategy as a proxy for the path integral evaluation. In the second part of this paper, we analyze and numerically assess the concatenation of the GKP code with the toric code. When toric code measurements and GKP error correction measurements are perfect, we find that by using GKP error information the toric code threshold improves from 10% to 14%. When only the GKP error correction measurements are perfect we observe a threshold at 6%. In the more realistic setting when all error information is noisy, we show how to represent the maximum likelihood decoding problem for the toric-GKP code as a 3D compact QED model in the presence of a quenched random gauge field, an extension of the random-plaquette gauge model for the toric code. We present a decoder for this problem which shows the existence of a noise threshold at shift-error standard deviation σ0≈0.243 for toric code measurements, data errors and GKP ancilla errors. If the errors only come from having imperfect GKP states, then this corresponds to states with just four photons or more. Our last result is a no-go result for linear oscillator codes, encoding oscillators into oscillators. For the Gaussian displacement error model, we prove that encoding corresponds to squeezing the shift errors. This shows that linear oscillator codes are useless for quantum information protection against Gaussian shift errors. |
2018 |
Victor V Albert; Kyungjoo Noh; Kasper Duivenvoorden; Dylan J Young; R T Brierley; Philip Reinhold; Christophe Vuillot; Linshu Li; Chao Shen; S M Girvin; Barbara M Terhal; Liang Jiang Performance and structure of single-mode bosonic codes Journal Article Physical Review A, 97 (3), pp. 032346, 2018. @article{albert_performance_2018, title = {Performance and structure of single-mode bosonic codes}, author = {Victor V Albert and Kyungjoo Noh and Kasper Duivenvoorden and Dylan J Young and R T Brierley and Philip Reinhold and Christophe Vuillot and Linshu Li and Chao Shen and S M Girvin and Barbara M Terhal and Liang Jiang}, url = {https://arxiv.org/abs/1708.05010}, doi = {10.1103/PhysRevA.97.032346}, year = {2018}, date = {2018-03-01}, urldate = {2018-04-06}, journal = {Physical Review A}, volume = {97}, number = {3}, pages = {032346}, abstract = {The early Gottesman, Kitaev, and Preskill (GKP) proposal for encoding a qubit in an oscillator has recently been followed by cat- and binomial-code proposals. Numerically optimized codes have also been proposed, and we introduce codes of this type here. These codes have yet to be compared using the same error model; we provide such a comparison by determining the entanglement fidelity of all codes with respect to the bosonic pure-loss channel (i.e., photon loss) after the optimal recovery operation. We then compare achievable communication rates of the combined encoding-error-recovery channel by calculating the channel's hashing bound for each code. Cat and binomial codes perform similarly, with binomial codes outperforming cat codes at small loss rates. Despite not being designed to protect against the pure-loss channel, GKP codes significantly outperform all other codes for most values of the loss rate. We show that the performance of GKP and some binomial codes increases monotonically with increasing average photon number of the codes. In order to corroborate our numerical evidence of the cat-binomial-GKP order of performance occurring at small loss rates, we analytically evaluate the quantum error-correction conditions of those codes. For GKP codes, we find an essential singularity in the entanglement fidelity in the limit of vanishing loss rate. In addition to comparing the codes, we draw parallels between binomial codes and discrete-variable systems. First, we characterize one- and two-mode binomial as well as multiqubit permutation-invariant codes in terms of spin-coherent states. Such a characterization allows us to introduce check operators and error-correction procedures for binomial codes. Second, we introduce a generalization of spin-coherent states, extending our characterization to qudit binomial codes and yielding a multiqudit code.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The early Gottesman, Kitaev, and Preskill (GKP) proposal for encoding a qubit in an oscillator has recently been followed by cat- and binomial-code proposals. Numerically optimized codes have also been proposed, and we introduce codes of this type here. These codes have yet to be compared using the same error model; we provide such a comparison by determining the entanglement fidelity of all codes with respect to the bosonic pure-loss channel (i.e., photon loss) after the optimal recovery operation. We then compare achievable communication rates of the combined encoding-error-recovery channel by calculating the channel's hashing bound for each code. Cat and binomial codes perform similarly, with binomial codes outperforming cat codes at small loss rates. Despite not being designed to protect against the pure-loss channel, GKP codes significantly outperform all other codes for most values of the loss rate. We show that the performance of GKP and some binomial codes increases monotonically with increasing average photon number of the codes. In order to corroborate our numerical evidence of the cat-binomial-GKP order of performance occurring at small loss rates, we analytically evaluate the quantum error-correction conditions of those codes. For GKP codes, we find an essential singularity in the entanglement fidelity in the limit of vanishing loss rate. In addition to comparing the codes, we draw parallels between binomial codes and discrete-variable systems. First, we characterize one- and two-mode binomial as well as multiqubit permutation-invariant codes in terms of spin-coherent states. Such a characterization allows us to introduce check operators and error-correction procedures for binomial codes. Second, we introduce a generalization of spin-coherent states, extending our characterization to qudit binomial codes and yielding a multiqudit code. |
Christophe Vuillot Is error detection helpful on IBM 5Q chips ? Journal Article Quantum Information and Computation, 18 (11&12), pp. 0949–0964, 2018. @article{vuillot_is_2018, title = {Is error detection helpful on IBM 5Q chips ?}, author = {Christophe Vuillot}, url = {https://site.vuillot.info/perso/wp-content/uploads/2019/12/vuillot_fault_tolerant_demo.pdf https://arxiv.org/abs/1705.08957}, doi = {10.26421/QIC18.11-12}, year = {2018}, date = {2018-01-01}, urldate = {2018-04-06}, journal = {Quantum Information and Computation}, volume = {18}, number = {11&12}, pages = {0949--0964}, abstract = {This paper reports on experiments realized on several IBM 5Q chips which show evidence for the advantage of using error detection and fault-tolerant design of quantum circuits. We show an average improvement of the task of sampling from states that can be fault-tolerantly prepared in the $[[4,2,2]]$ code, when using a fault-tolerant technique well suited to the layout of the chip. By showing that fault-tolerant quantum computation is already within our reach, the author hopes to encourage this approach.}, keywords = {}, pubstate = {published}, tppubtype = {article} } This paper reports on experiments realized on several IBM 5Q chips which show evidence for the advantage of using error detection and fault-tolerant design of quantum circuits. We show an average improvement of the task of sampling from states that can be fault-tolerantly prepared in the $[[4,2,2]]$ code, when using a fault-tolerant technique well suited to the layout of the chip. By showing that fault-tolerant quantum computation is already within our reach, the author hopes to encourage this approach. |
2017 |
Earl T Campbell; Barbara M Terhal; Christophe Vuillot Roads towards fault-tolerant universal quantum computation Journal Article Nature, 549 (7671), pp. 172–179, 2017, ISSN: 1476-4687. @article{campbell_roads_2017, title = {Roads towards fault-tolerant universal quantum computation}, author = {Earl T Campbell and Barbara M Terhal and Christophe Vuillot}, url = {https://site.vuillot.info/perso/wp-content/uploads/2019/12/SteepRoad_arXiv_V2.pdf https://arxiv.org/abs/1612.07330}, doi = {10.1038/nature23460}, issn = {1476-4687}, year = {2017}, date = {2017-09-01}, urldate = {2019-03-19}, journal = {Nature}, volume = {549}, number = {7671}, pages = {172--179}, abstract = {A practical quantum computer must not merely store information, but also process it. To prevent errors introduced by noise from multiplying and spreading, a fault-tolerant computational architecture is required. Current experiments are taking the first steps toward noise-resilient logical qubits. But to convert these quantum devices from memories to processors, it is necessary to specify how a universal set of gates is performed on them. The leading proposals for doing so, such as magic-state distillation and colour-code techniques, have high resource demands. Alternative schemes, such as those that use high-dimensional quantum codes in a modular architecture, have potential benefits, but need to be explored further.}, keywords = {}, pubstate = {published}, tppubtype = {article} } A practical quantum computer must not merely store information, but also process it. To prevent errors introduced by noise from multiplying and spreading, a fault-tolerant computational architecture is required. Current experiments are taking the first steps toward noise-resilient logical qubits. But to convert these quantum devices from memories to processors, it is necessary to specify how a universal set of gates is performed on them. The leading proposals for doing so, such as magic-state distillation and colour-code techniques, have high resource demands. Alternative schemes, such as those that use high-dimensional quantum codes in a modular architecture, have potential benefits, but need to be explored further. |
Nikolas P Breuckmann; Christophe Vuillot; Earl Campbell; Anirudh Krishna; Barbara M Terhal Hyperbolic and semi-hyperbolic surface codes for quantum storage Journal Article Quantum Science and Technology, 2 (3), pp. 035007, 2017, ISSN: 2058-9565. @article{breuckmann_hyperbolic_2017, title = {Hyperbolic and semi-hyperbolic surface codes for quantum storage}, author = {Nikolas P Breuckmann and Christophe Vuillot and Earl Campbell and Anirudh Krishna and Barbara M Terhal}, url = {https://arxiv.org/abs/1703.00590}, doi = {10.1088/2058-9565/aa7d3b}, issn = {2058-9565}, year = {2017}, date = {2017-01-01}, urldate = {2018-04-06}, journal = {Quantum Science and Technology}, volume = {2}, number = {3}, pages = {035007}, abstract = {We show how a hyperbolic surface code could be used for overhead-efficient quantum storage. We give numerical evidence for a noise threshold of 1.3% for the 4,5-hyperbolic surface code in a phenomenological noise model (as compared to 2.9% for the toric code). In this code family parity checks are of weight 4 and 5 while each qubit participates in 4 different parity checks. We introduce a family of semi-hyperbolic codes which interpolate between the toric code and the 4,5-hyperbolic surface code in terms of encoding rate and threshold. We show how these hyperbolic codes outperform the toric code in terms of qubit overhead for a target logical error probability. We show how Dehn twists and lattice code surgery can be used to read and write individual qubits to this quantum storage medium.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We show how a hyperbolic surface code could be used for overhead-efficient quantum storage. We give numerical evidence for a noise threshold of 1.3% for the 4,5-hyperbolic surface code in a phenomenological noise model (as compared to 2.9% for the toric code). In this code family parity checks are of weight 4 and 5 while each qubit participates in 4 different parity checks. We introduce a family of semi-hyperbolic codes which interpolate between the toric code and the 4,5-hyperbolic surface code in terms of encoding rate and threshold. We show how these hyperbolic codes outperform the toric code in terms of qubit overhead for a target logical error probability. We show how Dehn twists and lattice code surgery can be used to read and write individual qubits to this quantum storage medium. |
2012 |
Erwan Faou; Fabio Nobile; Christophe Vuillot Sparse spectral approximations for computing polynomial functionals Unpublished 2012. @unpublished{faou_sparse_2012, title = {Sparse spectral approximations for computing polynomial functionals}, author = {Erwan Faou and Fabio Nobile and Christophe Vuillot}, url = {http://arxiv.org/abs/1207.3728}, year = {2012}, date = {2012-01-01}, urldate = {2018-04-06}, journal = {arXiv:1207.3728 [math]}, abstract = {We give a new fast method for evaluating sprectral approximations of nonlinear polynomial functionals. We prove that the new algorithm is convergent if the functions considered are smooth enough, under a general assumption on the spectral eigenfunctions that turns out to be satisfied in many cases, including the Fourier and Hermite basis.}, keywords = {}, pubstate = {published}, tppubtype = {unpublished} } We give a new fast method for evaluating sprectral approximations of nonlinear polynomial functionals. We prove that the new algorithm is convergent if the functions considered are smooth enough, under a general assumption on the spectral eigenfunctions that turns out to be satisfied in many cases, including the Fourier and Hermite basis. |