Pub Date : 2024-08-07DOI: 10.22331/q-2024-08-07-1432
Andrew M. Projansky, Joshuah T. Heath, James D. Whitfield
The entanglement level statistics of a quantum state have recently been proposed to be a signature of universality in the underlying quantum circuit. This is a consequence of level repulsion in the entanglement spectra being tied to the integrability of entanglement generated. However, such studies of the level-spacing statistics in the entanglement spectrum have thus far been limited to the output states of Clifford and Haar random circuits on product state inputs. In this work, we provide the first example of a circuit which is composed of a simulable gate set, yet has a Wigner-Dyson distributed entanglement level spectrum without any perturbing universal element. We first show that, for matchgate circuits acting on random product states, Wigner-Dyson statistics emerge by virtue of a single SWAP gate, in direct analog to previous studies on Clifford circuits. We then examine the entanglement spectrum of matchgate circuits with varied input states, and find a sharp jump in the complexity of entanglement as we go from two- to three-qubit entangled inputs. Studying Clifford and matchgate hybrid circuits, we find examples of classically simulable circuits whose output states exhibit Wigner-Dyson entanglement level statistics in the absence of universal quantum gate elements. Our study thus provides strong evidence that entanglement spectrum is not strongly connected to notions of simulability in any given quantum circuit.
{"title":"Entanglement spectrum of matchgate circuits with universal and non-universal resources","authors":"Andrew M. Projansky, Joshuah T. Heath, James D. Whitfield","doi":"10.22331/q-2024-08-07-1432","DOIUrl":"https://doi.org/10.22331/q-2024-08-07-1432","url":null,"abstract":"The entanglement level statistics of a quantum state have recently been proposed to be a signature of universality in the underlying quantum circuit. This is a consequence of level repulsion in the entanglement spectra being tied to the integrability of entanglement generated. However, such studies of the level-spacing statistics in the entanglement spectrum have thus far been limited to the output states of Clifford and Haar random circuits on product state inputs. In this work, we provide the first example of a circuit which is composed of a simulable gate set, yet has a Wigner-Dyson distributed entanglement level spectrum without any perturbing universal element. We first show that, for matchgate circuits acting on random product states, Wigner-Dyson statistics emerge by virtue of a single SWAP gate, in direct analog to previous studies on Clifford circuits. We then examine the entanglement spectrum of matchgate circuits with varied input states, and find a sharp jump in the complexity of entanglement as we go from two- to three-qubit entangled inputs. Studying Clifford and matchgate hybrid circuits, we find examples of classically simulable circuits whose output states exhibit Wigner-Dyson entanglement level statistics in the absence of universal quantum gate elements. Our study thus provides strong evidence that entanglement spectrum is not strongly connected to notions of simulability in any given quantum circuit.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141899839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-02DOI: 10.22331/q-2024-08-02-1431
Stanisław Kurzyna, Bartosz Niewelt, Mateusz Mazelanik, Wojciech Wasilewski, Michał Parniak
Collective Rydberg excitations provide promising applications ranging from quantum information processing, and quantum computing to ultra-sensitive electrometry. However, their short lifetime is an immense obstacle in real-life scenarios. The state-of-the-art methods of prolonging the lifetime were mainly implemented for ground-state quantum memories and would require a redesign to effectively work on different atomic transitions. We propose a protocol for extending the Rydberg excitation lifetime, which in principle can freeze the spin-wave and completely cancel the effects of thermal dephasing. The protocol employs off-resonant ac-Stark lattice modulation of spin waves by interfering two laser beams on the atomic medium. Our implementation showed that the excitation lifetime can be extended by an order of magnitude, paving the way towards more complex protocols for collective Rydberg excitations.
{"title":"Long-lived collective Rydberg excitations in atomic gas achieved via ac-Stark lattice modulation","authors":"Stanisław Kurzyna, Bartosz Niewelt, Mateusz Mazelanik, Wojciech Wasilewski, Michał Parniak","doi":"10.22331/q-2024-08-02-1431","DOIUrl":"https://doi.org/10.22331/q-2024-08-02-1431","url":null,"abstract":"Collective Rydberg excitations provide promising applications ranging from quantum information processing, and quantum computing to ultra-sensitive electrometry. However, their short lifetime is an immense obstacle in real-life scenarios. The state-of-the-art methods of prolonging the lifetime were mainly implemented for ground-state quantum memories and would require a redesign to effectively work on different atomic transitions. We propose a protocol for extending the Rydberg excitation lifetime, which in principle can freeze the spin-wave and completely cancel the effects of thermal dephasing. The protocol employs off-resonant ac-Stark lattice modulation of spin waves by interfering two laser beams on the atomic medium. Our implementation showed that the excitation lifetime can be extended by an order of magnitude, paving the way towards more complex protocols for collective Rydberg excitations.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141877583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-02DOI: 10.22331/q-2024-08-02-1429
Linnea Grans-Samuelsson, Ryan V. Mishmash, David Aasen, Christina Knapp, Bela Bauer, Brad Lackey, Marcus P. da Silva, Parsa Bonderson
We devise a new realization of the surface code on a rectangular lattice of qubits utilizing single-qubit and nearest-neighbor two-qubit Pauli measurements and three auxiliary qubits per plaquette. This realization gains substantial advantages over prior pairwise measurement-based realizations of the surface code. It has a short operation period of 4 steps and our performance analysis for a standard circuit noise model yields a high fault-tolerance threshold of approximately $0.66% $. The syndrome extraction circuits avoid bidirectional hook errors, so we can achieve full code distance by choosing appropriate boundary conditions. We also construct variants of the syndrome extraction circuits that entirely prevent hook errors, at the cost of larger circuit depth. This achieves full distance regardless of boundary conditions, with only a modest decrease in the threshold. Furthermore, we propose an efficient strategy for dealing with dead components (qubits and measurements) in our surface code realization, which can be adopted more generally for other surface code realizations. This new surface code realization is highly optimized for Majorana-based hardware, accounting for constraints imposed by layouts and the implementation of measurements, making it competitive with the recently proposed Floquet codes.
{"title":"Improved Pairwise Measurement-Based Surface Code","authors":"Linnea Grans-Samuelsson, Ryan V. Mishmash, David Aasen, Christina Knapp, Bela Bauer, Brad Lackey, Marcus P. da Silva, Parsa Bonderson","doi":"10.22331/q-2024-08-02-1429","DOIUrl":"https://doi.org/10.22331/q-2024-08-02-1429","url":null,"abstract":"We devise a new realization of the surface code on a rectangular lattice of qubits utilizing single-qubit and nearest-neighbor two-qubit Pauli measurements and three auxiliary qubits per plaquette. This realization gains substantial advantages over prior pairwise measurement-based realizations of the surface code. It has a short operation period of 4 steps and our performance analysis for a standard circuit noise model yields a high fault-tolerance threshold of approximately $0.66% $. The syndrome extraction circuits avoid bidirectional hook errors, so we can achieve full code distance by choosing appropriate boundary conditions. We also construct variants of the syndrome extraction circuits that entirely prevent hook errors, at the cost of larger circuit depth. This achieves full distance regardless of boundary conditions, with only a modest decrease in the threshold. Furthermore, we propose an efficient strategy for dealing with dead components (qubits and measurements) in our surface code realization, which can be adopted more generally for other surface code realizations. This new surface code realization is highly optimized for Majorana-based hardware, accounting for constraints imposed by layouts and the implementation of measurements, making it competitive with the recently proposed Floquet codes.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141877584","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-02DOI: 10.22331/q-2024-08-02-1430
Iosifina Angelidi, Marcin Szyniszewski, Arijeet Pal
Long-range entangled states are vital for quantum information processing and quantum metrology. Preparing such states by combining measurements with unitary gates opened new possibilities for efficient protocols with finite-depth quantum circuits. The complexity of these algorithms is crucial for the resource requirements on a large-scale noisy quantum device, while their stability to perturbations decides the fate of their implementation. In this work, we consider stochastic quantum circuits in one and two dimensions comprising randomly applied unitary gates and local measurements. These operations preserve a class of discrete local symmetries, which are broken due to the stochasticity arising from timing and gate imperfections. In the absence of randomness, the protocol generates a symmetry-protected long-range entangled state in a finite-depth circuit. In the general case, by studying the time evolution under this hybrid circuit, we analyze the time to reach the target entangled state. We find two important time scales that we associate with the emergence of certain symmetry generators. The quantum trajectories embody the local symmetry with a time scaling logarithmically with system size, while global symmetries require exponentially long times. We devise error-mitigation protocols that significantly lower both time scales and investigate the stability of the algorithm to perturbations that naturally arise in experiments. We also generalize the protocol to realize toric code and Xu-Moore states in two dimensions, opening avenues for future studies of anyonic excitations. Our results unveil a fundamental relationship between symmetries and dynamics across a range of lattice geometries, which contributes to a broad understanding of the stability of preparation algorithms in terms of phase transitions. Our work paves the way for efficient error correction for quantum state preparation.
{"title":"Stabilization of symmetry-protected long-range entanglement in stochastic quantum circuits","authors":"Iosifina Angelidi, Marcin Szyniszewski, Arijeet Pal","doi":"10.22331/q-2024-08-02-1430","DOIUrl":"https://doi.org/10.22331/q-2024-08-02-1430","url":null,"abstract":"Long-range entangled states are vital for quantum information processing and quantum metrology. Preparing such states by combining measurements with unitary gates opened new possibilities for efficient protocols with finite-depth quantum circuits. The complexity of these algorithms is crucial for the resource requirements on a large-scale noisy quantum device, while their stability to perturbations decides the fate of their implementation. In this work, we consider stochastic quantum circuits in one and two dimensions comprising randomly applied unitary gates and local measurements. These operations preserve a class of discrete local symmetries, which are broken due to the stochasticity arising from timing and gate imperfections. In the absence of randomness, the protocol generates a symmetry-protected long-range entangled state in a finite-depth circuit. In the general case, by studying the time evolution under this hybrid circuit, we analyze the time to reach the target entangled state. We find two important time scales that we associate with the emergence of certain symmetry generators. The quantum trajectories embody the local symmetry with a time scaling logarithmically with system size, while global symmetries require exponentially long times. We devise error-mitigation protocols that significantly lower both time scales and investigate the stability of the algorithm to perturbations that naturally arise in experiments. We also generalize the protocol to realize toric code and Xu-Moore states in two dimensions, opening avenues for future studies of anyonic excitations. Our results unveil a fundamental relationship between symmetries and dynamics across a range of lattice geometries, which contributes to a broad understanding of the stability of preparation algorithms in terms of phase transitions. Our work paves the way for efficient error correction for quantum state preparation.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141877582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-30DOI: 10.22331/q-2024-07-30-1426
Abhijith Jayakumar, Stefano Chessa, Carleton Coffrin, Andrey Y. Lokhov, Marc Vuffray, Sidhant Misra
We present a general denoising algorithm for performing $textit{simultaneous tomography}$ of quantum states and measurement noise. This algorithm allows us to fully characterize state preparation and measurement (SPAM) errors present in any quantum system. Our method is based on the analysis of the properties of the linear operator space induced by unitary operations. Given any quantum system with a noisy measurement apparatus, our method can output the quantum state and the noise matrix of the detector up to a single gauge degree of freedom. We show that this gauge freedom is unavoidable in the general case, but this degeneracy can be generally broken using prior knowledge on the state or noise properties, thus fixing the gauge for several types of state-noise combinations with no assumptions about noise strength. Such combinations include pure quantum states with arbitrarily correlated errors, and arbitrary states with block independent errors. This framework can further use available prior information about the setting to systematically reduce the number of observations and measurements required for state and noise detection. Our method effectively generalizes existing approaches to the problem, and includes as special cases common settings considered in the literature requiring an uncorrelated or invertible noise matrix, or specific probe states.
{"title":"Universal framework for simultaneous tomography of quantum states and SPAM noise","authors":"Abhijith Jayakumar, Stefano Chessa, Carleton Coffrin, Andrey Y. Lokhov, Marc Vuffray, Sidhant Misra","doi":"10.22331/q-2024-07-30-1426","DOIUrl":"https://doi.org/10.22331/q-2024-07-30-1426","url":null,"abstract":"We present a general denoising algorithm for performing $textit{simultaneous tomography}$ of quantum states and measurement noise. This algorithm allows us to fully characterize state preparation and measurement (SPAM) errors present in any quantum system. Our method is based on the analysis of the properties of the linear operator space induced by unitary operations. Given any quantum system with a noisy measurement apparatus, our method can output the quantum state and the noise matrix of the detector up to a single gauge degree of freedom. We show that this gauge freedom is unavoidable in the general case, but this degeneracy can be generally broken using prior knowledge on the state or noise properties, thus fixing the gauge for several types of state-noise combinations with no assumptions about noise strength. Such combinations include pure quantum states with arbitrarily correlated errors, and arbitrary states with block independent errors. This framework can further use available prior information about the setting to systematically reduce the number of observations and measurements required for state and noise detection. Our method effectively generalizes existing approaches to the problem, and includes as special cases common settings considered in the literature requiring an uncorrelated or invertible noise matrix, or specific probe states.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141836749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-30DOI: 10.22331/q-2024-07-30-1428
Emma C. King, Luigi Giannelli, Raphaël Menu, Johannes N. Kriel, Giovanna Morigi
We analyze the efficiency of protocols for adiabatic quantum state transfer assisted by an engineered reservoir. The target dynamics is a quantum trajectory in the Hilbert space and is a fixed point of a time-dependent master equation in the limit of adiabatic dynamics. We specialize to quantum state transfer in a qubit and determine the optimal schedule for a class of time-dependent Lindblad equations. The speed limit on state transfer is extracted from a physical model of a qubit coupled to a reservoir, from which the Lindblad equation is derived in the Born-Markov limit. Our analysis shows that the resulting efficiency is comparable to the efficiency of the optimal unitary dynamics. Numerical studies indicate that reservoir-engineered protocols could outperform unitary protocols outside the regime of the Born-Markov master equation, namely, when correlations between the qubit and reservoir become relevant. Our study contributes to the theory of shortcuts to adiabaticity for open quantum systems and to the toolbox of protocols of the NISQ era.
{"title":"Adiabatic quantum trajectories in engineered reservoirs","authors":"Emma C. King, Luigi Giannelli, Raphaël Menu, Johannes N. Kriel, Giovanna Morigi","doi":"10.22331/q-2024-07-30-1428","DOIUrl":"https://doi.org/10.22331/q-2024-07-30-1428","url":null,"abstract":"We analyze the efficiency of protocols for adiabatic quantum state transfer assisted by an engineered reservoir. The target dynamics is a quantum trajectory in the Hilbert space and is a fixed point of a time-dependent master equation in the limit of adiabatic dynamics. We specialize to quantum state transfer in a qubit and determine the optimal schedule for a class of time-dependent Lindblad equations. The speed limit on state transfer is extracted from a physical model of a qubit coupled to a reservoir, from which the Lindblad equation is derived in the Born-Markov limit. Our analysis shows that the resulting efficiency is comparable to the efficiency of the optimal unitary dynamics. Numerical studies indicate that reservoir-engineered protocols could outperform unitary protocols outside the regime of the Born-Markov master equation, namely, when correlations between the qubit and reservoir become relevant. Our study contributes to the theory of shortcuts to adiabaticity for open quantum systems and to the toolbox of protocols of the NISQ era.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141836750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-30DOI: 10.22331/q-2024-07-30-1427
Jasmine Sinanan-Singh, Gabriel L. Mintzer, Isaac L. Chuang, Yuan Liu
Quantum systems of infinite dimension, such as bosonic oscillators, provide vast resources for quantum sensing. Yet, a general theory on how to manipulate such bosonic modes for sensing beyond parameter estimation is unknown. We present a general algorithmic framework, quantum signal processing interferometry (QSPI), for quantum sensing at the fundamental limits of quantum mechanics by generalizing Ramsey-type interferometry. Our QSPI sensing protocol relies on performing nonlinear polynomial transformations on the oscillator's quadrature operators by generalizing quantum signal processing (QSP) from qubits to hybrid qubit-oscillator systems. We use our QSPI sensing framework to make efficient binary decisions on a displacement channel in the single-shot limit. Theoretical analysis suggests the sensing accuracy, given a single-shot qubit measurement, scales inversely with the sensing time or circuit depth of the algorithm. We further concatenate a series of such binary decisions to perform parameter estimation in a bit-by-bit fashion. Numerical simulations are performed to support these statements. Our QSPI protocol offers a unified framework for quantum sensing using continuous-variable bosonic systems beyond parameter estimation and establishes a promising avenue toward efficient and scalable quantum control and quantum sensing schemes beyond the NISQ era.
{"title":"Single-shot Quantum Signal Processing Interferometry","authors":"Jasmine Sinanan-Singh, Gabriel L. Mintzer, Isaac L. Chuang, Yuan Liu","doi":"10.22331/q-2024-07-30-1427","DOIUrl":"https://doi.org/10.22331/q-2024-07-30-1427","url":null,"abstract":"Quantum systems of infinite dimension, such as bosonic oscillators, provide vast resources for quantum sensing. Yet, a general theory on how to manipulate such bosonic modes for sensing beyond parameter estimation is unknown. We present a general algorithmic framework, quantum signal processing interferometry (QSPI), for quantum sensing at the fundamental limits of quantum mechanics by generalizing Ramsey-type interferometry. Our QSPI sensing protocol relies on performing nonlinear polynomial transformations on the oscillator's quadrature operators by generalizing quantum signal processing (QSP) from qubits to hybrid qubit-oscillator systems. We use our QSPI sensing framework to make efficient binary decisions on a displacement channel in the single-shot limit. Theoretical analysis suggests the sensing accuracy, given a single-shot qubit measurement, scales inversely with the sensing time or circuit depth of the algorithm. We further concatenate a series of such binary decisions to perform parameter estimation in a bit-by-bit fashion. Numerical simulations are performed to support these statements. Our QSPI protocol offers a unified framework for quantum sensing using continuous-variable bosonic systems beyond parameter estimation and establishes a promising avenue toward efficient and scalable quantum control and quantum sensing schemes beyond the NISQ era.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141836758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-25DOI: 10.22331/q-2024-07-25-1424
Tim Möbus
The Trotter product formula and the quantum Zeno effect are both indispensable tools for constructing time-evolutions using experimentally feasible building blocks. In this work, we discuss assumptions under which quantitative bounds can be proven in the strong operator topology on Banach spaces and provide natural bosonic examples. Specially, we assume the existence of a continuously embedded Banach space, which relatively bounds the involved generators and creates an invariant subspace of the limiting semigroup with a stable restriction. The slightly stronger assumption of admissible subspaces is well-recognized in the realm of hyperbolic evolution systems (time-dependent semigroups), to which the results are extended. By assuming access to a hierarchy of continuously embedded Banach spaces, Suzuki-higher-order bounds can be demonstrated. In bosonic applications, these embedded Banach spaces naturally arise through the number operator, leading to a diverse set of examples encompassing notable instances such as the Ornstein-Uhlenbeck semigroup and multi-photon driven dissipation used in bosonic error correction.
{"title":"On Strong Bounds for Trotter and Zeno Product Formulas with Bosonic Applications","authors":"Tim Möbus","doi":"10.22331/q-2024-07-25-1424","DOIUrl":"https://doi.org/10.22331/q-2024-07-25-1424","url":null,"abstract":"The Trotter product formula and the quantum Zeno effect are both indispensable tools for constructing time-evolutions using experimentally feasible building blocks. In this work, we discuss assumptions under which quantitative bounds can be proven in the strong operator topology on Banach spaces and provide natural bosonic examples. Specially, we assume the existence of a continuously embedded Banach space, which relatively bounds the involved generators and creates an invariant subspace of the limiting semigroup with a stable restriction. The slightly stronger assumption of admissible subspaces is well-recognized in the realm of hyperbolic evolution systems (time-dependent semigroups), to which the results are extended. By assuming access to a hierarchy of continuously embedded Banach spaces, Suzuki-higher-order bounds can be demonstrated. In bosonic applications, these embedded Banach spaces naturally arise through the number operator, leading to a diverse set of examples encompassing notable instances such as the Ornstein-Uhlenbeck semigroup and multi-photon driven dissipation used in bosonic error correction.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141764291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-25DOI: 10.22331/q-2024-07-25-1425
Alejandro Pozas-Kerstjens, Senaida Hernández-Santana, José Ramón Pareja Monturiol, Marco Castrillón López, Giannicola Scarpa, Carlos E. González-Guillén, David Pérez-García
Tensor networks, widely used for providing efficient representations of low-energy states of local quantum many-body systems, have been recently proposed as machine learning architectures which could present advantages with respect to traditional ones. In this work we show that tensor-network architectures have especially prospective properties for privacy-preserving machine learning, which is important in tasks such as the processing of medical records. First, we describe a new privacy vulnerability that is present in feedforward neural networks, illustrating it in synthetic and real-world datasets. Then, we develop well-defined conditions to guarantee robustness to such vulnerability, which involve the characterization of models equivalent under gauge symmetry. We rigorously prove that such conditions are satisfied by tensor-network architectures. In doing so, we define a novel canonical form for matrix product states, which has a high degree of regularity and fixes the residual gauge that is left in the canonical forms based on singular value decompositions. We supplement the analytical findings with practical examples where matrix product states are trained on datasets of medical records, which show large reductions on the probability of an attacker extracting information about the training dataset from the model's parameters. Given the growing expertise in training tensor-network architectures, these results imply that one may not have to be forced to make a choice between accuracy in prediction and ensuring the privacy of the information processed.
{"title":"Privacy-preserving machine learning with tensor networks","authors":"Alejandro Pozas-Kerstjens, Senaida Hernández-Santana, José Ramón Pareja Monturiol, Marco Castrillón López, Giannicola Scarpa, Carlos E. González-Guillén, David Pérez-García","doi":"10.22331/q-2024-07-25-1425","DOIUrl":"https://doi.org/10.22331/q-2024-07-25-1425","url":null,"abstract":"Tensor networks, widely used for providing efficient representations of low-energy states of local quantum many-body systems, have been recently proposed as machine learning architectures which could present advantages with respect to traditional ones. In this work we show that tensor-network architectures have especially prospective properties for privacy-preserving machine learning, which is important in tasks such as the processing of medical records. First, we describe a new privacy vulnerability that is present in feedforward neural networks, illustrating it in synthetic and real-world datasets. Then, we develop well-defined conditions to guarantee robustness to such vulnerability, which involve the characterization of models equivalent under gauge symmetry. We rigorously prove that such conditions are satisfied by tensor-network architectures. In doing so, we define a novel canonical form for matrix product states, which has a high degree of regularity and fixes the residual gauge that is left in the canonical forms based on singular value decompositions. We supplement the analytical findings with practical examples where matrix product states are trained on datasets of medical records, which show large reductions on the probability of an attacker extracting information about the training dataset from the model's parameters. Given the growing expertise in training tensor-network architectures, these results imply that one may not have to be forced to make a choice between accuracy in prediction and ensuring the privacy of the information processed.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141764293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-24DOI: 10.22331/q-2024-07-24-1423
Grégoire de Gliniasty, Paul Hilaire, Pierre-Emmanuel Emeriau, Stephen C. Wein, Alexia Salavrakos, Shane Mansfield
We introduce an adaptable and modular hybrid architecture designed for fault-tolerant quantum computing. It combines quantum emitters and linear-optical entangling gates to leverage the strength of both matter-based and photonic-based approaches. A key feature of the architecture is its practicality, grounded in the utilisation of experimentally proven optical components. Our framework enables the execution of any quantum error correcting code, but in particular maintains scalability for low-density parity check codes by exploiting built-in non-local connectivity through distant optical links. To gauge its efficiency, we evaluated the architecture using a physically motivated error model. It exhibits loss tolerance comparable to existing all-photonic architecture but without the need for intricate linear-optical resource-state-generation modules that conventionally rely on resource-intensive multiplexing. The versatility of the architecture also offers uncharted avenues for further advancing performance standards.
{"title":"A Spin-Optical Quantum Computing Architecture","authors":"Grégoire de Gliniasty, Paul Hilaire, Pierre-Emmanuel Emeriau, Stephen C. Wein, Alexia Salavrakos, Shane Mansfield","doi":"10.22331/q-2024-07-24-1423","DOIUrl":"https://doi.org/10.22331/q-2024-07-24-1423","url":null,"abstract":"We introduce an adaptable and modular hybrid architecture designed for fault-tolerant quantum computing. It combines quantum emitters and linear-optical entangling gates to leverage the strength of both matter-based and photonic-based approaches. A key feature of the architecture is its practicality, grounded in the utilisation of experimentally proven optical components. Our framework enables the execution of any quantum error correcting code, but in particular maintains scalability for low-density parity check codes by exploiting built-in non-local connectivity through distant optical links. To gauge its efficiency, we evaluated the architecture using a physically motivated error model. It exhibits loss tolerance comparable to existing all-photonic architecture but without the need for intricate linear-optical resource-state-generation modules that conventionally rely on resource-intensive multiplexing. The versatility of the architecture also offers uncharted avenues for further advancing performance standards.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141755454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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