Pub Date : 2024-08-27DOI: 10.1088/1751-8121/ad6f7f
Jorge Romero, Carlos A Velasquez, J David Vergara
This work introduces a geometrical object that generalizes the quantum geometric tensor; we call it N-bein. Analogous to the vielbein (orthonormal frame) used in the Cartan formalism, the N-bein behaves like a ‘square root’ of the quantum geometric tensor. Using it, we present a quantum geometric tensor of two states that measures the possibility of moving from one state to another after two consecutive parameter variations. This new tensor determines the commutativity of such variations through its anti-symmetric part. In addition, we define a connection different from the Berry connection, and combining it with the N-bein allows us to introduce a notion of torsion and curvature à la Cartan that satisfies the Bianchi identities. Moreover, the torsion coincides with the anti-symmetric part of the two-state quantum geometric tensor previously mentioned, and thus, it is related to the commutativity of the parameter variations. We also describe our formalism using differential forms and discuss the possible physical interpretations of the new geometrical objects. Furthermore, we define different gauge invariants constructed from the geometrical quantities introduced in this work, resulting in new physical observables. Finally, we present two examples to illustrate these concepts: a harmonic oscillator and a generalized oscillator, both immersed in an electric field. We found that the new tensors quantify correlations between quantum states that were unavailable by other methods.
{"title":"N-bein formalism for the parameter space of quantum geometry","authors":"Jorge Romero, Carlos A Velasquez, J David Vergara","doi":"10.1088/1751-8121/ad6f7f","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6f7f","url":null,"abstract":"This work introduces a geometrical object that generalizes the quantum geometric tensor; we call it <italic toggle=\"yes\">N</italic>-bein. Analogous to the vielbein (orthonormal frame) used in the Cartan formalism, the <italic toggle=\"yes\">N</italic>-bein behaves like a ‘square root’ of the quantum geometric tensor. Using it, we present a quantum geometric tensor of two states that measures the possibility of moving from one state to another after two consecutive parameter variations. This new tensor determines the commutativity of such variations through its anti-symmetric part. In addition, we define a connection different from the Berry connection, and combining it with the <italic toggle=\"yes\">N</italic>-bein allows us to introduce a notion of torsion and curvature à la Cartan that satisfies the Bianchi identities. Moreover, the torsion coincides with the anti-symmetric part of the two-state quantum geometric tensor previously mentioned, and thus, it is related to the commutativity of the parameter variations. We also describe our formalism using differential forms and discuss the possible physical interpretations of the new geometrical objects. Furthermore, we define different gauge invariants constructed from the geometrical quantities introduced in this work, resulting in new physical observables. Finally, we present two examples to illustrate these concepts: a harmonic oscillator and a generalized oscillator, both immersed in an electric field. We found that the new tensors quantify correlations between quantum states that were unavailable by other methods.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"6 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-08-27DOI: 10.1088/1751-8121/ad6d1e
Leonie Vollmar, Rick Bebon, Julia Schimpf, Bastian Flietel, Sirin Celiksoy, Carsten Sönnichsen, Aljaž Godec, Thorsten Hugel
Single-molecule experiments provide insight into the motion (conformational dynamics) of individual protein molecules. Usually, a well-defined but coarse-grained intramolecular coordinate is measured and subsequently analysed with the help of hidden Markov models to deduce the kinetics of protein conformational changes. Such approaches rely on the assumption that the microscopic dynamics of the protein evolve according to a Markov-jump process on some network. However, the manifestation and extent of memory in the dynamics of the observable strongly depends on the chosen underlying Markov model, which is generally not known and therefore can lead to misinterpretations. Here, we combine extensive single-molecule plasmon ruler experiments on the heat shock protein Hsp90, computer simulations, and theory to infer and quantify memory in a model-free fashion. Our analysis is based on the bare definition of non-Markovian behaviour and does not require any underlying model. In the case of Hsp90 probed by a plasmon ruler, the Markov assumption is found to be clearly and conclusively violated on timescales up to roughly 50 s, which corresponds roughly to ∼50% of the inferred correlation time of the signal. The extent of memory is striking and reaches biologically relevant timescales. This implies that memory effects penetrate even the slowest observed motions. We provide clear and reproducible guidelines on how to test for the presence and duration of memory in experimental single-molecule data.
{"title":"Model-free inference of memory in conformational dynamics of a multi-domain protein","authors":"Leonie Vollmar, Rick Bebon, Julia Schimpf, Bastian Flietel, Sirin Celiksoy, Carsten Sönnichsen, Aljaž Godec, Thorsten Hugel","doi":"10.1088/1751-8121/ad6d1e","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6d1e","url":null,"abstract":"Single-molecule experiments provide insight into the motion (conformational dynamics) of individual protein molecules. Usually, a well-defined but coarse-grained intramolecular coordinate is measured and subsequently analysed with the help of hidden Markov models to deduce the kinetics of protein conformational changes. Such approaches rely on the assumption that the microscopic dynamics of the protein evolve according to a Markov-jump process on some network. However, the manifestation and extent of memory in the dynamics of the observable strongly depends on the chosen underlying Markov model, which is generally not known and therefore can lead to misinterpretations. Here, we combine extensive single-molecule plasmon ruler experiments on the heat shock protein Hsp90, computer simulations, and theory to infer and quantify memory in a model-free fashion. Our analysis is based on the bare definition of non-Markovian behaviour and does not require any underlying model. In the case of Hsp90 probed by a plasmon ruler, the Markov assumption is found to be clearly and conclusively violated on timescales up to roughly 50 s, which corresponds roughly to ∼50% of the inferred correlation time of the signal. The extent of memory is striking and reaches biologically relevant timescales. This implies that memory effects penetrate even the slowest observed motions. We provide clear and reproducible guidelines on how to test for the presence and duration of memory in experimental single-molecule data.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"3 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-08-27DOI: 10.1088/1751-8121/ad6daf
Ahmet Burak Çatlı, Nathan Wiebe
We provide in this paper a concrete method for training a quantum neural network to maximize the relevant information about a property that is transmitted through the network. This is significant because it gives an operationally well founded quantity to optimize when training autoencoders for problems where the inputs and outputs are fully quantum. We provide a rigorous algorithm for computing the value of the quantum information bottleneck quantity within error ε that requires O(log2(1/ϵ)+1/δ2) queries to a purification of the input density operator if its spectrum is supported on {0}⋃[δ,1−δ] for δ > 0 and the kernels of the relevant density matrices are disjoint. We further provide algorithms for estimating the derivatives of the QIB function, showing that quantum neural networks can be trained efficiently using the QIB quantity given that the number of gradient steps required is polynomial.
{"title":"Training quantum neural networks using the quantum information bottleneck method","authors":"Ahmet Burak Çatlı, Nathan Wiebe","doi":"10.1088/1751-8121/ad6daf","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6daf","url":null,"abstract":"We provide in this paper a concrete method for training a quantum neural network to maximize the relevant information about a property that is transmitted through the network. This is significant because it gives an operationally well founded quantity to optimize when training autoencoders for problems where the inputs and outputs are fully quantum. We provide a rigorous algorithm for computing the value of the quantum information bottleneck quantity within error <italic toggle=\"yes\">ε</italic> that requires <inline-formula>\u0000<tex-math><?CDATA $O(log^2(1/epsilon) + 1/delta^2)$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi>O</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msup><mml:mi>log</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo></mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>ϵ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msup><mml:mi>δ</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"aad6dafieqn1.gif\"></inline-graphic></inline-formula> queries to a purification of the input density operator if its spectrum is supported on <inline-formula>\u0000<tex-math><?CDATA ${0}~bigcup ~[delta,1-delta]$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mo fence=\"false\" stretchy=\"false\">{</mml:mo><mml:mn>0</mml:mn><mml:mo fence=\"false\" stretchy=\"false\">}</mml:mo><mml:mtext> </mml:mtext><mml:mo>⋃</mml:mo><mml:mtext> </mml:mtext><mml:mo stretchy=\"false\">[</mml:mo><mml:mi>δ</mml:mi><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>δ</mml:mi><mml:mo stretchy=\"false\">]</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"aad6dafieqn2.gif\"></inline-graphic></inline-formula> for <italic toggle=\"yes\">δ</italic> > 0 and the kernels of the relevant density matrices are disjoint. We further provide algorithms for estimating the derivatives of the QIB function, showing that quantum neural networks can be trained efficiently using the QIB quantity given that the number of gradient steps required is polynomial.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"1965 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-08-27DOI: 10.1088/1751-8121/ad6f7b
Wolter Groenevelt, Carel Wagenaar
In this paper, a generalized version of dynamic asymmetric simple exclusion process (ASEP) is introduced, and it is shown that the process has a Markov duality property with the same process on the reversed lattice. The duality functions are multivariate q-Racah polynomials, and the corresponding orthogonality measure is the reversible measure of the process. By taking limits in the generator of dynamic ASEP, its reversible measure, and the duality functions, we obtain orthogonal and triangular dualities for several other interacting particle systems. In this sense, the duality of dynamic ASEP sits on top of a hierarchy of many dualities. For the construction of the process, we rely on representation theory of the quantum algebra Uq(sl2). In the standard representation, the generator of generalized ASEP can be constructed from the coproduct of the Casimir. After a suitable change of representation, we obtain the generator of dynamic ASEP. The corresponding intertwiner is constructed from q-Krawtchouk polynomials, which arise as eigenfunctions of twisted primitive elements. This gives a duality between dynamic ASEP and generalized ASEP with q-Krawtchouk polynomials as duality functions. Using this duality, we show the (almost) self-duality of dynamic ASEP.
{"title":"A generalized dynamic asymmetric exclusion process: orthogonal dualities and degenerations","authors":"Wolter Groenevelt, Carel Wagenaar","doi":"10.1088/1751-8121/ad6f7b","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6f7b","url":null,"abstract":"In this paper, a generalized version of dynamic asymmetric simple exclusion process (ASEP) is introduced, and it is shown that the process has a Markov duality property with the same process on the reversed lattice. The duality functions are multivariate <italic toggle=\"yes\">q</italic>-Racah polynomials, and the corresponding orthogonality measure is the reversible measure of the process. By taking limits in the generator of dynamic ASEP, its reversible measure, and the duality functions, we obtain orthogonal and triangular dualities for several other interacting particle systems. In this sense, the duality of dynamic ASEP sits on top of a hierarchy of many dualities. For the construction of the process, we rely on representation theory of the quantum algebra <inline-formula>\u0000<tex-math><?CDATA $mathcal U_q(mathfrak{sl}_2)$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:msub><mml:mrow><mml:mi>U</mml:mi></mml:mrow><mml:mi>q</mml:mi></mml:msub><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"fraktur\">sl</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"aad6f7bieqn1.gif\"></inline-graphic></inline-formula>. In the standard representation, the generator of generalized ASEP can be constructed from the coproduct of the Casimir. After a suitable change of representation, we obtain the generator of dynamic ASEP. The corresponding intertwiner is constructed from <italic toggle=\"yes\">q</italic>-Krawtchouk polynomials, which arise as eigenfunctions of twisted primitive elements. This gives a duality between dynamic ASEP and generalized ASEP with <italic toggle=\"yes\">q</italic>-Krawtchouk polynomials as duality functions. Using this duality, we show the (almost) self-duality of dynamic ASEP.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"50 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-08-27DOI: 10.1088/1751-8121/ad6f7a
Alexander Osterkorn, Stefan Kehrein
We study the nonequilibrium dynamics after an interaction quench in the two-dimensional Hubbard model using the recently introduced fermionic truncated Wigner approximation (fTWA). To assess the range of validity of the method in a systematic way, we consider the SU(N) Hubbard model with the fermion degeneracy N as a natural semiclassical expansion parameter. Using both a numerical and a perturbative analytical approach we show that fTWA is exact at least up to and including the prethermalization dynamics. We discuss the limitations of the method beyond this regime.
我们利用最近引入的费米子截断维纳近似（fTWA）研究了二维哈伯德模型中相互作用淬火后的非平衡动力学。为了系统地评估该方法的有效范围，我们考虑了以费米子退变性 N 作为自然半经典扩展参数的 SU(N) Hubbard 模型。利用数值和微扰分析方法，我们证明了 fTWA 至少在热化前动力学（包括热化前动力学）之前是精确的。我们讨论了该方法在这一机制之外的局限性。
{"title":"Systematic large flavor fTWA approach to interaction quenches in the Hubbard model","authors":"Alexander Osterkorn, Stefan Kehrein","doi":"10.1088/1751-8121/ad6f7a","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6f7a","url":null,"abstract":"We study the nonequilibrium dynamics after an interaction quench in the two-dimensional Hubbard model using the recently introduced fermionic truncated Wigner approximation (fTWA). To assess the range of validity of the method in a systematic way, we consider the SU(<italic toggle=\"yes\">N</italic>) Hubbard model with the fermion degeneracy <italic toggle=\"yes\">N</italic> as a natural semiclassical expansion parameter. Using both a numerical and a perturbative analytical approach we show that fTWA is exact at least up to and including the prethermalization dynamics. We discuss the limitations of the method beyond this regime.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"27 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-08-27DOI: 10.1088/1751-8121/ad6f7e
Ginestra Bianconi
We propose a theory for coupling matter fields with discrete geometry on higher-order networks, i.e. cell complexes. The key idea of the approach is to associate to a higher-order network the quantum entropy of its metric. Specifically we propose an action having two contributions. The first contribution is proportional to the logarithm of the volume associated to the higher-order network by the metric. In the vacuum this contribution determines the entropy of the geometry. The second contribution is the quantum relative entropy between the metric of the higher-order network and the metric induced by the matter and gauge fields. The induced metric is defined in terms of the topological spinors and the discrete Dirac operators. The topological spinors, defined on nodes, edges and higher-dimensional cells, encode for the matter fields. The discrete Dirac operators act on topological spinors, and depend on the metric of the higher-order network as well as on the gauge fields via a discrete version of the minimal substitution. We derive the coupled dynamical equations for the metric, the matter and the gauge fields, providing an information theory principle to obtain the field theory equations in discrete curved space.
{"title":"Quantum entropy couples matter with geometry","authors":"Ginestra Bianconi","doi":"10.1088/1751-8121/ad6f7e","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6f7e","url":null,"abstract":"We propose a theory for coupling matter fields with discrete geometry on higher-order networks, i.e. cell complexes. The key idea of the approach is to associate to a higher-order network the quantum entropy of its metric. Specifically we propose an action having two contributions. The first contribution is proportional to the logarithm of the volume associated to the higher-order network by the metric. In the vacuum this contribution determines the entropy of the geometry. The second contribution is the quantum relative entropy between the metric of the higher-order network and the metric induced by the matter and gauge fields. The induced metric is defined in terms of the topological spinors and the discrete Dirac operators. The topological spinors, defined on nodes, edges and higher-dimensional cells, encode for the matter fields. The discrete Dirac operators act on topological spinors, and depend on the metric of the higher-order network as well as on the gauge fields via a discrete version of the minimal substitution. We derive the coupled dynamical equations for the metric, the matter and the gauge fields, providing an information theory principle to obtain the field theory equations in discrete curved space.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"42 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-08-22DOI: 10.1088/1751-8121/ad6cb7
Oğul Esen, Ayten Gezici, Hasan Gümral
We present the locally conformal generalization of the Euler–Lagrange equations. We determine the dual space of the LCS Hamiltonian vector fields. Within this dual space, we formulate the Lie–Poisson equation that governs the kinetic motion of Hamiltonian systems in the context of local conformality. By expressing the Lie–Poisson dynamics in terms of density functions, we derive locally conformal Vlasov dynamics. In addition, we outline a geometric pathway that connects LCS Hamiltonian particle motion to locally conformal kinetic motion.
{"title":"Variational aspect and kinetic theory of locally conformal dynamics","authors":"Oğul Esen, Ayten Gezici, Hasan Gümral","doi":"10.1088/1751-8121/ad6cb7","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6cb7","url":null,"abstract":"We present the locally conformal generalization of the Euler–Lagrange equations. We determine the dual space of the LCS Hamiltonian vector fields. Within this dual space, we formulate the Lie–Poisson equation that governs the kinetic motion of Hamiltonian systems in the context of local conformality. By expressing the Lie–Poisson dynamics in terms of density functions, we derive locally conformal Vlasov dynamics. In addition, we outline a geometric pathway that connects LCS Hamiltonian particle motion to locally conformal kinetic motion.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"36 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-08-22DOI: 10.1088/1751-8121/ad6c04
Pablo Fernández, Miguel A Martin-Delgado
We introduce a class of circuits that solve a particular case of the Bernstein–Vazirani recursive problem for second-level recursion. This class of circuits allows for the implementation of the oracle using a number of T-gates that grows linearly with the number of qubits in the problem. We find an application of this scheme to quantum homomorphic encryption (QHE), which is an important cryptographic technology useful for delegated quantum computing, allowing a remote server to perform quantum computations on encrypted quantum data, so that the server cannot know anything about the client’s data. Liang’s QHE schemes are suitable for circuits with a polynomial number of gates T/T†. Thus, the simplified circuits we have constructed can be evaluated homomorphically in an efficient manner.
我们介绍了一类电路，它能解决伯恩斯坦-瓦齐拉尼递归问题的一个特殊情况，即二级递归问题。这一类电路允许使用与问题中的量子比特数呈线性增长的 T 门来实现神谕。我们发现这一方案在量子同态加密（QHE）中的应用，QHE 是一种重要的加密技术，可用于委托量子计算，允许远程服务器对加密的量子数据进行量子计算，这样服务器就无法知道客户数据的任何信息。梁的 QHE 方案适用于具有多项式门数 T/T† 的电路。因此，我们构建的简化电路可以高效地进行同态评估。
{"title":"Homomorphic encryption of the k=2 Bernstein–Vazirani algorithm","authors":"Pablo Fernández, Miguel A Martin-Delgado","doi":"10.1088/1751-8121/ad6c04","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6c04","url":null,"abstract":"We introduce a class of circuits that solve a particular case of the Bernstein–Vazirani recursive problem for second-level recursion. This class of circuits allows for the implementation of the oracle using a number of <italic toggle=\"yes\">T</italic>-gates that grows linearly with the number of qubits in the problem. We find an application of this scheme to quantum homomorphic encryption (QHE), which is an important cryptographic technology useful for delegated quantum computing, allowing a remote server to perform quantum computations on encrypted quantum data, so that the server cannot know anything about the client’s data. Liang’s QHE schemes are suitable for circuits with a polynomial number of gates <inline-formula>\u0000<tex-math><?CDATA $T/T,^{dagger}$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi>T</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>T</mml:mi><mml:msup><mml:mstyle scriptlevel=\"0\"></mml:mstyle><mml:mrow><mml:mo>†</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math><inline-graphic xlink:href=\"aad6c04ieqn1.gif\"></inline-graphic></inline-formula>. Thus, the simplified circuits we have constructed can be evaluated homomorphically in an efficient manner.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"66 1 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-08-21DOI: 10.1088/1751-8121/ad6ab7
Yuta Sakamoto, Takahiro Sakaue
Statistics of stochastic processes are crucially influenced by the boundary conditions. In one spatial dimension, for example, the first passage time distribution in semi-infinite space (one absorbing boundary) is markedly different from that in a finite interval with two absorbing boundaries. Here, we propose a method, which we refer to as a method of filtration, that allows us to construct the latter from only the knowledge of the former. We demonstrate that our method yields two solution forms, a method of eigenfunction expansion-like form and a method of image-like form. In particular, we argue that the latter solution form is a generalization of the method of image applicable to a stochastic process for which the method of image generally does not work, e.g. the Ornstein–Uhlenbeck process.
{"title":"Method of filtration in first passage time problems","authors":"Yuta Sakamoto, Takahiro Sakaue","doi":"10.1088/1751-8121/ad6ab7","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6ab7","url":null,"abstract":"Statistics of stochastic processes are crucially influenced by the boundary conditions. In one spatial dimension, for example, the first passage time distribution in semi-infinite space (one absorbing boundary) is markedly different from that in a finite interval with two absorbing boundaries. Here, we propose a method, which we refer to as a method of filtration, that allows us to construct the latter from only the knowledge of the former. We demonstrate that our method yields two solution forms, a method of eigenfunction expansion-like form and a method of image-like form. In particular, we argue that the latter solution form is a generalization of the method of image applicable to a stochastic process for which the method of image generally does not work, e.g. the Ornstein–Uhlenbeck process.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"392 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-08-21DOI: 10.1088/1751-8121/ad6c00
M Avendaño-Camacho, J C Ruíz-Pantaleón, Yu Vorobiev
In the context of averaging method, we describe a reconstruction of invariant connection-dependent Poisson structures from canonical actions of compact Lie groups on fibered phase spaces. Some symmetry properties of Wong’s type equations are derived from the main results.
{"title":"On gauge Poisson brackets with prescribed symmetry","authors":"M Avendaño-Camacho, J C Ruíz-Pantaleón, Yu Vorobiev","doi":"10.1088/1751-8121/ad6c00","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6c00","url":null,"abstract":"In the context of averaging method, we describe a reconstruction of invariant connection-dependent Poisson structures from canonical actions of compact Lie groups on fibered phase spaces. Some symmetry properties of Wong’s type equations are derived from the main results.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"44 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：