Pub Date : 2024-09-13DOI: 10.1103/physrevresearch.6.033296
Tobias M. R. Wolf, Chunli Huang
We report the successful adaptation of the quasi-boson approximation, a technique traditionally employed in nuclear physics, to the analysis of the two-dimensional electron gas. We show that the correlation energy estimated from this approximation agrees closely with the results obtained from quantum Monte Carlo simulations. Our methodology comprehensively incorporates the exchange self-energy, direct scattering, and exchange scattering for a particle-hole pair excited out of the mean-field ground state within the equation-of-motion framework. The linearization of the equation of motion leads to a generalized random phase approximation (gRPA) eigenvalue equation whose spectrum indicates that the plasmon dispersion remains unaffected by exchange effects, while the particle-hole continuum experiences a marked upward shift due to the exchange self-energy. Using the gRPA excitation spectrum, we calculate the zero-point energy of the quasi-boson Hamiltonian, thereby approximating the correlation energy of the original Hamiltonian. This research highlights the potential and effectiveness of applying the quasi-boson approximation to the gRPA spectrum, a fundamental technique in nuclear physics, to extended condensed matter systems.
{"title":"Quasi-boson approximation yields accurate correlation energy in the 2D electron gas","authors":"Tobias M. R. Wolf, Chunli Huang","doi":"10.1103/physrevresearch.6.033296","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.033296","url":null,"abstract":"We report the successful adaptation of the quasi-boson approximation, a technique traditionally employed in nuclear physics, to the analysis of the two-dimensional electron gas. We show that the correlation energy estimated from this approximation agrees closely with the results obtained from quantum Monte Carlo simulations. Our methodology comprehensively incorporates the exchange self-energy, direct scattering, and exchange scattering for a particle-hole pair excited out of the mean-field ground state within the equation-of-motion framework. The linearization of the equation of motion leads to a generalized random phase approximation (gRPA) eigenvalue equation whose spectrum indicates that the plasmon dispersion remains unaffected by exchange effects, while the particle-hole continuum experiences a marked upward shift due to the exchange self-energy. Using the gRPA excitation spectrum, we calculate the zero-point energy of the quasi-boson Hamiltonian, thereby approximating the correlation energy of the original Hamiltonian. This research highlights the potential and effectiveness of applying the quasi-boson approximation to the gRPA spectrum, a fundamental technique in nuclear physics, to extended condensed matter systems.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-13DOI: 10.1103/physrevresearch.6.033297
Jian Li, Mark T. Mitchison, Saulo V. Moreira
In slowly driven classical systems, work is a stochastic quantity and its probability distribution is known to satisfy the work fluctuation-dissipation relation, which states that the mean and variance of the dissipated work are linearly related. Recently, it was shown that generation of quantum coherence in the instantaneous energy eigenbasis leads to a correction to this linear relation in the slow-driving regime. Here, we go even further by investigating nonclassical features of work fluctuations in setups with more than one system. To do this, we first generalize slow control protocols to encompass multipartite systems, allowing for the generation of quantum correlations during the driving process. Then, focusing on two-qubit systems, we show that entanglement generation leads to a positive contribution to the dissipated work, which is distinct from the quantum correction due to local coherence generation known from previous work. Our results show that entanglement generated during slow control protocols, e.g., as an unavoidable consequence of qubit crosstalk, comes at the cost of increased dissipation.
{"title":"Entanglement signature in quantum work statistics in the slow-driving regime","authors":"Jian Li, Mark T. Mitchison, Saulo V. Moreira","doi":"10.1103/physrevresearch.6.033297","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.033297","url":null,"abstract":"In slowly driven classical systems, work is a stochastic quantity and its probability distribution is known to satisfy the work fluctuation-dissipation relation, which states that the mean and variance of the dissipated work are linearly related. Recently, it was shown that generation of quantum coherence in the instantaneous energy eigenbasis leads to a correction to this linear relation in the slow-driving regime. Here, we go even further by investigating nonclassical features of work fluctuations in setups with more than one system. To do this, we first generalize slow control protocols to encompass multipartite systems, allowing for the generation of quantum correlations during the driving process. Then, focusing on two-qubit systems, we show that entanglement generation leads to a positive contribution to the dissipated work, which is distinct from the quantum correction due to local coherence generation known from previous work. Our results show that entanglement generated during slow control protocols, e.g., as an unavoidable consequence of qubit crosstalk, comes at the cost of increased dissipation.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-13DOI: 10.1103/physrevresearch.6.033295
Ming Li, Juan José García-Ripoll, Tomás Ramos
We propose an efficient, scalable, and deterministic scheme to generate multiple indistinguishable photons over independent channels, on demand. Our design relies on multiple single-photon sources, each coupled to a waveguide, all interacting with a common cavity mode. The cavity synchronizes and triggers the simultaneous emission of one photon by each source, which are collected by the waveguides. In a state-of-the-art circuit QED implementation, this scheme supports the creation of single photons with purity, indistinguishability, and efficiency at rates of . We also discuss conditions to produce up to 100 photons simultaneously with generation rates of hundreds of kHz. This is orders of magnitude more efficient than previous demultiplexed sources for boson sampling and enables the realization of deterministic multiphoton sources and scalable quantum information processing with photons.
我们提出了一种高效、可扩展和确定性的方案，可根据需要通过独立信道产生多个无差别光子。我们的设计依赖于多个单光子源，每个单光子源都与波导耦合，并与一个共同的空腔模式相互作用。空腔同步触发每个光源同时发射一个光子，并由波导收集。在最先进的电路 QED 实现中，该方案支持以 ∼MHz 的速率产生纯度达 99%、无差别和高效率的单光子。我们还讨论了同时产生多达 100 个光子的条件，其产生率高达数百千赫兹。这比以前用于玻色子采样的解复用源的效率要高出几个数量级，并能实现确定性多光子源和可扩展的光子量子信息处理。
{"title":"Scalable multiphoton generation from cavity-synchronized single-photon sources","authors":"Ming Li, Juan José García-Ripoll, Tomás Ramos","doi":"10.1103/physrevresearch.6.033295","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.033295","url":null,"abstract":"We propose an efficient, scalable, and deterministic scheme to generate multiple indistinguishable photons over independent channels, on demand. Our design relies on multiple single-photon sources, each coupled to a waveguide, all interacting with a common cavity mode. The cavity synchronizes and triggers the simultaneous emission of one photon by each source, which are collected by the waveguides. In a state-of-the-art circuit QED implementation, this scheme supports the creation of single photons with <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>99</mn><mo>%</mo></mrow></math> purity, indistinguishability, and efficiency at rates of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mo>∼</mo><mspace width=\"0.16em\"></mspace><mi>MHz</mi></mrow></math>. We also discuss conditions to produce up to 100 photons simultaneously with generation rates of hundreds of kHz. This is orders of magnitude more efficient than previous demultiplexed sources for boson sampling and enables the realization of deterministic multiphoton sources and scalable quantum information processing with photons.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-12DOI: 10.1103/physrevresearch.6.l032063
Ang-Kun Wu, Siddhartha Sarkar, Xiaohan Wan, Kai Sun, Shi-Zeng Lin
The quantum metric of single-particle wave functions in topological flat bands plays a crucial role in determining the stability of fractional Chern insulating (FCI) states. Here, we unravel that the quantum metric causes the many-body Chern number of the FCI states to deviate sharply from the expected value associated with partial filling of the single-particle topological flat band. Furthermore, the variation of the quantum metric in momentum space induces band dispersion through interactions, affecting the stability of the FCI states. This causes a reentrant transition into the Fermi liquid from the FCI phase as the interaction strength increases.
{"title":"Quantum-metric-induced quantum Hall conductance inversion and reentrant transition in fractional Chern insulators","authors":"Ang-Kun Wu, Siddhartha Sarkar, Xiaohan Wan, Kai Sun, Shi-Zeng Lin","doi":"10.1103/physrevresearch.6.l032063","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.l032063","url":null,"abstract":"The quantum metric of single-particle wave functions in topological flat bands plays a crucial role in determining the stability of fractional Chern insulating (FCI) states. Here, we unravel that the quantum metric causes the many-body Chern number of the FCI states to deviate sharply from the expected value associated with partial filling of the single-particle topological flat band. Furthermore, the variation of the quantum metric in momentum space induces band dispersion through interactions, affecting the stability of the FCI states. This causes a reentrant transition into the Fermi liquid from the FCI phase as the interaction strength increases.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-12DOI: 10.1103/physrevresearch.6.033292
Le Bin Ho
We investigate how squeezing techniques can improve the measurement precision in multiphase quantum metrology. While these methods are well studied and effectively used in single-phase estimations, their usage in multiphase situations has yet to be examined. We fill this gap by investigating the mechanism of quantum enhancement in the multiphase scenarios. Our analysis provides theoretical and numerical insights into the optimal condition for achieving the quantum Cramér-Rao bound, helping us understand the potential and mechanism for quantum-enhanced multiphase estimations with squeezing. In this paper, we open possibilities for advancements in quantum metrology and sensing technologies.
{"title":"Squeezing-induced quantum-enhanced multiphase estimation","authors":"Le Bin Ho","doi":"10.1103/physrevresearch.6.033292","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.033292","url":null,"abstract":"We investigate how squeezing techniques can improve the measurement precision in multiphase quantum metrology. While these methods are well studied and effectively used in single-phase estimations, their usage in multiphase situations has yet to be examined. We fill this gap by investigating the mechanism of quantum enhancement in the multiphase scenarios. Our analysis provides theoretical and numerical insights into the optimal condition for achieving the quantum Cramér-Rao bound, helping us understand the potential and mechanism for quantum-enhanced multiphase estimations with squeezing. In this paper, we open possibilities for advancements in quantum metrology and sensing technologies.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-12DOI: 10.1103/physrevresearch.6.033290
Guoqing Tian, Ying Wu, Xin-You Lü
We theoretically predict a kind of power-law-exponential (PLE) dipole-dipole interaction between quantum emitters in a 1D waveguide QED system. This unconventional long-range interaction is the combination of power-law growth and exponential decay couplings. Applying the PLE interaction to a spin model, we uncover the rich many-body phases. Most remarkably, we find that the PLE interaction can induce the ordered and critical spiral phases. These spiral phases emerge from the strong frustration generated by the power-law factor of the PLE interaction; hence they are absent for other types of long-range interaction, e.g., pure exponential and power-law decay interactions. Our work is also applicable for the higher-dimensional systems. It fundamentally broadens the realm of many-body physics and has significant applications in quantum simulation of strongly correlated matter.
我们从理论上预测了一维波导 QED 系统中量子发射器之间的一种幂律-指数（PLE）偶极子-偶极子相互作用。这种非常规的长程相互作用是幂律增长耦合和指数衰减耦合的结合。将 PLE 相互作用应用于自旋模型，我们发现了丰富的多体相。最值得注意的是，我们发现 PLE 相互作用可以诱发有序的临界螺旋相。这些螺旋相产生于 PLE 相互作用的幂律因子产生的强挫折；因此，其他类型的长程相互作用，如纯指数和幂律衰变相互作用，都不存在这些螺旋相。我们的工作也适用于高维系统。它从根本上拓宽了多体物理学的领域，在强相关物质的量子模拟中有着重要应用。
{"title":"Power-law-exponential interaction induced quantum spiral phases","authors":"Guoqing Tian, Ying Wu, Xin-You Lü","doi":"10.1103/physrevresearch.6.033290","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.033290","url":null,"abstract":"We theoretically predict a kind of power-law-exponential (PLE) dipole-dipole interaction between quantum emitters in a 1D waveguide QED system. This unconventional long-range interaction is the combination of power-law growth and exponential decay couplings. Applying the PLE interaction to a spin model, we uncover the rich many-body phases. Most remarkably, we find that the PLE interaction can induce the ordered and critical spiral phases. These spiral phases emerge from the strong frustration generated by the power-law factor of the PLE interaction; hence they are absent for other types of long-range interaction, e.g., pure exponential and power-law decay interactions. Our work is also applicable for the higher-dimensional systems. It fundamentally broadens the realm of many-body physics and has significant applications in quantum simulation of strongly correlated matter.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-12DOI: 10.1103/physrevresearch.6.033286
Alexander Altland, Kun Woo Kim, Tobias Micklitz, Maedeh Rezaei, Julian Sonner, Jacobus J. M. Verbaarschot
Recently, the physics of many-body quantum chaotic systems close to their ground states has come under intensified scrutiny. Such studies are motivated by the emergence of model systems exhibiting chaotic fluctuations throughout the entire spectrum [the Sachdev-Ye-Kitaev (SYK) model being a renowned representative] as well as by the physics of holographic principles, which likewise unfold close to ground states. Interpreting the edge of the spectrum as a quantum critical point, here we combine a wide range of analytical and numerical methods to the identification and comprehensive description of two different universality classes: the near edge physics of “sparse” and the near edge of “dense” chaotic systems. The distinction lies in the ratio between the number of a system's random parameters and its Hilbert space dimension, which is exponentially small or algebraically small in the sparse and dense case, respectively. Notable representatives of the two classes are generic chaotic many-body models (sparse) and invariant random matrix ensembles or chaotic gravitational systems (dense). While the two families share identical spectral correlations at energy scales comparable to the level spacing, the density of states and its fluctuations near the edge are different. Considering the SYK model as a representative of the sparse class, we apply a combination of field theory and exact diagonalization to a detailed discussion of its edge spectrum. Conversely, Jackiw-Teitelboim gravity is our reference model for the dense class, where an analysis of the gravitational path integral and random matrix theory reveal universal differences to the sparse class, whose implications for the construction of holographic principles we discuss.
{"title":"Quantum chaos on edge","authors":"Alexander Altland, Kun Woo Kim, Tobias Micklitz, Maedeh Rezaei, Julian Sonner, Jacobus J. M. Verbaarschot","doi":"10.1103/physrevresearch.6.033286","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.033286","url":null,"abstract":"Recently, the physics of many-body quantum chaotic systems close to their ground states has come under intensified scrutiny. Such studies are motivated by the emergence of model systems exhibiting chaotic fluctuations throughout the entire spectrum [the Sachdev-Ye-Kitaev (SYK) model being a renowned representative] as well as by the physics of holographic principles, which likewise unfold close to ground states. Interpreting the edge of the spectrum as a quantum critical point, here we combine a wide range of analytical and numerical methods to the identification and comprehensive description of two different universality classes: the near edge physics of “sparse” and the near edge of “dense” chaotic systems. The distinction lies in the ratio between the number of a system's random parameters and its Hilbert space dimension, which is exponentially small or algebraically small in the sparse and dense case, respectively. Notable representatives of the two classes are generic chaotic many-body models (sparse) and invariant random matrix ensembles or chaotic gravitational systems (dense). While the two families share identical spectral correlations at energy scales comparable to the level spacing, the density of states and its fluctuations near the edge are different. Considering the SYK model as a representative of the sparse class, we apply a combination of field theory and exact diagonalization to a detailed discussion of its edge spectrum. Conversely, Jackiw-Teitelboim gravity is our reference model for the dense class, where an analysis of the gravitational path integral and random matrix theory reveal universal differences to the sparse class, whose implications for the construction of holographic principles we discuss.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-12DOI: 10.1103/physrevresearch.6.033289
Bruno Focassio, Gabriel R. Schleder, Adalberto Fazzio, Rodrigo B. Capaz, Pedro V. Lopes, Jaime Ferreira, Carsten Enderlein, Marcello B. Silva Neto
We investigate the topological phase transitions driven by band warping, , and a transverse magnetic field, , for three-dimensional Weyl semimetals. First, we use the Chern number as a mathematical tool to derive the topological phase diagram. Next, we associate each of the topological sectors to a given angular momentum state of a rotating wave packet. Then we show how the position of the Weyl nodes can be manipulated by a transverse external magnetic field that ultimately quenches the wave packet rotation, first partially and then completely, thus resulting in a sequence of field-induced topological phase transitions. Finally, we calculate the current-induced magnetization and the anomalous Hall conductivity of a prototypical warped Weyl material. Both observables reflect the topological transitions associated with the wave packet rotation and can help to identify the elusive 3D quantum anomalous Hall effect in three-dimensional, warped Weyl materials.
{"title":"Magnetic control of Weyl nodes and wave packets in three-dimensional warped semimetals","authors":"Bruno Focassio, Gabriel R. Schleder, Adalberto Fazzio, Rodrigo B. Capaz, Pedro V. Lopes, Jaime Ferreira, Carsten Enderlein, Marcello B. Silva Neto","doi":"10.1103/physrevresearch.6.033289","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.033289","url":null,"abstract":"We investigate the topological phase transitions driven by band warping, <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>λ</mi></math>, and a transverse magnetic field, <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>B</mi></math>, for three-dimensional Weyl semimetals. First, we use the Chern number as a mathematical tool to derive the topological <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>λ</mi><mo>×</mo><mi>B</mi></mrow></math> phase diagram. Next, we associate each of the topological sectors to a given angular momentum state of a rotating wave packet. Then we show how the position of the Weyl nodes can be manipulated by a transverse external magnetic field that ultimately quenches the wave packet rotation, first partially and then completely, thus resulting in a sequence of field-induced topological phase transitions. Finally, we calculate the current-induced magnetization and the anomalous Hall conductivity of a prototypical warped Weyl material. Both observables reflect the topological transitions associated with the wave packet rotation and can help to identify the elusive 3D quantum anomalous Hall effect in three-dimensional, warped Weyl materials.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-12DOI: 10.1103/physrevresearch.6.033285
Tatsuhiko N. Ikeda, Hideki Kono, Keisuke Fujii
Trotterization is the most common and convenient approximation method for Hamiltonian simulations on digital quantum computers, but estimating its error accurately is computationally difficult for large quantum systems. Here, we develop a method for measuring the Trotter error without ancillary qubits on quantum circuits by combining the - and -order () Trotterizations rather than consulting with mathematical error bounds. Using this method, we make Trotterization precision guaranteed, developing an algorithm named Trotter, in which the Trotter error at each time step is within an error tolerance preset for our purpose. Trotter is applicable to both time-independent and -dependent Hamiltonians, and it adaptively chooses almost the largest step size , which keeps quantum circuits shallowest, within the error tolerance. Benchmarking it in a quantum spin chain, we find the adaptively chosen to be about 10 times larger than that inferred from known upper bounds of Trotter errors.
{"title":"Measuring Trotter error and its application to precision-guaranteed Hamiltonian simulations","authors":"Tatsuhiko N. Ikeda, Hideki Kono, Keisuke Fujii","doi":"10.1103/physrevresearch.6.033285","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.033285","url":null,"abstract":"Trotterization is the most common and convenient approximation method for Hamiltonian simulations on digital quantum computers, but estimating its error accurately is computationally difficult for large quantum systems. Here, we develop a method for measuring the Trotter error without ancillary qubits on quantum circuits by combining the <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>m</mi><mtext>th</mtext></mrow></math>- and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>n</mi><mtext>th</mtext></mrow></math>-order (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>m</mi><mo><</mo><mi>n</mi></mrow></math>) Trotterizations rather than consulting with mathematical error bounds. Using this method, we make Trotterization precision guaranteed, developing an algorithm named Trotter<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mo>(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>)</mo></mrow></math>, in which the Trotter error at each time step is within an error tolerance <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>ε</mi></math> preset for our purpose. Trotter<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mo>(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>)</mo></mrow></math> is applicable to both time-independent and -dependent Hamiltonians, and it adaptively chooses almost the largest step size <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>δ</mi><mi>t</mi></mrow></math>, which keeps quantum circuits shallowest, within the error tolerance. Benchmarking it in a quantum spin chain, we find the adaptively chosen <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>δ</mi><mi>t</mi></mrow></math> to be about 10 times larger than that inferred from known upper bounds of Trotter errors.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211073","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-12DOI: 10.1103/physrevresearch.6.033284
P. Djorwé, M. Asjad, Y. Pennec, D. Dutykh, B. Djafari-Rouhani
We propose a scheme to enhance the sensitivity of non-Hermitian optomechanical mass sensors. The benchmark system consists of two coupled optomechanical systems where the mechanical resonators are mechanically coupled. The optical cavities are driven either by a blue-detuned or red-detuned laser to produce gain and loss, respectively. Moreover, the mechanical resonators are parametrically driven through the modulation of their spring constant. For a specific strength of the optical driving field and without parametric driving, the system features an exceptional point (EP). Any perturbation to the mechanical frequency (dissipation) induces a splitting (shifting) of the EP, which scales as the square root of the perturbation strength, resulting in a sensitivity-factor enhancement compared with conventional optomechanical sensors. The sensitivity enhancement induced by the shifting scenario is weak as compared to the one based on the splitting phenomenon. By switching on parametric driving, the sensitivity of both sensing schemes is greatly improved, yielding to a better performance of the sensor. We have also confirmed these results through an analysis of the output spectra and the transmissions of the optical cavities. In addition to enhancing EP sensitivity, our scheme also reveals nonlinear effects on sensing under splitting and shifting scenarios. This work sheds light on mechanisms of enhancing the sensitivity of non-Hermitian mass sensors, paving a way to improve sensors performance for better nanoparticles or pollutants detection and for water treatment.
我们提出了一种提高非ermitian 光电机械质量传感器灵敏度的方案。基准系统由两个耦合光机械系统组成，其中机械谐振器是机械耦合的。光腔由蓝色调谐或红色调谐激光器驱动，分别产生增益和损耗。此外，机械谐振器通过调制其弹簧常数进行参数驱动。对于特定强度的光驱动场，在没有参数驱动的情况下，系统会出现一个特殊点（EP）。对机械频率的任何扰动（耗散）都会引起 EP 的分裂（移动），其规模为扰动强度的平方根，从而使灵敏度系数比传统光机械传感器有所提高。与基于分裂现象的灵敏度增强相比，移位情况引起的灵敏度增强较弱。通过切换参数驱动，这两种传感方案的灵敏度都得到了极大提高，从而使传感器的性能更佳。我们还通过分析输出光谱和光腔的透射率证实了这些结果。除了提高 EP 灵敏度外，我们的方案还揭示了分光和移光情况下传感的非线性效应。这项工作揭示了提高非赫米提质量传感器灵敏度的机制，为提高传感器性能，更好地检测纳米粒子或污染物以及进行水处理铺平了道路。
{"title":"Parametrically enhancing sensor sensitivity at an exceptional point","authors":"P. Djorwé, M. Asjad, Y. Pennec, D. Dutykh, B. Djafari-Rouhani","doi":"10.1103/physrevresearch.6.033284","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.033284","url":null,"abstract":"We propose a scheme to enhance the sensitivity of non-Hermitian optomechanical mass sensors. The benchmark system consists of two coupled optomechanical systems where the mechanical resonators are mechanically coupled. The optical cavities are driven either by a blue-detuned or red-detuned laser to produce gain and loss, respectively. Moreover, the mechanical resonators are parametrically driven through the modulation of their spring constant. For a specific strength of the optical driving field and without parametric driving, the system features an exceptional point (EP). Any perturbation to the mechanical frequency (dissipation) induces a splitting (shifting) of the EP, which scales as the square root of the perturbation strength, resulting in a sensitivity-factor enhancement compared with conventional optomechanical sensors. The sensitivity enhancement induced by the shifting scenario is weak as compared to the one based on the splitting phenomenon. By switching on parametric driving, the sensitivity of both sensing schemes is greatly improved, yielding to a better performance of the sensor. We have also confirmed these results through an analysis of the output spectra and the transmissions of the optical cavities. In addition to enhancing EP sensitivity, our scheme also reveals nonlinear effects on sensing under splitting and shifting scenarios. This work sheds light on mechanisms of enhancing the sensitivity of non-Hermitian mass sensors, paving a way to improve sensors performance for better nanoparticles or pollutants detection and for water treatment.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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