Pub Date : 2024-08-06DOI: 10.1103/prxquantum.5.030324
Niyaz R. Beysengulov, Øyvind S. Schøyen, Stian D. Bilek, Jonas B. Flaten, Oskar Leinonen, Morten Hjorth-Jensen, Johannes Pollanen, Håkon Emil Kristiansen, Zachary J. Stewart, Jared D. Weidman, Angela K. Wilson
The generation and evolution of entanglement in many-body systems is an active area of research that spans multiple fields, from quantum information science to the simulation of quantum many-body systems encountered in condensed matter, subatomic physics, and quantum chemistry. Motivated by recent experiments exploring quantum information processing systems with electrons trapped above the surface of cryogenic noble gas substrates, we theoretically investigate the generation of motional entanglement between two electrons via their unscreened Coulomb interaction. The model system consists of two electrons confined in separate electrostatic traps that establish microwave-frequency quantized states of their motion. We compute the motional energy spectra of the electrons, as well as their entanglement, by diagonalizing the model Hamiltonian with respect to a single-particle Hartree product basis. We also compare our results with the predictions of an effective Hamiltonian. The computational procedure outlined here can be employed for device design and guidance of experimental implementations. In particular, the theoretical tools developed here can be used for fine-tuning and optimization of control parameters in future experiments with electrons trapped above the surface of superfluid helium or solid neon.
{"title":"Coulomb Interaction-Driven Entanglement of Electrons on Helium","authors":"Niyaz R. Beysengulov, Øyvind S. Schøyen, Stian D. Bilek, Jonas B. Flaten, Oskar Leinonen, Morten Hjorth-Jensen, Johannes Pollanen, Håkon Emil Kristiansen, Zachary J. Stewart, Jared D. Weidman, Angela K. Wilson","doi":"10.1103/prxquantum.5.030324","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030324","url":null,"abstract":"The generation and evolution of entanglement in many-body systems is an active area of research that spans multiple fields, from quantum information science to the simulation of quantum many-body systems encountered in condensed matter, subatomic physics, and quantum chemistry. Motivated by recent experiments exploring quantum information processing systems with electrons trapped above the surface of cryogenic noble gas substrates, we theoretically investigate the generation of <i>motional</i> entanglement between two electrons via their unscreened Coulomb interaction. The model system consists of two electrons confined in separate electrostatic traps that establish microwave-frequency quantized states of their motion. We compute the motional energy spectra of the electrons, as well as their entanglement, by diagonalizing the model Hamiltonian with respect to a single-particle Hartree product basis. We also compare our results with the predictions of an effective Hamiltonian. The computational procedure outlined here can be employed for device design and guidance of experimental implementations. In particular, the theoretical tools developed here can be used for fine-tuning and optimization of control parameters in future experiments with electrons trapped above the surface of superfluid helium or solid neon.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933018","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 : 2024-08-06DOI: 10.1103/prxquantum.5.030325
Albert Cabot, Gian Luca Giorgi, Roberta Zambrini
We show a dissipative phase transition in a driven nonlinear quantum oscillator in which a discrete time-translation symmetry is spontaneously broken in two different ways. The corresponding regimes display either discrete or incommensurate time-crystal order, which we analyze numerically and analytically beyond the classical limit, addressing observable dynamics, phenomenology in different (laboratory and rotating) frames, Liouvillian spectral features, and quantum fluctuations. Via an effective semiclassical description, we show that phase diffusion dominates in the incommensurate time crystal (or continuous time crystal in the rotating frame), which manifests as a band of eigenmodes with a lifetime growing linearly with the mean-field excitation number. Instead, in the discrete time-crystal phase, the leading fluctuation process corresponds to quantum activation with a single mode that has an exponentially growing lifetime. Interestingly, the transition between these two regimes manifests itself already in the quantum regime as a spectral singularity, namely, as an exceptional point mediating between phase diffusion and quantum activation. Finally, we discuss this transition between different time-crystal orders in the context of synchronization phenomena.
{"title":"Nonequilibrium Transition between Dissipative Time Crystals","authors":"Albert Cabot, Gian Luca Giorgi, Roberta Zambrini","doi":"10.1103/prxquantum.5.030325","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030325","url":null,"abstract":"We show a dissipative phase transition in a driven nonlinear quantum oscillator in which a discrete time-translation symmetry is spontaneously broken in two different ways. The corresponding regimes display either discrete or incommensurate time-crystal order, which we analyze numerically and analytically beyond the classical limit, addressing observable dynamics, phenomenology in different (laboratory and rotating) frames, Liouvillian spectral features, and quantum fluctuations. Via an effective semiclassical description, we show that phase diffusion dominates in the incommensurate time crystal (or continuous time crystal in the rotating frame), which manifests as a band of eigenmodes with a lifetime growing linearly with the mean-field excitation number. Instead, in the discrete time-crystal phase, the leading fluctuation process corresponds to quantum activation with a single mode that has an exponentially growing lifetime. Interestingly, the transition between these two regimes manifests itself already in the quantum regime as a spectral singularity, namely, as an exceptional point mediating between phase diffusion and quantum activation. Finally, we discuss this transition between different time-crystal orders in the context of synchronization phenomena.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"2018 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933015","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 : 2024-08-05DOI: 10.1103/prxquantum.5.037001
Alberto Di Meglioet al.
Quantum computers offer an intriguing path for a paradigmatic change of computing in the natural sciences and beyond, with the potential for achieving a so-called quantum advantage—namely, a significant (in some cases exponential) speedup of numerical simulations. The rapid development of hardware devices with various realizations of qubits enables the execution of small-scale but representative applications on quantum computers. In particular, the high-energy physics community plays a pivotal role in accessing the power of quantum computing, since the field is a driving source for challenging computational problems. This concerns, on the theoretical side, the exploration of models that are very hard or even impossible to address with classical techniques and, on the experimental side, the enormous data challenge of newly emerging experiments, such as the upgrade of the Large Hadron Collider. In this Roadmap paper, led by CERN, DESY, and IBM, we provide the status of high-energy physics quantum computations and give examples of theoretical and experimental target benchmark applications, which can be addressed in the near future. Having in mind hardware with about 100 qubits capable of executing several thousand two-qubit gates, where possible, we also provide resource estimates for the examples given using error-mitigated quantum computing. The ultimate declared goal of this task force is therefore to trigger further research in the high-energy physics community to develop interesting use cases for demonstrations on near-term quantum computers.
量子计算机为自然科学及其他领域的计算模式变革提供了一条引人入胜的道路，有可能实现所谓的量子优势--即显著（在某些情况下呈指数级）加快数值模拟的速度。配备各种量子比特的硬件设备的快速发展，使得在量子计算机上执行小规模但具有代表性的应用成为可能。特别是，高能物理界在利用量子计算能力方面发挥着举足轻重的作用，因为该领域是挑战性计算问题的驱动源。在理论方面，这涉及对经典技术很难甚至不可能解决的模型的探索；在实验方面，新出现的实验（如大型强子对撞机的升级）所带来的巨大数据挑战。在这篇由欧洲核子研究中心、DESY 和 IBM 领导的路线图论文中，我们介绍了高能物理量子计算的现状，并举例说明了理论和实验目标基准应用，这些都可以在不久的将来解决。考虑到硬件约有 100 量子位，能够执行几千个双量子位门，我们还尽可能为使用误差缓解量子计算的示例提供资源估算。因此，本工作组宣布的最终目标是引发高能物理界的进一步研究，为近期量子计算机的演示开发有趣的用例。
{"title":"Quantum Computing for High-Energy Physics: State of the Art and Challenges","authors":"Alberto Di Meglioet al.","doi":"10.1103/prxquantum.5.037001","DOIUrl":"https://doi.org/10.1103/prxquantum.5.037001","url":null,"abstract":"Quantum computers offer an intriguing path for a paradigmatic change of computing in the natural sciences and beyond, with the potential for achieving a so-called quantum advantage—namely, a significant (in some cases exponential) speedup of numerical simulations. The rapid development of hardware devices with various realizations of qubits enables the execution of small-scale but representative applications on quantum computers. In particular, the high-energy physics community plays a pivotal role in accessing the power of quantum computing, since the field is a driving source for challenging computational problems. This concerns, on the theoretical side, the exploration of models that are very hard or even impossible to address with classical techniques and, on the experimental side, the enormous data challenge of newly emerging experiments, such as the upgrade of the Large Hadron Collider. In this Roadmap paper, led by CERN, DESY, and IBM, we provide the status of high-energy physics quantum computations and give examples of theoretical and experimental target benchmark applications, which can be addressed in the near future. Having in mind hardware with about 100 qubits capable of executing several thousand two-qubit gates, where possible, we also provide resource estimates for the examples given using error-mitigated quantum computing. The ultimate declared goal of this task force is therefore to trigger further research in the high-energy physics community to develop interesting use cases for demonstrations on near-term quantum computers.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933017","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 : 2024-08-05DOI: 10.1103/prxquantum.5.030323
Kévin Hémery, Khaldoon Ghanem, Eleanor Crane, Sara L. Campbell, Joan M. Dreiling, Caroline Figgatt, Cameron Foltz, John P. Gaebler, Jacob Johansen, Michael Mills, Steven A. Moses, Juan M. Pino, Anthony Ransford, Mary Rowe, Peter Siegfried, Russell P. Stutz, Henrik Dreyer, Alexander Schuckert, Ramil Nigmatullin
Calculating the equilibrium properties of condensed-matter systems is one of the promising applications of near-term quantum computing. Recently, hybrid quantum-classical time-series algorithms have been proposed to efficiently extract these properties from a measurement of the Loschmidt amplitude from initial states and a time evolution under the Hamiltonian up to short times . In this work, we study the operation of this algorithm on a present-day quantum computer. Specifically, we measure the Loschmidt amplitude for the Fermi-Hubbard model on a -site ladder geometry (32 orbitals) on the Quantinuum H2-1 trapped-ion device. We assess the effect of noise on the Loschmidt amplitude and implement algorithm-specific error-mitigation techniques. By using a thus-motivated error model, we numerically analyze the influence of noise on the full operation of the quantum-classical algorithm by measuring expectation values of local observables at finite energies. Finally, we estimate the resources needed for scaling up the algorithm.
{"title":"Measuring the Loschmidt Amplitude for Finite-Energy Properties of the Fermi-Hubbard Model on an Ion-Trap Quantum Computer","authors":"Kévin Hémery, Khaldoon Ghanem, Eleanor Crane, Sara L. Campbell, Joan M. Dreiling, Caroline Figgatt, Cameron Foltz, John P. Gaebler, Jacob Johansen, Michael Mills, Steven A. Moses, Juan M. Pino, Anthony Ransford, Mary Rowe, Peter Siegfried, Russell P. Stutz, Henrik Dreyer, Alexander Schuckert, Ramil Nigmatullin","doi":"10.1103/prxquantum.5.030323","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030323","url":null,"abstract":"Calculating the equilibrium properties of condensed-matter systems is one of the promising applications of near-term quantum computing. Recently, hybrid quantum-classical time-series algorithms have been proposed to efficiently extract these properties from a measurement of the Loschmidt amplitude <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo fence=\"false\" stretchy=\"false\">⟨</mo><mi>ψ</mi><mrow><mo stretchy=\"false\">|</mo></mrow><msup><mi>e</mi><mrow><mo>−</mo><mi>i</mi><mrow><mover><mi>H</mi><mo stretchy=\"false\">^</mo></mover></mrow><mi>t</mi></mrow></msup><mrow><mo stretchy=\"false\">|</mo></mrow><mi>ψ</mi><mo fence=\"false\" stretchy=\"false\">⟩</mo></math> from initial states <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mo stretchy=\"false\">|</mo></mrow><mi>ψ</mi><mo fence=\"false\" stretchy=\"false\">⟩</mo></math> and a time evolution under the Hamiltonian <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mover><mi>H</mi><mo stretchy=\"false\">^</mo></mover></mrow></math> up to short times <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>t</mi></math>. In this work, we study the operation of this algorithm on a present-day quantum computer. Specifically, we measure the Loschmidt amplitude for the Fermi-Hubbard model on a <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>16</mn></math>-site ladder geometry (32 orbitals) on the Quantinuum H2-1 trapped-ion device. We assess the effect of noise on the Loschmidt amplitude and implement algorithm-specific error-mitigation techniques. By using a thus-motivated error model, we numerically analyze the influence of noise on the full operation of the quantum-classical algorithm by measuring expectation values of local observables at finite energies. Finally, we estimate the resources needed for scaling up the algorithm.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141932970","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}
Hybridizing different degrees of freedom or physical platforms potentially offers various advantages in building scalable quantum architectures. Here, we introduce a fault-tolerant hybrid quantum computation by building on the advantages of both discrete-variable (DV) and continuous-variable (CV) systems. In particular, we define a CV-DV hybrid qubit with a bosonic cat code and a single photon, which is implementable in current photonic platforms. Due to the cat code encoded in the CV part, the predominant loss errors are readily correctable without multiqubit encoding, while the logical basis is inherently orthogonal due to the DV part. We design fault-tolerant architectures by concatenating hybrid qubits and an outer DV quantum error-correction code such as a topological code, exploring their potential merit in developing scalable quantum computation. We demonstrate by numerical simulations that our scheme is at least an order of magnitude more resource efficient compared to all previous proposals in photonic platforms, allowing us to achieve a record-high loss threshold among existing CV and hybrid approaches. We discuss the realization of our approach not only in all-photonic platforms but also in other hybrid platforms including superconducting and trapped-ion systems, which allows us to find various efficient routes toward fault-tolerant quantum computing.
混合使用不同的自由度或物理平台可能为构建可扩展的量子架构提供各种优势。在这里，我们利用离散变量（DV）和连续变量（CV）系统的优势，介绍了一种容错混合量子计算。特别是，我们定义了一种具有玻色猫码和单光子的 CV-DV 混合量子比特，它可以在当前的光子平台上实现。由于猫码编码在 CV 部分，主要的损耗错误无需多量子比特编码即可轻松纠正，而由于 DV 部分，逻辑基础本质上是正交的。我们通过串联混合量子比特和外层 DV 量子纠错码（如拓扑码）来设计容错架构，探索它们在开发可扩展量子计算中的潜在优势。我们通过数值模拟证明，与之前在光子平台上提出的所有建议相比，我们的方案至少提高了一个数量级的资源效率，使我们在现有的 CV 和混合方法中达到了创纪录的高损耗阈值。我们不仅讨论了在全光子平台上实现我们的方法，还讨论了在其他混合平台（包括超导和俘获离子系统）上实现我们的方法，这使我们能够找到实现容错量子计算的各种高效途径。
{"title":"Fault-Tolerant Quantum Computation by Hybrid Qubits with Bosonic Cat Code and Single Photons","authors":"Jaehak Lee, Nuri Kang, Seok-Hyung Lee, Hyunseok Jeong, Liang Jiang, Seung-Woo Lee","doi":"10.1103/prxquantum.5.030322","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030322","url":null,"abstract":"Hybridizing different degrees of freedom or physical platforms potentially offers various advantages in building scalable quantum architectures. Here, we introduce a fault-tolerant hybrid quantum computation by building on the advantages of both discrete-variable (DV) and continuous-variable (CV) systems. In particular, we define a CV-DV hybrid qubit with a bosonic cat code and a single photon, which is implementable in current photonic platforms. Due to the cat code encoded in the CV part, the predominant loss errors are readily correctable without multiqubit encoding, while the logical basis is inherently orthogonal due to the DV part. We design fault-tolerant architectures by concatenating hybrid qubits and an outer DV quantum error-correction code such as a topological code, exploring their potential merit in developing scalable quantum computation. We demonstrate by numerical simulations that our scheme is at least an order of magnitude more resource efficient compared to all previous proposals in photonic platforms, allowing us to achieve a record-high loss threshold among existing CV and hybrid approaches. We discuss the realization of our approach not only in all-photonic platforms but also in other hybrid platforms including superconducting and trapped-ion systems, which allows us to find various efficient routes toward fault-tolerant quantum computing.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141882260","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 : 2024-08-01DOI: 10.1103/prxquantum.5.030321
M.C. Smith, A.D. Leu, M.F. Gely, D.M. Lucas
A leading approach to implementing small-scale quantum computers has been to use laser beams, focused to micron spot sizes, to address and entangle trapped ions in a linear crystal. Here we propose a method to implement individually addressed entangling gate interactions, but driven by microwave fields, with a spatial resolution of a few microns, corresponding to microwave wavelengths. We experimentally demonstrate the ability to suppress the effect of the state-dependent force using a single ion, and find the required interaction introduces error per emulated gate in a single-qubit benchmarking sequence. We model the scheme for a 17-qubit ion crystal, and find that any pair of ions should be addressable with an average crosstalk error of approximately .
{"title":"Individually Addressed Quantum Gate Interactions Using Dynamical Decoupling","authors":"M.C. Smith, A.D. Leu, M.F. Gely, D.M. Lucas","doi":"10.1103/prxquantum.5.030321","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030321","url":null,"abstract":"A leading approach to implementing small-scale quantum computers has been to use laser beams, focused to micron spot sizes, to address and entangle trapped ions in a linear crystal. Here we propose a method to implement individually addressed entangling gate interactions, but driven by microwave fields, with a spatial resolution of a few microns, corresponding to <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math> microwave wavelengths. We experimentally demonstrate the ability to suppress the effect of the state-dependent force using a single ion, and find the required interaction introduces <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>3.7</mn><mo stretchy=\"false\">(</mo><mn>4</mn><mo stretchy=\"false\">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math> error per emulated gate in a single-qubit benchmarking sequence. We model the scheme for a 17-qubit ion crystal, and find that any pair of ions should be addressable with an average crosstalk error of approximately <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math>.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"171 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141868115","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 : 2024-07-31DOI: 10.1103/prxquantum.5.030320
Maxwell T. West, Jamie Heredge, Martin Sevior, Muhammad Usman
Exploiting the power of quantum computation to realize superior machine learning algorithms has been a major research focus of recent years, but the prospects of quantum machine learning (QML) remain dampened by considerable technical challenges. A particularly significant issue is that generic QML models suffer from so-called barren plateaus in their training landscapes—large regions where cost function gradients vanish exponentially in the number of qubits employed, rendering large models effectively untrainable. A leading strategy for combating this effect is to build problem-specific models that take into account the symmetries of their data in order to focus on a smaller, relevant subset of Hilbert space. In this work, we introduce a family of rotationally equivariant QML models built upon the quantum Fourier transform, and leverage recent insights from the Lie-algebraic study of QML models to prove that (a subset of) our models do not exhibit barren plateaus. In addition to our analytical results we numerically test our rotationally equivariant models on a dataset of simulated scanning tunneling microscope images of phosphorus impurities in silicon, where rotational symmetry naturally arises, and find that they dramatically outperform their generic counterparts in practice.
{"title":"Provably Trainable Rotationally Equivariant Quantum Machine Learning","authors":"Maxwell T. West, Jamie Heredge, Martin Sevior, Muhammad Usman","doi":"10.1103/prxquantum.5.030320","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030320","url":null,"abstract":"Exploiting the power of quantum computation to realize superior machine learning algorithms has been a major research focus of recent years, but the prospects of quantum machine learning (QML) remain dampened by considerable technical challenges. A particularly significant issue is that generic QML models suffer from so-called barren plateaus in their training landscapes—large regions where cost function gradients vanish exponentially in the number of qubits employed, rendering large models effectively untrainable. A leading strategy for combating this effect is to build problem-specific models that take into account the symmetries of their data in order to focus on a smaller, relevant subset of Hilbert space. In this work, we introduce a family of rotationally equivariant QML models built upon the quantum Fourier transform, and leverage recent insights from the Lie-algebraic study of QML models to prove that (a subset of) our models do not exhibit barren plateaus. In addition to our analytical results we numerically test our rotationally equivariant models on a dataset of simulated scanning tunneling microscope images of phosphorus impurities in silicon, where rotational symmetry naturally arises, and find that they dramatically outperform their generic counterparts in practice.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141868194","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 : 2024-07-30DOI: 10.1103/prxquantum.5.030319
A.G. Catalano, S.M. Giampaolo, O. Morsch, V. Giovannetti, F. Franchini
We propose to use a quantum spin chain as a device to store and release energy coherently and we investigate the interplay between its internal correlations and outside decoherence. We employ the quantum Ising chain in a transverse field and our charging protocol consists of a sudden global quantum quench in the external field to take the system out of equilibrium. Interactions with the environment and decoherence phenomena can dissipate part of the work that the chain can supply after being charged, measured by the ergotropy. We find that overall, the system shows remarkably better performance, in terms of resilience, charging time, and energy storage, when topological frustration is introduced by setting antiferromagnetic interactions with an odd number of sites and periodic boundary conditions. Moreover, we show that in a simple discharging protocol to an external spin, only the frustrated chain can transfer work and not just heat.
{"title":"Frustrating Quantum Batteries","authors":"A.G. Catalano, S.M. Giampaolo, O. Morsch, V. Giovannetti, F. Franchini","doi":"10.1103/prxquantum.5.030319","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030319","url":null,"abstract":"We propose to use a quantum spin chain as a device to store and release energy coherently and we investigate the interplay between its internal correlations and outside decoherence. We employ the quantum Ising chain in a transverse field and our charging protocol consists of a sudden global quantum quench in the external field to take the system out of equilibrium. Interactions with the environment and decoherence phenomena can dissipate part of the work that the chain can supply after being charged, measured by the ergotropy. We find that overall, the system shows remarkably better performance, in terms of resilience, charging time, and energy storage, when topological frustration is introduced by setting antiferromagnetic interactions with an odd number of sites and periodic boundary conditions. Moreover, we show that in a simple discharging protocol to an external spin, only the frustrated chain can transfer work and not just heat.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"156 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141868116","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 : 2024-07-29DOI: 10.1103/prxquantum.5.030318
Paul M. Riechers, Chaitanya Gupta, Artemy Kolchinsky, Mile Gu
We investigate and ascertain the ideal inputs to any finite-time physical process. We demonstrate that the expectation values of entropy flow, heat, and work can all be determined via Hermitian observables of the initial state. These Hermitian operators encapsulate the breadth of behavior and the ideal inputs for common thermodynamic objectives. We show how to construct these Hermitian operators from measurements of thermodynamic output from a finite number of effectively arbitrary inputs. The behavior of a small number of test inputs thus determines the full range of thermodynamic behavior from all inputs. For any process, entropy flow, heat, and work can all be extremized by pure input states—eigenstates of the respective operators. In contrast, the input states that minimize entropy production or maximize the change in free energy are nonpure mixed states obtained from the operators as the solution of a convex-optimization problem. To attain these, we provide an easily implementable gradient-descent method on the manifold of density matrices, where an analytic solution yields a valid direction of descent at each iterative step. Ideal inputs within a limited domain, and their associated thermodynamic operators, are obtained with less effort. This allows analysis of ideal thermodynamic inputs within quantum subspaces of infinite-dimensional quantum systems; it also allows analysis of ideal inputs in the classical limit. Our examples illustrate the diversity of “ideal” inputs: distinct initial states minimize entropy production, extremize the change in free energy, and maximize work extraction.
{"title":"Thermodynamically Ideal Quantum State Inputs to Any Device","authors":"Paul M. Riechers, Chaitanya Gupta, Artemy Kolchinsky, Mile Gu","doi":"10.1103/prxquantum.5.030318","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030318","url":null,"abstract":"We investigate and ascertain the ideal inputs to any finite-time physical process. We demonstrate that the expectation values of entropy flow, heat, and work can all be determined via Hermitian observables of the initial state. These Hermitian operators encapsulate the breadth of behavior and the ideal inputs for common thermodynamic objectives. We show how to construct these Hermitian operators from measurements of thermodynamic output from a finite number of effectively arbitrary inputs. The behavior of a small number of test inputs thus determines the full range of thermodynamic behavior from all inputs. For any process, entropy flow, heat, and work can all be extremized by pure input states—eigenstates of the respective operators. In contrast, the input states that minimize entropy production or maximize the change in free energy are nonpure mixed states obtained from the operators as the solution of a convex-optimization problem. To attain these, we provide an easily implementable gradient-descent method on the manifold of density matrices, where an analytic solution yields a valid direction of descent at each iterative step. Ideal inputs within a limited domain, and their associated thermodynamic operators, are obtained with less effort. This allows analysis of ideal thermodynamic inputs within quantum subspaces of infinite-dimensional quantum systems; it also allows analysis of ideal inputs in the classical limit. Our examples illustrate the diversity of “ideal” inputs: distinct initial states minimize entropy production, extremize the change in free energy, and maximize work extraction.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"360 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141868159","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 : 2024-07-26DOI: 10.1103/prxquantum.5.030317
Bill Fefferman, Soumik Ghosh, Michael Gullans, Kohdai Kuroiwa, Kunal Sharma
In this work, drawing inspiration from the type of noise present in real hardware, we study the output distribution of random quantum circuits under practical nonunital noise sources with constant noise rates. We show that even in the presence of unital sources such as the depolarizing channel, the distribution, under the combined noise channel, never resembles a maximally entropic distribution at any depth. To show this, we prove that the output distribution of such circuits never anticoncentrates—meaning that it is never too “flat”—regardless of the depth of the circuit. This is in stark contrast to the behavior of noiseless random quantum circuits or those with only unital noise, both of which anticoncentrate at sufficiently large depths. As a consequence, our results shows that the complexity of random-circuit sampling under realistic noise is still an open question, since anticoncentration is a critical property exploited by both state-of-the-art classical hardness and easiness results.
{"title":"Effect of Nonunital Noise on Random-Circuit Sampling","authors":"Bill Fefferman, Soumik Ghosh, Michael Gullans, Kohdai Kuroiwa, Kunal Sharma","doi":"10.1103/prxquantum.5.030317","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030317","url":null,"abstract":"In this work, drawing inspiration from the type of noise present in real hardware, we study the output distribution of random quantum circuits under practical nonunital noise sources with constant noise rates. We show that even in the presence of unital sources such as the depolarizing channel, the distribution, under the combined noise channel, never resembles a maximally entropic distribution at any depth. To show this, we prove that the output distribution of such circuits never anticoncentrates—meaning that it is never too “flat”—regardless of the depth of the circuit. This is in stark contrast to the behavior of noiseless random quantum circuits or those with only unital noise, both of which anticoncentrate at sufficiently large depths. As a consequence, our results shows that the complexity of random-circuit sampling under realistic noise is still an open question, since anticoncentration is a critical property exploited by both state-of-the-art classical hardness and easiness results.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141783989","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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