Pub Date : 2024-07-11DOI: 10.1103/prxquantum.5.030101
Tanvirul Islam, Jasminder S. Sidhu, Brendon L. Higgins, Thomas Brougham, Tom Vergoossen, Daniel K.L. Oi, Thomas Jennewein, Alexander Ling
In satellite-based quantum-key-distribution (QKD), the number of secret bits that can be generated in a single satellite pass over the ground station is severely restricted by the pass duration and the free-space optical channel loss. High channel loss may decrease the signal-to-noise ratio due to background noise, reduce the number of generated raw key bits, and increase the quantum bit error rate (QBER), all of which have detrimental effects on the output secret key length. Under finite-size security analysis, a higher QBER increases the minimum raw key length necessary for nonzero secret-key-length extraction due to less efficient reconciliation and postprocessing overheads. We show that recent developments in finite-key analysis allow three different small-satellite-based QKD projects, CQT-Sat, the United Kingdom QUARC-ROKS, and QEYSSat, to produce secret keys even under conditions of very high loss, improving on estimates based on previous finite-key bounds. This suggests that satellites in low Earth orbit can satisfy finite-size security requirements but that this remains challenging for satellites further from Earth. We analyze the performance of each mission to provide an informed route toward improving the performance of small-satellite QKD missions. We highlight the short- and long-term perspectives on the challenges and potential future developments in small-satellite-based QKD and quantum networks. In particular, we discuss some of the experimental and theoretical bottlenecks and the improvements necessary to achieve QKD and wider quantum networking capabilities in daylight and at different altitudes.
{"title":"Finite-Resource Performance of Small-Satellite-Based Quantum-Key-Distribution Missions","authors":"Tanvirul Islam, Jasminder S. Sidhu, Brendon L. Higgins, Thomas Brougham, Tom Vergoossen, Daniel K.L. Oi, Thomas Jennewein, Alexander Ling","doi":"10.1103/prxquantum.5.030101","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030101","url":null,"abstract":"In satellite-based quantum-key-distribution (QKD), the number of secret bits that can be generated in a single satellite pass over the ground station is severely restricted by the pass duration and the free-space optical channel loss. High channel loss may decrease the signal-to-noise ratio due to background noise, reduce the number of generated raw key bits, and increase the quantum bit error rate (QBER), all of which have detrimental effects on the output secret key length. Under finite-size security analysis, a higher QBER increases the minimum raw key length necessary for nonzero secret-key-length extraction due to less efficient reconciliation and postprocessing overheads. We show that recent developments in finite-key analysis allow three different small-satellite-based QKD projects, CQT-Sat, the United Kingdom QUARC-ROKS, and QEYSSat, to produce secret keys even under conditions of very high loss, improving on estimates based on previous finite-key bounds. This suggests that satellites in low Earth orbit can satisfy finite-size security requirements but that this remains challenging for satellites further from Earth. We analyze the performance of each mission to provide an informed route toward improving the performance of small-satellite QKD missions. We highlight the short- and long-term perspectives on the challenges and potential future developments in small-satellite-based QKD and quantum networks. In particular, we discuss some of the experimental and theoretical bottlenecks and the improvements necessary to achieve QKD and wider quantum networking capabilities in daylight and at different altitudes.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141587756","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 : 2024-07-10DOI: 10.1103/prxquantum.5.030306
Refik Mansuroglu, Arsalan Adil, Michael J. Hartmann, Zoë Holmes, Andrew T. Sornborger
The Schmidt decomposition is the go-to tool for measuring bipartite entanglement of pure quantum states. Similarly, it is possible to study the entangling features of a quantum operation using its operator-Schmidt or tensor-product decomposition. While quantum technological implementations of the former are thoroughly studied, entangling properties on the operator level are harder to extract in the quantum computational framework because of the exponential nature of sample complexity. Here, we present an algorithm for unbalanced partitions into a small subsystem and a large one (the environment) to compute the tensor-product decomposition of a unitary the effect of which on the small subsystem is captured in classical memory, while the effect on the environment is accessible as a quantum resource. This quantum algorithm may be used to make predictions about operator nonlocality and effective open quantum dynamics on a subsystem, as well as for finding low-rank approximations and low-depth compilations of quantum circuit unitaries. We demonstrate the method and its applications on a time-evolution unitary of an isotropic Heisenberg model in two dimensions.
{"title":"Quantum Tensor-Product Decomposition from Choi-State Tomography","authors":"Refik Mansuroglu, Arsalan Adil, Michael J. Hartmann, Zoë Holmes, Andrew T. Sornborger","doi":"10.1103/prxquantum.5.030306","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030306","url":null,"abstract":"The Schmidt decomposition is the go-to tool for measuring bipartite entanglement of pure quantum states. Similarly, it is possible to study the entangling features of a quantum operation using its operator-Schmidt or tensor-product decomposition. While quantum technological implementations of the former are thoroughly studied, entangling properties on the operator level are harder to extract in the quantum computational framework because of the exponential nature of sample complexity. Here, we present an algorithm for unbalanced partitions into a small subsystem and a large one (the environment) to compute the tensor-product decomposition of a unitary the effect of which on the small subsystem is captured in classical memory, while the effect on the environment is accessible as a quantum resource. This quantum algorithm may be used to make predictions about operator nonlocality and effective open quantum dynamics on a subsystem, as well as for finding low-rank approximations and low-depth compilations of quantum circuit unitaries. We demonstrate the method and its applications on a time-evolution unitary of an isotropic Heisenberg model in two dimensions.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141568963","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 : 2024-07-09DOI: 10.1103/prxquantum.5.030305
Félix Hoffet, Jan Lowinski, Lukas Heller, Auxiliadora Padrón-Brito, Hugues de Riedmatten
Generating indistinguishable photons from independent nodes is an important challenge for the development of quantum networks. In this work, we demonstrate the generation of highly indistinguishable single photons from two dissimilar atomic quantum nodes. One node is based on a fully blockaded cold Rydberg ensemble and generates on-demand single photons. The other node is a quantum repeater node based on a Duan-Lukin-Cirac-Zoller quantum memory and emits heralded single photons after a controllable memory time that is used to synchronize the two sources. We demonstrate an indistinguishability of for a temporal window including of the photons. This advancement opens new possibilities for interconnecting quantum repeater and processing nodes with high-fidelity Bell state measurement without sacrificing its efficiency.
{"title":"Near-Unity Indistinguishability of Single Photons Emitted from Dissimilar and Independent Atomic Quantum Nodes","authors":"Félix Hoffet, Jan Lowinski, Lukas Heller, Auxiliadora Padrón-Brito, Hugues de Riedmatten","doi":"10.1103/prxquantum.5.030305","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030305","url":null,"abstract":"Generating indistinguishable photons from independent nodes is an important challenge for the development of quantum networks. In this work, we demonstrate the generation of highly indistinguishable single photons from two dissimilar atomic quantum nodes. One node is based on a fully blockaded cold Rydberg ensemble and generates on-demand single photons. The other node is a quantum repeater node based on a Duan-Lukin-Cirac-Zoller quantum memory and emits heralded single photons after a controllable memory time that is used to synchronize the two sources. We demonstrate an indistinguishability of <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>94.6</mn><mo>±</mo><mn>5.2</mn></mrow><mspace width=\"0.1em\"></mspace><mrow><mi mathvariant=\"normal\">%</mi></mrow></math> for a temporal window including <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>90</mn><mspace width=\"0.1em\"></mspace><mrow><mi mathvariant=\"normal\">%</mi></mrow></math> of the photons. This advancement opens new possibilities for interconnecting quantum repeater and processing nodes with high-fidelity Bell state measurement without sacrificing its efficiency.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"65 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141568964","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 : 2024-07-08DOI: 10.1103/prxquantum.5.030304
Dawid Paszko, Dominic C. Rose, Marzena H. Szymańska, Arijeet Pal
Topological order offers possibilities for processing quantum information that can be immune to imperfections. However, the question of its stability out of equilibrium is relevant for experiments, where coupling to an environment is unavoidable. In this work, we demonstrate the robustness of certain aspects of symmetry-protected topological (SPT) order against a wide class of dissipation channels in the Lindblad and quantum trajectory formalisms of an open quantum system. This is illustrated using the one-dimensional cluster Hamiltonian along with Pauli-string jump operators. We show that certain choices of dissipation retaining strong symmetries support a steady-state manifold consisting of two nonlocal logical qubits and for Hamiltonian perturbations preserving the global symmetry, states in this manifold remain metastable. In contrast, this metastability is destroyed upon breaking the above-mentioned symmetry. While the localized edge qubits of the cluster Hamiltonian are not conserved by the Lindbladian evolution, they do correspond to weak symmetries and thus retain a memory of their initial state at all times in the quantum trajectories. We utilize this feature to construct protocols to retrieve the quantum information either by monitoring jumps or error mitigation. Our work thus proposes a novel framework to study the dynamics of dissipative SPT phases and opens up the possibility of engineering entangled states relevant to quantum information processing.
{"title":"Edge Modes and Symmetry-Protected Topological States in Open Quantum Systems","authors":"Dawid Paszko, Dominic C. Rose, Marzena H. Szymańska, Arijeet Pal","doi":"10.1103/prxquantum.5.030304","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030304","url":null,"abstract":"Topological order offers possibilities for processing quantum information that can be immune to imperfections. However, the question of its stability out of equilibrium is relevant for experiments, where coupling to an environment is unavoidable. In this work, we demonstrate the robustness of certain aspects of <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>Z</mi><mn>2</mn></msub><mo>×</mo><msub><mi>Z</mi><mn>2</mn></msub></math> symmetry-protected topological (SPT) order against a wide class of dissipation channels in the Lindblad and quantum trajectory formalisms of an open quantum system. This is illustrated using the one-dimensional <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>Z</mi><mi>X</mi><mi>Z</mi></math> cluster Hamiltonian along with Pauli-string jump operators. We show that certain choices of dissipation retaining strong symmetries support a steady-state manifold consisting of two nonlocal <i>logical</i> qubits and for Hamiltonian perturbations preserving the global symmetry, states in this manifold remain metastable. In contrast, this metastability is destroyed upon breaking the above-mentioned symmetry. While the localized <i>edge</i> qubits of the cluster Hamiltonian are not conserved by the Lindbladian evolution, they do correspond to weak symmetries and thus retain a memory of their initial state at all times in the quantum trajectories. We utilize this feature to construct protocols to retrieve the quantum information either by monitoring jumps or error mitigation. Our work thus proposes a novel framework to study the dynamics of dissipative SPT phases and opens up the possibility of engineering entangled states relevant to quantum information processing.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141568965","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 : 2024-07-03DOI: 10.1103/prxquantum.5.030303
Ruvi Lecamwasam, Syed Assad, Joseph J. Hope, Ping Koy Lam, Jayne Thompson, Mile Gu
The ability of quantum states to be in superposition is one of the key features that sets them apart from the classical world. This “coherence” is rigorously quantified by resource theories, which aim to understand how such properties may be exploited in quantum technologies. There has been much research on what the resource theory of coherence can reveal about quantum metrology, almost all of which has been from the viewpoint of Fisher information. We prove, however, that the relative entropy of coherence, and its recent generalization to positive operator-valued measures (POVMs), naturally quantify the performance of Bayesian metrology. In particular, we show how a coherence measure can be applied to an ensemble of states. We then prove that during parameter estimation, the ensemble relative entropy of coherence (C) is equal to the difference between the optimal Holevo information (X), and the mutual information attained by a measurement (I). We call this relation the CXI equality. The ensemble coherence lets us visualize how much information is locked away in superposition and hence is inaccessible with a given measurement scheme and quantifies the advantage that would be gained by using a joint measurement on multiple states. Our results hold regardless of how the parameter is encoded in the state, encompassing unitary, dissipative, and discrete settings. We consider both projective measurements and general POVMs. This work suggests new directions for research in coherence, provides a novel operation interpretation for the relative entropy of coherence and its POVM generalization, and introduces a new tool to study the role of quantum features in metrology.
{"title":"Relative Entropy of Coherence Quantifies Performance in Bayesian Metrology","authors":"Ruvi Lecamwasam, Syed Assad, Joseph J. Hope, Ping Koy Lam, Jayne Thompson, Mile Gu","doi":"10.1103/prxquantum.5.030303","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030303","url":null,"abstract":"The ability of quantum states to be in superposition is one of the key features that sets them apart from the classical world. This “coherence” is rigorously quantified by resource theories, which aim to understand how such properties may be exploited in quantum technologies. There has been much research on what the resource theory of coherence can reveal about quantum metrology, almost all of which has been from the viewpoint of Fisher information. We prove, however, that the relative entropy of coherence, and its recent generalization to positive operator-valued measures (POVMs), naturally quantify the performance of Bayesian metrology. In particular, we show how a coherence measure can be applied to an ensemble of states. We then prove that during parameter estimation, the ensemble relative entropy of coherence (C) is equal to the difference between the optimal Holevo information (X), and the mutual information attained by a measurement (I). We call this relation the CXI equality. The ensemble coherence lets us visualize how much information is locked away in superposition and hence is inaccessible with a given measurement scheme and quantifies the advantage that would be gained by using a joint measurement on multiple states. Our results hold regardless of how the parameter is encoded in the state, encompassing unitary, dissipative, and discrete settings. We consider both projective measurements and general POVMs. This work suggests new directions for research in coherence, provides a novel operation interpretation for the relative entropy of coherence and its POVM generalization, and introduces a new tool to study the role of quantum features in metrology.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141513865","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 : 2024-07-02DOI: 10.1103/prxquantum.5.030302
Slawomir Simbierowicz, Massimo Borrelli, Volodymyr Monarkha, Ville Nuutinen, Russell E. Lake
Qubit-specific measurement in a superconducting quantum processor requires physical interconnects that traverse 4 orders of magnitude in temperature from 293 K to 10 mK. Although the quantum processor can be thermalized and shielded from electromagnetic noise, the interconnects themselves introduce an unavoidable remote heat bath that causes decoherence of quantum states. In the present work, we report quantitative and device-independent measurements of the power radiated to the quantum processor from its control lines. Our results have been obtained using a calibrated bolometer that operates within a millikelvin environment with time-resolved measurement capability. In the limit of zero applied power, the noise power emitted to the quantum processor is equivalent to that of a blackbody with temperature 63–71 mK for the prototypical drive lines in the study. Experimentally, we increase the applied power of a simulated control signal to map out the resulting temperature rise and thermal time constant of five prototypical drive-line varieties. We input the data to an open quantum system model to demonstrate the trade-off between dissipated signal power, transmon-qubit lifetime, pure dephasing, gate fidelity, and the implied decoherence rates due to self-heating during microwave operations. Beyond explaining dephasing rates observed in the literature, our work sets the stage for accurate noise modeling in novel quantum computer interfacing methods due to our device-agnostic approach.
{"title":"Inherent Thermal-Noise Problem in Addressing Qubits","authors":"Slawomir Simbierowicz, Massimo Borrelli, Volodymyr Monarkha, Ville Nuutinen, Russell E. Lake","doi":"10.1103/prxquantum.5.030302","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030302","url":null,"abstract":"Qubit-specific measurement in a superconducting quantum processor requires physical interconnects that traverse 4 orders of magnitude in temperature from 293 K to 10 mK. Although the quantum processor can be thermalized and shielded from electromagnetic noise, the interconnects themselves introduce an unavoidable remote heat bath that causes decoherence of quantum states. In the present work, we report quantitative and device-independent measurements of the power radiated to the quantum processor from its control lines. Our results have been obtained using a calibrated bolometer that operates within a millikelvin environment with time-resolved measurement capability. In the limit of zero applied power, the noise power emitted to the quantum processor is equivalent to that of a blackbody with temperature 63–71 mK for the prototypical drive lines in the study. Experimentally, we increase the applied power of a simulated control signal to map out the resulting temperature rise and thermal time constant of five prototypical drive-line varieties. We input the data to an open quantum system model to demonstrate the trade-off between dissipated signal power, transmon-qubit lifetime, pure dephasing, gate fidelity, and the implied decoherence rates due to self-heating during microwave operations. Beyond explaining dephasing rates observed in the literature, our work sets the stage for accurate noise modeling in novel quantum computer interfacing methods due to our device-agnostic approach.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551324","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 : 2024-07-01DOI: 10.1103/prxquantum.5.030301
Josias Langbehn, Kyrylo Snizhko, Igor Gornyi, Giovanna Morigi, Yuval Gefen, Christiane P. Koch
Cooling a quantum system to its ground state is important for the characterization of nontrivial interacting systems and in the context of a variety of quantum information platforms. It can be achieved by employing measurement-based passive steering protocols, where the steering steps are predetermined and are not based on measurement readouts. However, measurements realized by coupling the system to auxiliary quantum degrees of freedom (“detectors”) are rather costly and protocols in which the number of detectors scales with system size will have limited practical applicability. Here, we identify conditions under which measurement-based cooling protocols can be taken to the ultimate dilute limit where the number of detectors is independent of system size. For two examples of frustration-free one-dimensional spin chains, we show that steering on a single link is sufficient to cool these systems into their unique ground states. We corroborate our analytical arguments with finite-size numerical simulations and discuss further applications of dilute cooling.
{"title":"Dilute Measurement-Induced Cooling into Many-Body Ground States","authors":"Josias Langbehn, Kyrylo Snizhko, Igor Gornyi, Giovanna Morigi, Yuval Gefen, Christiane P. Koch","doi":"10.1103/prxquantum.5.030301","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030301","url":null,"abstract":"Cooling a quantum system to its ground state is important for the characterization of nontrivial interacting systems and in the context of a variety of quantum information platforms. It can be achieved by employing measurement-based passive steering protocols, where the steering steps are predetermined and are not based on measurement readouts. However, measurements realized by coupling the system to auxiliary quantum degrees of freedom (“detectors”) are rather costly and protocols in which the number of detectors scales with system size will have limited practical applicability. Here, we identify conditions under which measurement-based cooling protocols can be taken to the ultimate dilute limit where the number of detectors is independent of system size. For two examples of frustration-free one-dimensional spin chains, we show that steering on a single link is sufficient to cool these systems into their unique ground states. We corroborate our analytical arguments with finite-size numerical simulations and discuss further applications of dilute cooling.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"56 4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141513855","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 : 2024-06-28DOI: 10.1103/prxquantum.5.020368
Danial Motlagh, Nathan Wiebe
Quantum signal processing (QSP) and quantum singular value transformation (QSVT) currently stand as the most efficient techniques for implementing functions of block-encoded matrices, a central task that lies at the heart of most prominent quantum algorithms. However, current QSP approaches face several challenges, such as the restrictions imposed on the family of achievable polynomials and the difficulty of calculating the required phase angles for specific transformations. In this paper, we present a generalized quantum signal processing (GQSP) approach, employing general SU(2) rotations as our signal-processing operators, rather than relying solely on rotations in a single basis. Our approach lifts all practical restrictions on the family of achievable transformations, with the sole remaining condition being that , a restriction necessary due to the unitary nature of quantum computation. Furthermore, GQSP provides a straightforward recursive formula for determining the rotation angles needed to construct the polynomials in cases where and are known. In cases where only is known, we provide an efficient optimization algorithm capable of identifying in under a minute of GPU time, a corresponding for polynomials of degree on the order of . We further illustrate GQSP simplifies QSP-based strategies for Hamiltonian simulation, offer an optimal solution to the -approximate fractional query problem that requires queries to perform where is a proved lower bound, and introduces novel approaches for implementing bosonic operators. Moreover, we propose a nov
{"title":"Generalized Quantum Signal Processing","authors":"Danial Motlagh, Nathan Wiebe","doi":"10.1103/prxquantum.5.020368","DOIUrl":"https://doi.org/10.1103/prxquantum.5.020368","url":null,"abstract":"Quantum signal processing (QSP) and quantum singular value transformation (QSVT) currently stand as the most efficient techniques for implementing functions of block-encoded matrices, a central task that lies at the heart of most prominent quantum algorithms. However, current QSP approaches face several challenges, such as the restrictions imposed on the family of achievable polynomials and the difficulty of calculating the required phase angles for specific transformations. In this paper, we present a generalized quantum signal processing (GQSP) approach, employing general SU(2) rotations as our signal-processing operators, rather than relying solely on rotations in a single basis. Our approach lifts all practical restrictions on the family of achievable transformations, with the sole remaining condition being that <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mo stretchy=\"false\">|</mo></mrow><mi>P</mi><mrow><mo stretchy=\"false\">|</mo></mrow><mo>≤</mo><mn>1</mn></math>, a restriction necessary due to the unitary nature of quantum computation. Furthermore, GQSP provides a straightforward recursive formula for determining the rotation angles needed to construct the polynomials in cases where <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>P</mi></math> and <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>Q</mi></math> are known. In cases where only <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>P</mi></math> is known, we provide an efficient optimization algorithm capable of identifying in under a minute of GPU time, a corresponding <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>Q</mi></math> for polynomials of degree on the order of <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mn>10</mn><mn>7</mn></msup></math>. We further illustrate GQSP simplifies QSP-based strategies for Hamiltonian simulation, offer an optimal solution to the <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>ϵ</mi></math>-approximate fractional query problem that requires <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi mathvariant=\"script\">O</mi></mrow><mrow><mo>(</mo><mo stretchy=\"false\">(</mo><mn>1</mn><mo>/</mo><mi>δ</mi><mo stretchy=\"false\">)</mo><mo>+</mo><mi>log</mi><mo></mo><mo stretchy=\"false\">(</mo><mn>1</mn><mo>/</mo><mi>ϵ</mi><mo stretchy=\"false\">)</mo><mo>)</mo></mrow></math> queries to perform where <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi mathvariant=\"script\">O</mi></mrow><mo stretchy=\"false\">(</mo><mn>1</mn><mo>/</mo><mi>δ</mi><mo stretchy=\"false\">)</mo></math> is a proved lower bound, and introduces novel approaches for implementing bosonic operators. Moreover, we propose a nov","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"364 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551325","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 : 2024-06-27DOI: 10.1103/prxquantum.5.020367
Marco Fanizza, Yihui Quek, Matteo Rosati
We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process governed by classical parameters that are out of one’s control. This framework is applicable, for example, to the study of astronomical phenomena, disordered systems and biological processes not controlled by the observer. We provide an algorithm for learning with high probability in this setting with a finite amount of samples, even if the concept class is infinite. To do this, we review and adapt existing algorithms for shadow tomography and hypothesis selection, and combine their guarantees with the uniform convergence on the data of the loss functions of interest. As a byproduct, we obtain sufficient conditions for performing shadow tomography of classical-quantum states with a number of copies, which depends on the dimension of the quantum register, but not on the dimension of the classical one. We give concrete examples of processes that can be learned in this manner, based on quantum circuits or physically motivated classes, such as systems governed by Hamiltonians with random perturbations or data-dependent phase shifts.
{"title":"Learning Quantum Processes Without Input Control","authors":"Marco Fanizza, Yihui Quek, Matteo Rosati","doi":"10.1103/prxquantum.5.020367","DOIUrl":"https://doi.org/10.1103/prxquantum.5.020367","url":null,"abstract":"We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process governed by classical parameters that are out of one’s control. This framework is applicable, for example, to the study of astronomical phenomena, disordered systems and biological processes not controlled by the observer. We provide an algorithm for learning with high probability in this setting with a finite amount of samples, even if the concept class is infinite. To do this, we review and adapt existing algorithms for shadow tomography and hypothesis selection, and combine their guarantees with the uniform convergence on the data of the loss functions of interest. As a byproduct, we obtain sufficient conditions for performing shadow tomography of classical-quantum states with a number of copies, which depends on the dimension of the quantum register, but not on the dimension of the classical one. We give concrete examples of processes that can be learned in this manner, based on quantum circuits or physically motivated classes, such as systems governed by Hamiltonians with random perturbations or data-dependent phase shifts.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551326","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 : 2024-06-26DOI: 10.1103/prxquantum.5.020366
Philippe Lewalle, Yipei Zhang, K. Birgitta Whaley
The quantum Zeno effect asserts that quantum measurements inhibit simultaneous unitary dynamics when the “collapse” events are sufficiently strong and frequent. This applies in the limit of strong continuous measurement or dissipation. It is possible to implement a dissipative control that is known as “Zeno dragging” by dynamically varying the monitored observable, and hence also the eigenstates, which are attractors under Zeno dynamics. This is similar to adiabatic processes, in that the Zeno-dragging fidelity is highest when the rate of eigenstate change is slow compared to the measurement rate. We demonstrate here two theoretical methods for using such dynamics to achieve control of quantum systems. The first, which we shall refer to as “shortcut to Zeno,” is analogous to the shortcuts to adiabaticity (counterdiabatic driving) that are frequently used to accelerate unitary adiabatic evolution. In the second approach, we apply the Chantasri-Dressel-Jordan stochastic action [PRA 88, 042110 (2013)], and demonstrate that the extremal-probability readout paths derived from this are well suited to setting up a Pontryagin-style optimization of the Zeno-dragging schedule. A fundamental contribution of the latter approach is to show that an action suitable for measurement-driven control optimization can be derived quite generally from statistical arguments. Implementing these methods on the Zeno dragging of a qubit, we find that both approaches yield the same solution, namely, that the optimal control is a unitary that matches the motion of the Zeno-monitored eigenstate. We then show that such a solution can be more robust than a unitary-only operation and we comment on solvable generalizations of our qubit example embedded in larger systems. These methods open up new pathways toward systematically developing dynamic control of Zeno subspaces to realize dissipatively stabilized quantum operations.
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