1
|
Lyu N, Miano A, Tsioutsios I, Cortiñas RG, Jung K, Wang Y, Hu Z, Geva E, Kais S, Batista VS. Mapping Molecular Hamiltonians into Hamiltonians of Modular cQED Processors. J Chem Theory Comput 2023; 19:6564-6576. [PMID: 37733472 DOI: 10.1021/acs.jctc.3c00620] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/23/2023]
Abstract
We introduce a general method based on the operators of the Dyson-Masleev transformation to map the Hamiltonian of an arbitrary model system into the Hamiltonian of a circuit Quantum Electrodynamics (cQED) processor. Furthermore, we introduce a modular approach to programming a cQED processor with components corresponding to the mapping Hamiltonian. The method is illustrated as applied to quantum dynamics simulations of the Fenna-Matthews-Olson (FMO) complex and the spin-boson model of charge transfer. Beyond applications to molecular Hamiltonians, the mapping provides a general approach to implement any unitary operator in terms of a sequence of unitary transformations corresponding to powers of creation and annihilation operators of a single bosonic mode in a cQED processor.
Collapse
Affiliation(s)
- Ningyi Lyu
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Alessandro Miano
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, United States
- Department of Physics, Yale University, New Haven, Connecticut 06520, United States
- Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, United States
| | - Ioannis Tsioutsios
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, United States
- Department of Physics, Yale University, New Haven, Connecticut 06520, United States
- Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, United States
| | - Rodrigo G Cortiñas
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, United States
- Department of Physics, Yale University, New Haven, Connecticut 06520, United States
- Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, United States
| | - Kenneth Jung
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Yuchen Wang
- Department of Chemistry, Department of Physics and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, United States
| | - Zixuan Hu
- Department of Chemistry, Department of Physics and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, United States
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Sabre Kais
- Department of Chemistry, Department of Physics and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, United States
| | - Victor S Batista
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
- Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, United States
| |
Collapse
|
2
|
Rossini M, Maile D, Ankerhold J, Donvil BIC. Single-Qubit Error Mitigation by Simulating Non-Markovian Dynamics. PHYSICAL REVIEW LETTERS 2023; 131:110603. [PMID: 37774275 DOI: 10.1103/physrevlett.131.110603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2023] [Revised: 06/09/2023] [Accepted: 08/16/2023] [Indexed: 10/01/2023]
Abstract
Quantum simulation is a powerful tool to study the properties of quantum systems. The dynamics of open quantum systems are often described by completely positive (CP) maps, for which several quantum simulation schemes exist. Such maps, however, represent only a subset of a larger class of maps: the general dynamical maps which are linear, Hermitian preserving, and trace preserving but not necessarily positivity preserving. Here we present a simulation scheme for these general dynamical maps, which occur when the underlying system-reservoir model undergoes entangling (and thus non-Markovian) dynamics. Such maps also arise as the inverse of CP maps, which are commonly used in error mitigation. We illustrate our simulation scheme on an IBM quantum processor, demonstrating its ability to recover the initial state of a Lindblad evolution. This paves the way for a novel form of quantum error mitigation. Our scheme only requires one ancilla qubit as an overhead and a small number of one and two qubit gates. Consequently, we expect it to be of practical use in near-term quantum devices.
Collapse
Affiliation(s)
- Mirko Rossini
- Institute for Complex Quantum Systems and IQST, Ulm University-Albert-Einstein-Allee 11, D-89069 Ulm, Germany
| | - Dominik Maile
- Institute for Complex Quantum Systems and IQST, Ulm University-Albert-Einstein-Allee 11, D-89069 Ulm, Germany
| | - Joachim Ankerhold
- Institute for Complex Quantum Systems and IQST, Ulm University-Albert-Einstein-Allee 11, D-89069 Ulm, Germany
| | - Brecht I C Donvil
- Institute for Complex Quantum Systems and IQST, Ulm University-Albert-Einstein-Allee 11, D-89069 Ulm, Germany
| |
Collapse
|
3
|
Zhang Y, Hu Z, Wang Y, Kais S. Quantum Simulation of the Radical Pair Dynamics of the Avian Compass. J Phys Chem Lett 2023; 14:832-837. [PMID: 36655839 DOI: 10.1021/acs.jpclett.2c03617] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
The simulation of open quantum dynamics on quantum circuits has attracted wide interests recently with a variety of quantum algorithms developed and demonstrated. Among these, one particular design of a unitary-dilation-based quantum algorithm is capable of simulating general and complex physical systems. In this paper, we apply this quantum algorithm to simulating the dynamics of the radical pair mechanism in the avian compass. This application is demonstrated on the IBM QASM quantum simulator. This work is the first application of any quantum algorithm to simulating the radical pair mechanism in the avian compass, which not only demonstrates the generality of the quantum algorithm but also opens new opportunities for studying the avian compass with quantum computing devices.
Collapse
Affiliation(s)
| | - Zixuan Hu
- Department of Chemistry, Department of Physics, and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana47907, United States
| | - Yuchen Wang
- Department of Chemistry, Department of Physics, and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana47907, United States
| | - Sabre Kais
- Department of Chemistry, Department of Physics, and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana47907, United States
| |
Collapse
|
4
|
Miessen A, Ollitrault PJ, Tacchino F, Tavernelli I. Quantum algorithms for quantum dynamics. NATURE COMPUTATIONAL SCIENCE 2023; 3:25-37. [PMID: 38177956 DOI: 10.1038/s43588-022-00374-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2021] [Accepted: 11/12/2022] [Indexed: 01/06/2024]
Abstract
Among the many computational challenges faced across different disciplines, quantum-mechanical systems pose some of the hardest ones and offer a natural playground for the growing field of quantum technologies. In this Perspective, we discuss quantum algorithmic solutions for quantum dynamics, reporting on the latest developments and offering a viewpoint on their potential and current limitations. We present some of the most promising areas of application and identify possible research directions for the coming years.
Collapse
Affiliation(s)
| | - Pauline J Ollitrault
- IBM Quantum, IBM Research - Zurich, Rüschlikon, Switzerland
- QC Ware, Palo Alto, CA, USA
| | | | | |
Collapse
|
5
|
Han J, Cai W, Hu L, Mu X, Ma Y, Xu Y, Wang W, Wang H, Song YP, Zou CL, Sun L. Experimental Simulation of Open Quantum System Dynamics via Trotterization. PHYSICAL REVIEW LETTERS 2021; 127:020504. [PMID: 34296922 DOI: 10.1103/physrevlett.127.020504] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2020] [Revised: 04/23/2021] [Accepted: 06/14/2021] [Indexed: 06/13/2023]
Abstract
Digital quantum simulators provide a diversified tool for solving the evolution of quantum systems with complicated Hamiltonians and hold great potential for a wide range of applications. Although much attention is paid to the unitary evolution of closed quantum systems, dissipation and noise are vital in understanding the dynamics of practical quantum systems. In this work, we experimentally demonstrate a digital simulation of an open quantum system in a controllable Markovian environment with the assistance of a single ancillary qubit. By Trotterizing the quantum Liouvillians, the continuous evolution of an open quantum system is effectively realized, and its application in error mitigation is demonstrated by adjusting the simulated noise intensities. High-order Trotter for open quantum dynamics is also experimentally investigated and shows higher accuracy. Our results represent a significant step toward hardware-efficient simulation of open quantum systems and error mitigation in quantum algorithms in noisy intermediate-scale quantum systems.
Collapse
Affiliation(s)
- J Han
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - W Cai
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - L Hu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - X Mu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Y Ma
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Y Xu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - W Wang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - H Wang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Y P Song
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - C-L Zou
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - L Sun
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| |
Collapse
|
6
|
Cattaneo M, De Chiara G, Maniscalco S, Zambrini R, Giorgi GL. Collision Models Can Efficiently Simulate Any Multipartite Markovian Quantum Dynamics. PHYSICAL REVIEW LETTERS 2021; 126:130403. [PMID: 33861108 DOI: 10.1103/physrevlett.126.130403] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2020] [Accepted: 03/02/2021] [Indexed: 06/12/2023]
Abstract
We introduce the multipartite collision model, defined in terms of elementary interactions between subsystems and ancillas, and show that it can simulate the Markovian dynamics of any multipartite open quantum system. We develop a method to estimate an analytical error bound for any repeated interactions model, and we use it to prove that the error of our scheme displays an optimal scaling. Finally, we provide a simple decomposition of the multipartite collision model into elementary quantum gates, and show that it is efficiently simulable on a quantum computer according to the dissipative quantum Church-Turing theorem, i.e., it requires a polynomial number of resources.
Collapse
Affiliation(s)
- Marco Cattaneo
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
- QTF Centre of Excellence, Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turun Yliopisto, Finland
- QTF Centre of Excellence, Department of Physics, University of Helsinki, P.O. Box 43, FI-00014 Helsinki, Finland
| | - Gabriele De Chiara
- Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
| | - Sabrina Maniscalco
- QTF Centre of Excellence, Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turun Yliopisto, Finland
- QTF Centre of Excellence, Department of Physics, University of Helsinki, P.O. Box 43, FI-00014 Helsinki, Finland
- QTF Centre of Excellence, Department of Applied Physics, School of Science, Aalto University, FI-00076 Aalto, Finland
| | - Roberta Zambrini
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Gian Luca Giorgi
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| |
Collapse
|
7
|
Dynamical and thermodynamical approaches to open quantum systems. Sci Rep 2020; 10:2607. [PMID: 32054893 PMCID: PMC7018693 DOI: 10.1038/s41598-020-59241-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2019] [Accepted: 01/08/2020] [Indexed: 12/02/2022] Open
Abstract
The non-Markovian dynamics of open quantum systems is studied from two different points of view. The first one coincides with the traditional tracing out of the environmental degrees of freedom, presented in classical textbooks on open quantum systems. The second one is an approximation of the exact density operator with the knowledge of only several dynamical variables in the spirit of non-equilibrium thermodynamics. The approximation is based on the principle of maximal entropy. We discuss the information and the Renyi entropies, which lead to different approximations. The time-convolutionless master equation governs the dynamics of both traditional and approximated reduced density operator with a particular projection operator. Considering the example of two interacting qubits in a thermal environment, we compare the traditional and thermodynamical approaches.
Collapse
|
8
|
Cao Y, Romero J, Olson JP, Degroote M, Johnson PD, Kieferová M, Kivlichan ID, Menke T, Peropadre B, Sawaya NPD, Sim S, Veis L, Aspuru-Guzik A. Quantum Chemistry in the Age of Quantum Computing. Chem Rev 2019; 119:10856-10915. [PMID: 31469277 DOI: 10.1021/acs.chemrev.8b00803] [Citation(s) in RCA: 261] [Impact Index Per Article: 52.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
Abstract
Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced, the complexity of quantum mechanics remains hard to appease. The advent of quantum computation brings new pathways to navigate this challenging and complex landscape. By manipulating quantum states of matter and taking advantage of their unique features such as superposition and entanglement, quantum computers promise to efficiently deliver accurate results for many important problems in quantum chemistry, such as the electronic structure of molecules. In the past two decades, significant advances have been made in developing algorithms and physical hardware for quantum computing, heralding a revolution in simulation of quantum systems. This Review provides an overview of the algorithms and results that are relevant for quantum chemistry. The intended audience is both quantum chemists who seek to learn more about quantum computing and quantum computing researchers who would like to explore applications in quantum chemistry.
Collapse
Affiliation(s)
- Yudong Cao
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Jonathan Romero
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Jonathan P Olson
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Matthias Degroote
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Department of Chemistry , University of Toronto , Toronto , Ontario M5G 1Z8 , Canada.,Department of Computer Science , University of Toronto , Toronto , Ontario M5G 1Z8 , Canada
| | - Peter D Johnson
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Mária Kieferová
- Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States.,Department of Physics and Astronomy , Macquarie University , Sydney , NSW 2109 , Australia.,Institute for Quantum Computing and Department of Physics and Astronomy , University of Waterloo , Waterloo , Ontario N2L 3G1 , Canada
| | - Ian D Kivlichan
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Department of Physics , Harvard University , Cambridge , Massachusetts 02138 , United States
| | - Tim Menke
- Department of Physics , Harvard University , Cambridge , Massachusetts 02138 , United States.,Research Laboratory of Electronics , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States.,Department of Physics , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
| | - Borja Peropadre
- Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Nicolas P D Sawaya
- Intel Laboratories , Intel Corporation , Santa Clara , California 95054 United States
| | - Sukin Sim
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Libor Veis
- J. Heyrovský Institute of Physical Chemistry , Academy of Sciences of the Czech Republic v.v.i. , Doleǰskova 3 , 18223 Prague 8, Czech Republic
| | - Alán Aspuru-Guzik
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States.,Department of Chemistry , University of Toronto , Toronto , Ontario M5G 1Z8 , Canada.,Department of Computer Science , University of Toronto , Toronto , Ontario M5G 1Z8 , Canada.,Canadian Institute for Advanced Research , Toronto , Ontario M5G 1Z8 , Canada.,Vector Institute for Artificial Intelligence , Toronto , Ontario M5S 1M1 , Canada
| |
Collapse
|
9
|
Carrasquilla J, Torlai G, Melko RG, Aolita L. Reconstructing quantum states with generative models. NAT MACH INTELL 2019. [DOI: 10.1038/s42256-019-0028-1] [Citation(s) in RCA: 121] [Impact Index Per Article: 24.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
|
10
|
Experimental repetitive quantum channel simulation. Sci Bull (Beijing) 2018; 63:1551-1557. [PMID: 36751075 DOI: 10.1016/j.scib.2018.11.010] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2018] [Revised: 11/17/2018] [Accepted: 11/19/2018] [Indexed: 11/22/2022]
Abstract
Universal control of quantum systems is a major goal to be achieved for quantum information processing, which demands thorough understanding of fundamental quantum mechanics and promises applications of quantum technologies. So far, most studies concentrate on ideally isolated quantum systems governed by unitary evolutions, while practical quantum systems are open and described by quantum channels due to their inevitable coupling to environment. Here, we experimentally simulate arbitrary quantum channels for an open quantum system, i.e. a single photonic qubit in a superconducting quantum circuit. The arbitrary channel simulation is achieved with minimum resource of only one ancilla qubit and measurement-based adaptive control. By repetitively implementing the quantum channel simulation, we realize an arbitrary Liouvillian for a continuous evolution of an open quantum system for the first time. Our experiment provides not only a testbed for understanding quantum noise and decoherence, but also a powerful tool for full control of practical open quantum systems.
Collapse
|
11
|
Barthel T, Lu J. Fundamental Limitations for Measurements in Quantum Many-Body Systems. PHYSICAL REVIEW LETTERS 2018; 121:080406. [PMID: 30192598 DOI: 10.1103/physrevlett.121.080406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2018] [Revised: 06/20/2018] [Indexed: 06/08/2023]
Abstract
Dynamical measurement schemes are an important tool for the investigation of quantum many-body systems, especially in the age of quantum simulation. Here, we address the question whether generic measurements can be implemented efficiently if we have access to a certain set of experimentally realizable measurements and can extend it through time evolution. For the latter, two scenarios are considered: (a) evolution according to unitary circuits and (b) evolution due to Hamiltonians that we can control in a time-dependent fashion. We find that the time needed to realize a certain measurement to a predefined accuracy scales in general exponentially with the system size-posing a fundamental limitation. The argument is based on the construction of ϵ-packings for manifolds of observables with identical spectra and a comparison of their cardinalities to those of ϵ-coverings for quantum circuits and unitary time-evolution operators. The former is related to the study of Grassmann manifolds.
Collapse
Affiliation(s)
- Thomas Barthel
- Department of Physics, Duke University, Durham, North Carolina 27708, USA
| | - Jianfeng Lu
- Department of Physics, Duke University, Durham, North Carolina 27708, USA
- Department of Mathematics, Duke University, Durham, North Carolina 27708, USA
| |
Collapse
|
12
|
Gatti G, Barberena D, Sanz M, Solano E. Protected State Transfer via an Approximate Quantum Adder. Sci Rep 2017; 7:6964. [PMID: 28761133 PMCID: PMC5537370 DOI: 10.1038/s41598-017-06425-3] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2017] [Accepted: 06/12/2017] [Indexed: 11/13/2022] Open
Abstract
We propose a decoherence protected protocol for sending single photon quantum states through depolarizing channels. This protocol is implemented via an approximate quantum adder engineered through spontaneous parametric down converters, and shows higher success probability than distilled quantum teleportation protocols for distances below a threshold depending on the properties of the channel.
Collapse
Affiliation(s)
- G Gatti
- Departamento de Ciencias, Sección Física, Pontificia Universidad Católica del Perú, Apartado, 1761, Lima, Peru
| | - D Barberena
- Departamento de Ciencias, Sección Física, Pontificia Universidad Católica del Perú, Apartado, 1761, Lima, Peru
| | - M Sanz
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, E-48080, Bilbao, Spain.
| | - E Solano
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, E-48080, Bilbao, Spain.,IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48011, Bilbao, Spain
| |
Collapse
|
13
|
Chenu A, Beau M, Cao J, Del Campo A. Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise. PHYSICAL REVIEW LETTERS 2017; 118:140403. [PMID: 28430494 DOI: 10.1103/physrevlett.118.140403] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2016] [Indexed: 06/07/2023]
Abstract
We introduce a scheme for the quantum simulation of many-body decoherence based on the unitary evolution of a stochastic Hamiltonian. Modulating the strength of the interactions with stochastic processes, we show that the noise-averaged density matrix simulates an effectively open dynamics governed by k-body Lindblad operators. Markovian dynamics can be accessed with white-noise fluctuations; non-Markovian dynamics requires colored noise. The time scale governing the fidelity decay under many-body decoherence is shown to scale as N^{-2k} with the system size N. Our proposal can be readily implemented in a variety of quantum platforms including optical lattices, superconducting circuits, and trapped ions.
Collapse
Affiliation(s)
- A Chenu
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
| | - M Beau
- Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA
| | - J Cao
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
| | - A Del Campo
- Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA
| |
Collapse
|
14
|
Werner AH, Jaschke D, Silvi P, Kliesch M, Calarco T, Eisert J, Montangero S. Positive Tensor Network Approach for Simulating Open Quantum Many-Body Systems. PHYSICAL REVIEW LETTERS 2016; 116:237201. [PMID: 27341253 DOI: 10.1103/physrevlett.116.237201] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2015] [Indexed: 06/06/2023]
Abstract
Open quantum many-body systems play an important role in quantum optics and condensed matter physics, and capture phenomena like transport, the interplay between Hamiltonian and incoherent dynamics, and topological order generated by dissipation. We introduce a versatile and practical method to numerically simulate one-dimensional open quantum many-body dynamics using tensor networks. It is based on representing mixed quantum states in a locally purified form, which guarantees that positivity is preserved at all times. Moreover, the approximation error is controlled with respect to the trace norm. Hence, this scheme overcomes various obstacles of the known numerical open-system evolution schemes. To exemplify the functioning of the approach, we study both stationary states and transient dissipative behavior, for various open quantum systems ranging from few to many bodies.
Collapse
Affiliation(s)
- A H Werner
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - D Jaschke
- Institute for Complex Quantum Systems & Center for Integrated Quantum Science and Technologies (IQST), Universität Ulm, 89069 Ulm, Germany
- Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA
| | - P Silvi
- Institute for Complex Quantum Systems & Center for Integrated Quantum Science and Technologies (IQST), Universität Ulm, 89069 Ulm, Germany
| | - M Kliesch
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - T Calarco
- Institute for Complex Quantum Systems & Center for Integrated Quantum Science and Technologies (IQST), Universität Ulm, 89069 Ulm, Germany
| | - J Eisert
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - S Montangero
- Institute for Complex Quantum Systems & Center for Integrated Quantum Science and Technologies (IQST), Universität Ulm, 89069 Ulm, Germany
| |
Collapse
|
15
|
Quantum Simulation of Dissipative Processes without Reservoir Engineering. Sci Rep 2015; 5:9981. [PMID: 26024437 PMCID: PMC4448689 DOI: 10.1038/srep09981] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2014] [Accepted: 03/23/2015] [Indexed: 11/23/2022] Open
Abstract
We present a quantum algorithm to simulate general finite dimensional Lindblad master equations without the requirement of engineering the system-environment interactions. The proposed method is able to simulate both Markovian and non-Markovian quantum dynamics. It consists in the quantum computation of the dissipative corrections to the unitary evolution of the system of interest, via the reconstruction of the response functions associated with the Lindblad operators. Our approach is equally applicable to dynamics generated by effectively non-Hermitian Hamiltonians. We confirm the quality of our method providing specific error bounds that quantify its accuracy.
Collapse
|
16
|
Yung MH, Whitfield JD, Boixo S, Tempel DG, Aspuru-Guzik A. Introduction to Quantum Algorithms for Physics and Chemistry. ADVANCES IN CHEMICAL PHYSICS 2014. [DOI: 10.1002/9781118742631.ch03] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/04/2022]
|
17
|
Cai Z, Barthel T. Algebraic versus Exponential Decoherence in Dissipative Many-Particle Systems. PHYSICAL REVIEW LETTERS 2013; 111:150403. [PMID: 24160582 DOI: 10.1103/physrevlett.111.150403] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2013] [Indexed: 06/02/2023]
Abstract
The interplay between dissipation and internal interactions in quantum many-body systems gives rise to a wealth of novel phenomena. Here we investigate spin-1/2 chains with uniform local couplings to a Markovian environment using the time-dependent density matrix renormalization group. For the open XXZ model, we discover that the decoherence time diverges in the thermodynamic limit. The coherence decay is then algebraic instead of exponential. This is due to a vanishing gap in the spectrum of the corresponding Liouville superoperator and can be explained on the basis of a perturbative treatment. In contrast, decoherence in the open transverse-field Ising model is found to be always exponential. In this case, the internal interactions can both facilitate and impede the environment-induced decoherence.
Collapse
Affiliation(s)
- Zi Cai
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, 80333 Munich, Germany
| | | |
Collapse
|
18
|
Kou X, He L, Lang M, Fan Y, Wong K, Jiang Y, Nie T, Jiang W, Upadhyaya P, Xing Z, Wang Y, Xiu F, Schwartz RN, Wang KL. Manipulating surface-related ferromagnetism in modulation-doped topological insulators. NANO LETTERS 2013; 13:4587-4593. [PMID: 24020459 DOI: 10.1021/nl4020638] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
A new class of devices based on topological insulators (TI) can be achieved by the direct engineering of the time-reversal-symmetry (TRS) protected surface states. In the meantime, a variety of interesting phenomena are also expected when additional ferromagnetism is introduced to the original topological order. In this Letter, we report the magnetic responses from the magnetically modulation-doped (Bi(z)Sb(1-z))2Te3/Cr(x)(Bi(y)Sb(1-y))2Te3 bilayer films. By electrically tuning the Fermi level across the Dirac point, we show that the top TI surface carriers can effectively mediate the magnetic impurities and generate robust ferromagnetic order. More importantly, such surface magneto-electric effects can be either enhanced or suppressed, depending on the magnetic interaction range inside the TI heterostructures. The manipulation of surface-related ferromagnetism realized in our modulation-doped TI device is important for the realization of TRS-breaking topological physics, and it may also lead to new applications of TI-based multifunctional heterostructures.
Collapse
Affiliation(s)
- Xufeng Kou
- Device Research Laboratory, Department of Electrical Engineering, University of California , Los Angeles, California 90095, United States
| | | | | | | | | | | | | | | | | | | | | | | | | | | |
Collapse
|
19
|
Wang DS, Berry DW, de Oliveira MC, Sanders BC. Solovay-Kitaev decomposition strategy for single-qubit channels. PHYSICAL REVIEW LETTERS 2013; 111:130504. [PMID: 24116760 DOI: 10.1103/physrevlett.111.130504] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2013] [Indexed: 06/02/2023]
Abstract
Inspired by the Solovay-Kitaev decomposition for approximating unitary operations as a sequence of operations selected from a universal quantum computing gate set, we introduce a method for approximating any single-qubit channel using single-qubit gates and the controlled-not (cnot). Our approach uses the decomposition of the single-qubit channel into a convex combination of "quasiextreme" channels. Previous techniques for simulating general single-qubit channels would require as many as 20 cnot gates, whereas ours only needs one, bringing it within the range of current experiments.
Collapse
Affiliation(s)
- Dong-Sheng Wang
- Institute for Quantum Science and Technology, University of Calgary, Alberta T2N 1N4, Canada
| | | | | | | |
Collapse
|
20
|
Barthel T, Kliesch M. Quasilocality and efficient simulation of markovian quantum dynamics. PHYSICAL REVIEW LETTERS 2012; 108:230504. [PMID: 23003931 DOI: 10.1103/physrevlett.108.230504] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2011] [Indexed: 06/01/2023]
Abstract
We consider open many-body systems governed by a time-dependent quantum master equation with short-range interactions. With a generalized Lieb-Robinson bound, we show that the evolution in this very generic framework is quasilocal; i.e., the evolution of observables can be approximated by implementing the dynamics only in a vicinity of the observables' support. The precision increases exponentially with the diameter of the considered subsystem. Hence, time evolution can be simulated on classical computers with a cost that is independent of the system size. Providing error bounds for Trotter decompositions, we conclude that the simulation on a quantum computer is additionally efficient in time. For experiments and simulations in the Schrödinger picture, our result can be used to rigorously bound finite-size effects.
Collapse
Affiliation(s)
- Thomas Barthel
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | | |
Collapse
|
21
|
Dorner R, Goold J, Vedral V. Towards quantum simulations of biological information flow. Interface Focus 2012; 2:522-8. [PMID: 23919131 DOI: 10.1098/rsfs.2011.0109] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2011] [Accepted: 03/06/2012] [Indexed: 11/12/2022] Open
Abstract
Recent advances in the spectroscopy of biomolecules have highlighted the possibility of quantum coherence playing an active role in biological energy transport. The revelation that quantum coherence can survive in the hot and wet environment of biology has generated a lively debate across both the physics and biology communities. In particular, it remains unclear to what extent non-trivial quantum effects are used in biology and what advantage, if any, they afford. We propose an analogue quantum simulator, based on currently available techniques in ultra-cold atom physics, to study a model of energy and electron transport based on the Holstein Hamiltonian. By simulating the salient aspects of a biological system in a tunable laboratory set-up, we hope to gain insight into the validity of several theoretical models of biological quantum transport in a variety of relevant parameter regimes.
Collapse
Affiliation(s)
- Ross Dorner
- Blackett Laboratory, Imperial College London, London, UK ; Clarendon Laboratory, University of Oxford, Oxford, UK
| | | | | |
Collapse
|