1
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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.
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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
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2
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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.
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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
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3
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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.
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Affiliation(s)
| | - Pauline J Ollitrault
- IBM Quantum, IBM Research - Zurich, Rüschlikon, Switzerland
- QC Ware, Palo Alto, CA, USA
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4
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Lockyer S, Chiesa A, Brookfield A, Timco GA, Whitehead GFS, McInnes EJL, Carretta S, Winpenny REP. Five-Spin Supramolecule for Simulating Quantum Decoherence of Bell States. J Am Chem Soc 2022; 144:16086-16092. [PMID: 36007954 PMCID: PMC9460766 DOI: 10.1021/jacs.2c06384] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2022] [Indexed: 11/28/2022]
Abstract
We report a supramolecule that contains five spins of two different types and with, crucially, two different and predictable interaction energies between the spins. The supramolecule is characterized, and the interaction energies are demonstrated by electron paramagnetic resonance (EPR) spectroscopy. Based on the measured parameters, we propose experiments that would allow this designed supramolecule to be used to simulate quantum decoherence in maximally entangled Bell states that could be used in quantum teleportation.
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Affiliation(s)
- Selena
J. Lockyer
- Department
of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, U.K.
| | - Alessandro Chiesa
- Dipartimento
di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, I-43124 Parma, Italy
- INFN−Sezione
di Milano-Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy
- UdR
Parma, INSTM, I-43124 Parma, Italy
| | - Adam Brookfield
- Department
of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, U.K.
| | - Grigore A. Timco
- Department
of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, U.K.
| | - George F. S. Whitehead
- Department
of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, U.K.
| | - Eric J. L. McInnes
- Department
of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, U.K.
| | - Stefano Carretta
- Dipartimento
di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, I-43124 Parma, Italy
- INFN−Sezione
di Milano-Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy
- UdR
Parma, INSTM, I-43124 Parma, Italy
| | - Richard E. P. Winpenny
- Department
of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, U.K.
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5
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Chen JF, Li Y, Dong H. Simulating Finite-Time Isothermal Processes with Superconducting Quantum Circuits. ENTROPY (BASEL, SWITZERLAND) 2021; 23:353. [PMID: 33809653 PMCID: PMC8002232 DOI: 10.3390/e23030353] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/09/2021] [Revised: 03/12/2021] [Accepted: 03/12/2021] [Indexed: 11/16/2022]
Abstract
Finite-time isothermal processes are ubiquitous in quantum-heat-engine cycles, yet complicated due to the coexistence of the changing Hamiltonian and the interaction with the thermal bath. Such complexity prevents classical thermodynamic measurements of a performed work. In this paper, the isothermal process is decomposed into piecewise adiabatic and isochoric processes to measure the performed work as the internal energy change in adiabatic processes. The piecewise control scheme allows the direct simulation of the whole process on a universal quantum computer, which provides a new experimental platform to study quantum thermodynamics. We implement the simulation on ibmqx2 to show the 1/τ scaling of the extra work in finite-time isothermal processes.
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Affiliation(s)
- Jin-Fu Chen
- Beijing Computational Science Research Center, Beijing 100193, China;
- Graduate School of China Academy of Engineering Physics, No. 10 Xibeiwang East Road, Haidian District, Beijing 100193, China;
| | - Ying Li
- Graduate School of China Academy of Engineering Physics, No. 10 Xibeiwang East Road, Haidian District, Beijing 100193, China;
| | - Hui Dong
- Graduate School of China Academy of Engineering Physics, No. 10 Xibeiwang East Road, Haidian District, Beijing 100193, China;
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6
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Head-Marsden K, Flick J, Ciccarino CJ, Narang P. Quantum Information and Algorithms for Correlated Quantum Matter. Chem Rev 2020; 121:3061-3120. [PMID: 33326218 DOI: 10.1021/acs.chemrev.0c00620] [Citation(s) in RCA: 37] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Discoveries in quantum materials, which are characterized by the strongly quantum-mechanical nature of electrons and atoms, have revealed exotic properties that arise from correlations. It is the promise of quantum materials for quantum information science superimposed with the potential of new computational quantum algorithms to discover new quantum materials that inspires this Review. We anticipate that quantum materials to be discovered and developed in the next years will transform the areas of quantum information processing including communication, storage, and computing. Simultaneously, efforts toward developing new quantum algorithmic approaches for quantum simulation and advanced calculation methods for many-body quantum systems enable major advances toward functional quantum materials and their deployment. The advent of quantum computing brings new possibilities for eliminating the exponential complexity that has stymied simulation of correlated quantum systems on high-performance classical computers. Here, we review new algorithms and computational approaches to predict and understand the behavior of correlated quantum matter. The strongly interdisciplinary nature of the topics covered necessitates a common language to integrate ideas from these fields. We aim to provide this common language while weaving together fields across electronic structure theory, quantum electrodynamics, algorithm design, and open quantum systems. Our Review is timely in presenting the state-of-the-art in the field toward algorithms with nonexponential complexity for correlated quantum matter with applications in grand-challenge problems. Looking to the future, at the intersection of quantum information science and algorithms for correlated quantum matter, we envision seminal advances in predicting many-body quantum states and describing excitonic quantum matter and large-scale entangled states, a better understanding of high-temperature superconductivity, and quantifying open quantum system dynamics.
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Affiliation(s)
- Kade Head-Marsden
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Johannes Flick
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
| | - Christopher J Ciccarino
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States.,Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Prineha Narang
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
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7
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A quantum algorithm for evolving open quantum dynamics on quantum computing devices. Sci Rep 2020; 10:3301. [PMID: 32094482 PMCID: PMC7039952 DOI: 10.1038/s41598-020-60321-x] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2019] [Accepted: 02/07/2020] [Indexed: 11/08/2022] Open
Abstract
Designing quantum algorithms for simulating quantum systems has seen enormous progress, yet few studies have been done to develop quantum algorithms for open quantum dynamics despite its importance in modeling the system-environment interaction found in most realistic physical models. In this work we propose and demonstrate a general quantum algorithm to evolve open quantum dynamics on quantum computing devices. The Kraus operators governing the time evolution can be converted into unitary matrices with minimal dilation guaranteed by the Sz.-Nagy theorem. This allows the evolution of the initial state through unitary quantum gates, while using significantly less resource than required by the conventional Stinespring dilation. We demonstrate the algorithm on an amplitude damping channel using the IBM Qiskit quantum simulator and the IBM Q 5 Tenerife quantum device. The proposed algorithm does not require particular models of dynamics or decomposition of the quantum channel, and thus can be easily generalized to other open quantum dynamical models.
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8
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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.
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9
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Mancino L, Cavina V, De Pasquale A, Sbroscia M, Booth RI, Roccia E, Gianani I, Giovannetti V, Barbieri M. Geometrical Bounds on Irreversibility in Open Quantum Systems. PHYSICAL REVIEW LETTERS 2018; 121:160602. [PMID: 30387653 DOI: 10.1103/physrevlett.121.160602] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2018] [Revised: 08/01/2018] [Indexed: 06/08/2023]
Abstract
The Clausius inequality has deep implications for reversibility and the arrow of time. Quantum theory is able to extend this result for closed systems by inspecting the trajectory of the density matrix on its manifold. Here we show that this approach can provide an upper and lower bound to the irreversible entropy production for open quantum systems as well. These provide insights on how the information on the initial state is forgotten through a thermalization process. Limits of the applicability of our bounds are discussed and demonstrated in a quantum photonic simulator.
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Affiliation(s)
- Luca Mancino
- Dipartimento di Scienze, Università degli Studi Roma Tre, Via della Vasca Navale 84, 00146, Rome, Italy
| | - Vasco Cavina
- NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, Piazza dei Cavalieri 7, I-56126, Pisa, Italy
| | - Antonella De Pasquale
- NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, Piazza dei Cavalieri 7, I-56126, Pisa, Italy
- Dipartimento di Fisica, Università di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino (FI), Italy
- INFN Sezione di Firenze, via G.Sansone 1, I-50019 Sesto Fiorentino (FI), Italy
| | - Marco Sbroscia
- Dipartimento di Scienze, Università degli Studi Roma Tre, Via della Vasca Navale 84, 00146, Rome, Italy
| | - Robert I Booth
- Dipartimento di Scienze, Università degli Studi Roma Tre, Via della Vasca Navale 84, 00146, Rome, Italy
- Institut de Physique, Sorbonne Université, 4 Place Jussieu, 75005, Paris, France
| | - Emanuele Roccia
- Dipartimento di Scienze, Università degli Studi Roma Tre, Via della Vasca Navale 84, 00146, Rome, Italy
| | - Ilaria Gianani
- Dipartimento di Scienze, Università degli Studi Roma Tre, Via della Vasca Navale 84, 00146, Rome, Italy
| | - Vittorio Giovannetti
- NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, Piazza dei Cavalieri 7, I-56126, Pisa, Italy
| | - Marco Barbieri
- Dipartimento di Scienze, Università degli Studi Roma Tre, Via della Vasca Navale 84, 00146, Rome, Italy
- Istituto Nazionale di Ottica-CNR, Largo Enrico Fermi 6, 50125, Florence, Italy
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10
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Tham WK, Ferretti H, Sadashivan AV, Steinberg AM. Simulating and Optimising Quantum Thermometry Using Single Photons. Sci Rep 2016; 6:38822. [PMID: 27974836 PMCID: PMC5156908 DOI: 10.1038/srep38822] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2016] [Accepted: 11/14/2016] [Indexed: 11/09/2022] Open
Abstract
A classical thermometer typically works by exchanging energy with the system being measured until it comes to equilibrium, at which point the readout is related to the final energy state of the thermometer. A recent paper noted that with a quantum thermometer consisting of a single spin/qubit, temperature discrimination is better achieved at finite times rather than once equilibration is essentially complete. Furthermore, preparing a qubit thermometer in a state with quantum coherence instead of an incoherent one improves its sensitivity to temperature differences. Implementing a recent proposal for efficiently emulating an arbitrary quantum channel, we use the quantum polarisation state of individual photons as models of "single-qubit thermometers" which evolve for a certain time in contact with a thermal bath. We investigate the optimal thermometer states for temperature discrimination, and the optimal interaction times, confirming that there is a broad regime where quantum coherence provides a significant improvement. We also discuss the more practical question of thermometers composed of a finite number of spins/qubits (greater than one), and characterize the performance of an adaptive protocol for making optimal use of all the qubits.
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Affiliation(s)
- W K Tham
- Centre for Quantum Information &Quantum Control and Institute for Optical Sciences, Department of Physics, University of Toronto, 60 St. George St, Toronto, Ontario, M5S 1A7, Canada
| | - H Ferretti
- Centre for Quantum Information &Quantum Control and Institute for Optical Sciences, Department of Physics, University of Toronto, 60 St. George St, Toronto, Ontario, M5S 1A7, Canada
| | - A V Sadashivan
- Centre for Quantum Information &Quantum Control and Institute for Optical Sciences, Department of Physics, University of Toronto, 60 St. George St, Toronto, Ontario, M5S 1A7, Canada
| | - A M Steinberg
- Centre for Quantum Information &Quantum Control and Institute for Optical Sciences, Department of Physics, University of Toronto, 60 St. George St, Toronto, Ontario, M5S 1A7, Canada.,Canadian Institute For Advanced Research, 180 Dundas St. W., Toronto, Ontario, M5G 1Z8, Canada
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