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Marvian I, Liu H, Hulse A. Rotationally Invariant Circuits: Universality with the Exchange Interaction and Two Ancilla Qubits. PHYSICAL REVIEW LETTERS 2024; 132:130201. [PMID: 38613310 DOI: 10.1103/physrevlett.132.130201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2022] [Revised: 12/14/2023] [Accepted: 02/13/2024] [Indexed: 04/14/2024]
Abstract
Universality of local unitary transformations is one of the cornerstones of quantum computing with many applications and implications that go beyond this field. However, it has recently been shown that this universality does not hold in the presence of continuous symmetries: generic symmetric unitaries on a composite system cannot be implemented, even approximately, using local symmetric unitaries on the subsystems. In this Letter, we show that, despite these constraints, any SU(2) rotationally invariant unitary can be realized with the Heisenberg exchange interaction, which is 2-local and rotationally invariant, provided that the system interacts with a pair of ancilla qubits. We also show that a single ancilla is not enough to achieve universality. Furthermore, we study qubit circuits formed from k-local rotationally invariant unitaries and fully characterize the constraints imposed by locality on the realizable unitaries. We also find an interpretation of these constraints in terms of the average energy of states with a fixed angular momentum.
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Affiliation(s)
- Iman Marvian
- Departments of Physics, Duke University, Durham, North Carolina 27708, USA
- Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, USA
- Duke Quantum Center, Durham, North Carolina 27708, USA
| | - Hanqing Liu
- Departments of Physics, Duke University, Durham, North Carolina 27708, USA
| | - Austin Hulse
- Departments of Physics, Duke University, Durham, North Carolina 27708, USA
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Alvertis AM, Schröder FAYN, Chin AW. Non-equilibrium relaxation of hot states in organic semiconductors: Impact of mode-selective excitation on charge transfer. J Chem Phys 2019; 151:084104. [PMID: 31470711 DOI: 10.1063/1.5115239] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
The theoretical study of open quantum systems strongly coupled to a vibrational environment remains computationally challenging due to the strongly non-Markovian characteristics of the dynamics. We study this problem in the case of a molecular dimer of the organic semiconductor tetracene, the exciton states of which are strongly coupled to a few hundreds of molecular vibrations. To do so, we employ a previously developed tensor network approach, based on the formalism of matrix product states. By analyzing the entanglement structure of the system wavefunction, we can expand it in a tree tensor network state, which allows us to perform a fully quantum mechanical time evolution of the exciton-vibrational system, including the effect of 156 molecular vibrations. We simulate the dynamics of hot states, i.e., states resulting from excess energy photoexcitation, by constructing various initial bath states, and show that the exciton system indeed has a memory of those initial configurations. In particular, the specific pathway of vibrational relaxation is shown to strongly affect the quantum coherence between exciton states in time scales relevant for the ultrafast dynamics of application-relevant processes such as charge transfer. The preferential excitation of low-frequency modes leads to a limited number of relaxation pathways, thus "protecting" quantum coherence and leading to a significant increase in the charge transfer yield in the dimer structure.
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Affiliation(s)
- Antonios M Alvertis
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Florian A Y N Schröder
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Alex W Chin
- CNRS, Institut des NanoSciences de Paris, Sorbonne Université, 4 place Jussieu boite courrier 840, 75252 Paris Cedex 05, France
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Marvian I, Lidar DA. Quantum Speed Limits for Leakage and Decoherence. PHYSICAL REVIEW LETTERS 2015; 115:210402. [PMID: 26636833 DOI: 10.1103/physrevlett.115.210402] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2015] [Indexed: 06/05/2023]
Abstract
We introduce state-independent, nonperturbative Hamiltonian quantum speed limits for population leakage and fidelity loss, for a gapped open system interacting with a reservoir. These results hold in the presence of initial correlations between the system and the reservoir, under the sole assumption that their interaction and its commutator with the reservoir Hamiltonian are norm bounded. The reservoir need not be thermal and can be time dependent. We study the significance of energy mismatch between the system and the local degrees of freedom of the reservoir that directly interact with the system. We demonstrate that, in general, by increasing the system gap we may reduce this energy mismatch, and, consequently, drive the system and the reservoir into resonance; this can accelerate fidelity loss, irrespective of the thermal properties or state of the reservoir. This implies that quantum error suppression strategies based on increasing the gap are not uniformly beneficial. Our speed limits also yield an elementary lower bound on the relaxation time of spin systems.
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Affiliation(s)
- Iman Marvian
- Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089, USA
- Department of Physics, University of Southern California, Los Angeles, California 90089, USA
| | - Daniel A Lidar
- Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089, USA
- Department of Physics, University of Southern California, Los Angeles, California 90089, USA
- Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
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Douçot B, Ioffe LB. Physical implementation of protected qubits. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2012; 75:072001. [PMID: 22790777 DOI: 10.1088/0034-4885/75/7/072001] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We review the general notion of topological protection of quantum states in spin models and its relation with the ideas of quantum error correction. We show that topological protection can be viewed as a Hamiltonian realization of error correction: for a quantum code for which the minimal number of errors that remain undetected is N, the corresponding Hamiltonian model of the effects of the environment noise appears only in the Nth order of the perturbation theory.We discuss the simplest model Hamiltonians that realize topological protection and their implementation in superconducting arrays. We focus on two dual realizations: in one the protected state is stored in the parity of the Cooper pair number, in the other, in the parity of the flux number. In both cases the superconducting arrays allow a number of fault-tolerant operations that should make the universal quantum computation possible.
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Affiliation(s)
- B Douçot
- Laboratoire de Physique Théorique et Hautes Énergies, CNRS UMR 7589 et Université Paris 6, Boîte 126, 4 place Jussieu, 75252 Paris Cedex 05, France
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Coudreau T, Douçot B, Dubessy R, Andreoli D, Milman P. Robust preparation and manipulation of protected qubits using time-varying Hamiltonians. PHYSICAL REVIEW LETTERS 2011; 107:030502. [PMID: 21838338 DOI: 10.1103/physrevlett.107.030502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2010] [Indexed: 05/31/2023]
Abstract
We show that it is possible to initialize and manipulate in a deterministic manner protected qubits using time-varying Hamiltonians. Taking advantage of the symmetries of the system, we predict the effect of the noise during the initialization and manipulation. These predictions are in good agreement with numerical simulations. Our study shows that the topological protection remains efficient under realistic experimental conditions.
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Affiliation(s)
- Thomas Coudreau
- Laboratoire Matériaux et Phénomènes Quantiques, CNRS UMR 7162, Université Paris Diderot, 75013 Paris, France.
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Shinkai G, Hayashi T, Ota T, Fujisawa T. Correlated coherent oscillations in coupled semiconductor charge qubits. PHYSICAL REVIEW LETTERS 2009; 103:056802. [PMID: 19792523 DOI: 10.1103/physrevlett.103.056802] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2009] [Indexed: 05/28/2023]
Abstract
We study coherent dynamics of two spatially separated electrons in a coupled semiconductor double quantum dot (DQD). Coherent oscillations in one DQD are strongly influenced by electronic states of the other DQD, or the two electrons simultaneously tunnel in a correlated manner. The observed coherent oscillations are interpreted as various two-qubit operations. The results encourage searching quantum entanglement in electronic devices.
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Affiliation(s)
- Gou Shinkai
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, 243-0198, Japan
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Lidar DA. Towards fault tolerant adiabatic quantum computation. PHYSICAL REVIEW LETTERS 2008; 100:160506. [PMID: 18518178 DOI: 10.1103/physrevlett.100.160506] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2007] [Revised: 11/04/2007] [Indexed: 05/26/2023]
Abstract
I show how to protect adiabatic quantum computation (AQC) against decoherence and certain control errors, using a hybrid methodology involving dynamical decoupling, subsystem and stabilizer codes, and energy gaps. Corresponding error bounds are derived. As an example, I show how to perform decoherence-protected AQC against local noise using at most two-body interactions.
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Affiliation(s)
- Daniel A Lidar
- Department of Chemistry, Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089, USA
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Brown WG, Santos LF, Starling DJ, Viola L. Quantum chaos, delocalization, and entanglement in disordered Heisenberg models. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:021106. [PMID: 18351986 DOI: 10.1103/physreve.77.021106] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2007] [Indexed: 05/26/2023]
Abstract
We investigate disordered one- and two-dimensional Heisenberg spin lattices across the transition from integrability to quantum chaos from both statistical many-body and quantum-information perspectives. Special emphasis is devoted to quantitatively exploring the interplay between eigenvector statistics, delocalization, and entanglement in the presence of nontrivial symmetries. The implication of the basis dependence of state delocalization indicators (such as the number of principal components) is addressed, and a measure of relative delocalization is proposed in order to robustly characterize the onset of chaos in the presence of disorder. Both standard multipartite and generalized entanglement are investigated in a wide parameter regime by using a family of spin- and fermion-purity measures, their dependence on delocalization and on energy spectrum statistics being examined. A distinctive correlation between entanglement, delocalization, and integrability is uncovered, which may be generic to systems described by the two-body random ensemble and may point to a new diagnostic tool for quantum chaos. Analytical estimates for typical entanglement of random pure states restricted to a proper subspace of the full Hilbert space are also established and compared with random matrix theory predictions.
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Affiliation(s)
- Winton G Brown
- Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755, USA.
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Weinstein YS, Hellberg CS. Scalable architecture for coherence-preserving qubits. PHYSICAL REVIEW LETTERS 2007; 98:110501. [PMID: 17501034 DOI: 10.1103/physrevlett.98.110501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2006] [Indexed: 05/15/2023]
Abstract
We propose scalable architectures for the coherence-preserving qubits introduced by Bacon, Brown, and Whaley [Phys. Rev. Lett. 87, 247902 (2001)]. These architectures employ extra qubits providing additional degrees of freedom to the system. These extra degrees of freedom can be used to counter coupling strength errors within the coherence-preserving qubit and combat interactions with environmental qubits. Importantly, these architectures provide flexibility in qubit arrangement, allowing all physical qubits to be arranged in two spatial dimensions.
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Affiliation(s)
- Yaakov S Weinstein
- Quantum Information Science Group, The Mitre Corporation, Eatontown, New Jersey 07724, USA.
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Fonseca-Romero KM, Kohler S, Hänggi P. Coherence stabilization of a two-qubit gate by ac fields. PHYSICAL REVIEW LETTERS 2005; 95:140502. [PMID: 16241635 DOI: 10.1103/physrevlett.95.140502] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2004] [Indexed: 05/05/2023]
Abstract
We consider a CNOT gate operation under the influence of quantum bit-flip noise and demonstrate that ac fields can change the qubit Hamiltonian in such a way that it approximately commutes with the bath coupling. Then the noise effectively acts as phase noise which improves coherence up to several orders of magnitude while the gate operation time remains unchanged. Within a high-frequency approximation, both purity and fidelity of the gate operation are studied analytically. The numerical treatment with a Bloch-Redfield master equation confirms the analytical results.
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Affiliation(s)
- Karen M Fonseca-Romero
- Institut für Physik, Universität Augsburg, Universitätsstrasse 1, D-86135 Augsburg, Germany
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Grigorenko IA, Khveshchenko DV. Single-step implementation of universal quantum gates. PHYSICAL REVIEW LETTERS 2005; 95:110501. [PMID: 16196990 DOI: 10.1103/physrevlett.95.110501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2005] [Indexed: 05/04/2023]
Abstract
We construct optimized implementations of the controlled-NOT and other universal two-qubit gates that, unlike many of the previously proposed protocols, are carried out in a single step. The new protocols require tunable interqubit couplings but, in return, show a significant improvement in the quality of gate operations. We make specific predictions for coupled Josephson junction qubits and compare them with the results of recent experiments.
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Affiliation(s)
- I A Grigorenko
- Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599, USA
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Grigorenko IA, Khveshchenko DV. Robust two-qubit quantum registers. PHYSICAL REVIEW LETTERS 2005; 94:040506. [PMID: 15783543 DOI: 10.1103/physrevlett.94.040506] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2003] [Indexed: 05/24/2023]
Abstract
We carry out a systematic analysis of a pair of coupled qubits, each of which is subject to its own dissipative environment, and argue that a combination of the interqubit couplings which provides for the lowest possible decoherence rates corresponds to the incidence of a double spectral degeneracy in the two-qubit system. We support this general argument by the results of an evolutionary genetic algorithm which can also be used for optimizing time-dependent processes (gates) and their sequences that implement various quantum computing protocols.
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Affiliation(s)
- I A Grigorenko
- Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 27599, USA
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Meier F, Levy J, Loss D. Quantum computing with spin cluster qubits. PHYSICAL REVIEW LETTERS 2003; 90:047901. [PMID: 12570460 DOI: 10.1103/physrevlett.90.047901] [Citation(s) in RCA: 87] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2002] [Indexed: 05/24/2023]
Abstract
We study the low energy states of finite spin chains with isotropic (Heisenberg) and anisotropic (XY and Ising-like) antiferromagnetic exchange interaction with uniform and nonuniform coupling constants. We show that for an odd number of sites a spin cluster qubit can be defined in terms of the ground state doublet. This qubit is remarkably insensitive to the placement and coupling anisotropy of spins within the cluster. One- and two-qubit quantum gates can be generated by magnetic fields and intercluster exchange, and leakage during quantum gate operation is small. Spin cluster qubits inherit the long decoherence times and short gate operation times of single spins. Control of single spins is hence not necessary for the realization of universal quantum gates.
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Affiliation(s)
- Florian Meier
- Department of Physics and Astronomy, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
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Lidar DA, Birgitta Whaley K. Decoherence-Free Subspaces and Subsystems. IRREVERSIBLE QUANTUM DYNAMICS 2003. [DOI: 10.1007/3-540-44874-8_5] [Citation(s) in RCA: 129] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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Byrd MS, Lidar DA. Comprehensive encoding and decoupling solution to problems of decoherence and design in solid-state quantum computing. PHYSICAL REVIEW LETTERS 2002; 89:047901. [PMID: 12144500 DOI: 10.1103/physrevlett.89.047901] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2002] [Indexed: 05/23/2023]
Abstract
Proposals for scalable quantum computing devices suffer not only from decoherence due to the interaction with their environment, but also from severe engineering constraints. Here we introduce a practical solution to these major concerns, addressing solid-state proposals in particular. Decoherence is first reduced by encoding a logical qubit into two qubits, then completely eliminated by an efficient set of decoupling pulse sequences. The same encoding removes the need for single-qubit operations, which pose a difficult design constraint. We further show how the dominant decoherence processes can be identified empirically, in order to optimize the decoupling pulses.
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Affiliation(s)
- Mark S Byrd
- Chemical Physics Theory Group, University of Toronto, 80 St. George Street, Toronto, Ontario, Canada M5S 3H6
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