Quantum Speed Limit under Brachistochrone Evolution

Dou, Fu-Quan; Han, Min-Peng; Shu, Chuan-Cun

doi:10.1103/physrevapplied.20.014031

Cited by 6 publications

(4 citation statements)

References 65 publications

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“…Moreover, motivated by our revisitation of GA methods in quantum information science together with our findings appeared in Refs. [68,69], we think that the application of the GA language (with special emphasis on the concept of rotation) can be naturally extended (for gaining deeper physical insights) to the analysis of the propagation of light with maximal degree of coherence [68,70,71] and, in addition, to the characterization of the geometry of quantum evolutions [69,[72][73][74][75][76][77].…”

Section: Discussionmentioning

confidence: 99%

From Entanglement to Universality: A Multiparticle Spacetime Algebra Approach to Quantum Computational Gates Revisited

Cafaro,

Bahreyni,

Rossetti

2024

Symmetry

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Alternative mathematical explorations in quantum computing can be of great scientific interest, especially if they come with penetrating physical insights. In this paper, we present a critical revisitation of our application of geometric (Clifford) algebras (GAs) in quantum computing as originally presented in [C. Cafaro and S. Mancini, Adv. Appl. Clifford Algebras 21, 493 (2011)]. Our focus is on testing the usefulness of geometric algebras (GAs) techniques in two quantum computing applications. First, making use of the geometric algebra of a relativistic configuration space (namely multiparticle spacetime algebra or MSTA), we offer an explicit algebraic characterization of one- and two-qubit quantum states together with a MSTA description of one- and two-qubit quantum computational gates. In this first application, we devote special attention to the concept of entanglement, focusing on entangled quantum states and two-qubit entangling quantum gates. Second, exploiting the previously mentioned MSTA characterization together with the GA depiction of the Lie algebras SO3;R and SU2;C depending on the rotor group Spin+3,0 formalism, we focus our attention to the concept of universality in quantum computing by reevaluating Boykin’s proof on the identification of a suitable set of universal quantum gates. At the end of our mathematical exploration, we arrive at two main conclusions. Firstly, the MSTA perspective leads to a powerful conceptual unification between quantum states and quantum operators. More specifically, the complex qubit space and the complex space of unitary operators acting on them merge in a single multivectorial real space. Secondly, the GA viewpoint on rotations based on the rotor group Spin+3,0 carries both conceptual and computational advantages compared to conventional vectorial and matricial methods.

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Section: Discussionmentioning

confidence: 99%

From Entanglement to Universality: A Multiparticle Spacetime Algebra Approach to Quantum Computational Gates Revisited

Cafaro,

Bahreyni,

Rossetti

2024

Symmetry

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

“…A tight QSL is given on the basis of the unified bound of MT and ML bounds [10,28]. Then, the QSLs of MT and ML bounds have been broadly used to characterize quantum dynamics in closed systems [29,30], many-body systems [31,32], time-dependent driven systems [33,34], time-dependent non-Hermitian systems [35,36], thermodynamic system [37,38], others open quantum systems [39,40], and see more in the review papers [14,41].Recently, QSLs from the point of view of the total system consisting of the open system and its environment have been proposed, and its relationship with entanglement has been widely studied [42][43][44]. Meanwhile,the recent advancements in QSLs extensions to How quickly an observable change, or a finite speed that is constrained by the topological structure of the underlying dynamics [28,37,[45][46][47][48][49][50]].…”

mentioning

confidence: 99%

Quantum evolution speed and its limit in the driven double‐well system

Xu,

Zhang,

Huang

2023

Int J of Quantum Chemistry

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We investigate quantum evolution speed in the driven double‐well system using the entangled trajectory molecular dynamics method. We emphasize not only the evolution speed of the quantum state but also its limit according to different definitions. The Wasserstein 1‐distance is used to quantify the distance between distinguishable quantum states in the phase space, the quantum speed limit based on the geometry has been shown to be the strictest one. The single trajectory's contribution to the quantum speed limit is discussed, which is related to both the time evolution of the trajectory and its position in the total Wigner function. The resonance and chaos strongly enhance the evolution speed and its limit in the driven double‐well system. The resonance effect makes a large proportion of representative points pass through the well as a whole, nevertheless, the chaos makes the Wigner function disperse in the phase space.

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“…Two well-known formulae are the Mandelstam-Tamm (MT) [30] and Margolus-Levitin (ML) [31] relations, which establish a lower bound on the evolution time in closed quantum systems under unitary evolution with a time-independent Hamiltonian. [32] Subsequent developments in the field have expanded these formulae to address a broader range of quantum complexities, including time-dependent Hamiltonian, [33][34][35] open quantum systems, [36][37][38][39][40] and many-body systems, [41][42][43] etc. The QSL can be applied to quantum systems immersed in a field that cannot be altered by the control Hamiltonian, which is also known as the quantum Zermelo navigation problem.…”

mentioning

confidence: 99%

Balancing the Quantum Speed Limit and Instantaneous Energy Cost in Adiabatic Quantum Evolution

Xu 徐,

Zhang 张,

Zheng 郑

et al. 2024

Chinese Phys. Lett.

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Adiabatic time-optimal quantum controls are extensively used in quantum technologies to break the constraints imposed by short coherence times. However, in practical, it is crucial to consider the trade-off between the quantum evolution speed and instantaneous energy cost of process because of the constraints in the available control Hamiltonian. Here, we experimentally show using a transmon qubit that, even in the presence of vanishing energy gaps, it is possible to reach a highly time-optimal adiabatic quantum driving at low energy cost in the whole evolution process. This validates the recently derived general solution of the quantum Zermelo navigation problem, paving the way for energy-efficient quantum control which is usually overlooked in conventional speed-up schemes, including the well-known counter-diabatic driving. By designing the control Hamiltonian based on the quantum speed limit bound quantified by the changing rate of phase in the interaction picture, we reveal the relationship between the quantum speed limit and instantaneous energy cost. Consequently, we demonstrate fast and high-fidelity quantum adiabatic processes by employing energy-efficient driving strengths, indicating a promising strategy for expanding the applications of time-optimal quantum controls in superconducting quantum circuits.

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Quantum Speed Limit under Brachistochrone Evolution

Cited by 6 publications

References 65 publications

From Entanglement to Universality: A Multiparticle Spacetime Algebra Approach to Quantum Computational Gates Revisited

From Entanglement to Universality: A Multiparticle Spacetime Algebra Approach to Quantum Computational Gates Revisited

Quantum evolution speed and its limit in the driven double‐well system

Balancing the Quantum Speed Limit and Instantaneous Energy Cost in Adiabatic Quantum Evolution

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