Minimum Evolution Time Research Articles

Quantum speed limit time: role of coherence

The minimum evolution time between multi-qubit quantum states is estimated for non-Markovian quantum channels. We consider the maximally coherent pure and mixed states as well as multi-qubit X states as initial states and discuss the impact of initial coherence and the behaviour of coherence on their speed of evolution for both dephasing and dissipative processes. The role of the non-zero value of initial coherence under information backflow conditions for the non-unital dissipative process is revealed by the flow of quantum speed limit time (τ QSL ). The trade-off between mixedness and coherence on the speed limit time reveals the nature of the quantum process the states undergo. The complementarity effect between mixedness and coherence is more prominent in the quantum non-unital dissipation process. The parametric trajectory of speed limit time vividly depicts the difference in the evolution of pure and mixed initial states, and this could be used to distinguish between the unital and non-unital channels studied in this work. Our investigation of quantum speed limit time on multi-qubit entangled X states reveals that τ QSL can be identified as a potential dynamical witness to distinguish multi-qubit states in the course of evolution.

Quantum Speed Limit Quantified by the Changing Rate of Phase.

The quantum speed limit is important in determining the minimum evolution time of a quantum system,and thus is essential for quantum community. In this Letter, we derive a novel unified quantum speed limit bound for Hermitian and non-Hermitian quantum systems. The bound is quantified by the changing rate of phase of the quantum system, which represents the transmission mode of the quantum states over their evolution. The bound leads to further insights beyond the previous bounds on concrete evolution modes of the quantum system, such as horizontal or parallel transition or horizontal joining of the two quantum states in Hilbert space. The bound is linked to the feasibility of the evolutions of the state vectors, and provides a tighter upper bound. In addition, the generalized Margolus-Levitin bound is discussed.

Efficient Realization of Unitary Transformation at the Quantum Speed Limit

We numerically investigate the minimum time required to implement a target unitary transformation in a qubit network in which each qubit can be locally controlled. The speed limits are explicitly analyzed for qubit graphs used to represent simple models of a Ising spin chain, or a central spin which describes electron-nuclear spin interactions in NV centers. We study the tightness of the obtained speed limits via comparing with the bound derived by Arenz et al. It is shown that the limits capture the coupling constant present in the graph dependence of the minimum evolution time remarkably well.

Geometric quantum speed limits and short-time accessibility to unitary operations

The notion of quantum speed limit (QSL) refers to the fundamental fact that two quantum states become completely distinguishable upon dynamical evolution only after a finite amount time, called the QSL time. A different, but related concept is that of minimum control time (MCT), which is the minimum evolution time needed for a state to be driven (by suitable, generally time-dependent, control fields) to a given target state. While the QSL can give information about the MCT, it usually imposes little restrictions to it, and is thus unpractical for control purposes. In this work we revisit this issue by first presenting a theory of geometrical QSL for unitary transformations, rather than for states, and discuss its implications and limitations. Then, we propose a framework for bounding the MCT for realizing unitary transformations that goes beyond the QSL results and gives much more meaningful information to understand the controlled dynamics of the system at short times.

LA-ICP-MS U/Pb zircon timescale constraints of the Pleistocene latest magmatic activity in the Sancy stratovolcano (French Massif Central)

It has been demonstrated for several years that the UPb zircon system can provide useful dating information for understanding the time-evolution of the volcanic systems. In addition, in situ techniques were successfully used for determining the formation age of young Pliocene and Pleistocene volcanic rocks and to record the spatial and temporal distribution and the lifetime evolution of the magma chambers, generally in the case of large volcanic domains.Here we show that it is possible to obtain a precision at the percent level on zircon from a short-size and late volcanic event from the Sancy stratovolcano (French Massif Central). LA-ICP-MS dating of Pleistocene magmatic zircons allow to distinguish the timescale of these late magmatic events within the complex volcanic activity of this large stratovolcano. A syenite xenolith enclosed into a trachyte pumice flow were dated at 277.6 ± 3.2 ka and 260.1 ± 3.6 ka, respectively, whereas an earlier trachyandesite dome was emplaced at 284.4 ± 4.2 ka. These different ages allow to propose a minimum evolution time of about 24 ± 8 kyrs for a differentiated magma chamber, which corresponds to a short lifetime associated with low magma volumes. The duration of this discrete volcanic event should be compared to the hundreds of thousands of years reported for the large volcanic systems. Interestingly, the zircon crystals from the pumices were embedded into a thin layer of glass of trachytic composition, demonstrating that these zircons crystallized into the melt only a short time before eruption.

Impact of initial states on the quantum speed limits metric in linear molecules

Quantum speed limit (QSL) in a quantum system originates from the essential principle of the quantum mechanics. It gives a maximum speed of evolution or a minimum evolution time of the quantum system, which has potential applications in the fields of quantum information, quantum communication and quantum control and so on. In the last decades, the QSL bounds have been explored from the isolated quantum systems to the open quantum systems, several different geometric measures have been adopted to investigate the distinguishability between the initial and the evolved state. The QSL bounds in many systems have been discussed, indicating that the tightness of the QSL metric is related to the researched dynamical system. However, the QSL problem for the molecular system has rarely been reported. The study of the quantum speed limits in the different molecular systems is helpful for realizing the quantum information technology based on the molecules. In this paper, the generalized quantum speed limit metric for linear molecular dynamics is studied by the algebraic approach. The quantum Fisher information metric and the Wigner-Yanase information metric are both used to study the QSLs in the dynamical evolution of the two linear molecules. Here the dynamical evolutions begin with the two kinds of vibrational states, Fock initial state and coherent initial state. The results show that the quantum Fisher information metric is more appropriate than the Wigner-Yanase information metric for HCN and DCN molecules. The relative differences between the generalized geometric QSL and the two geodesic QSL metrics become bigger gradually with the increase of the initial vibrational quantum number. However, the relative difference for the DCN molecule is smaller than for the HCN molecule. The relative difference between the strong coherent states is smaller, which indicates that the generalized geometric quantum speed limit is suitable to describing high-coherent case. In conclusion, the different QSL metrics reveal the discrepancy in the evolution of the molecular system, and the relative difference is related to the initial state of the molecules and molecular parameters. More molecular systems need to be investigated in order to obtain the criteria between the QSL metrics and the molecular parameters.

Investigating the lower bound of minimum gate times using optimal control

Motivated by a bound derived in a recent work [C. Arenz, B. Russell, D. Burgarth and H. Rabitz, New J. Phys. 19 (2017) 103015], we apply optimal control theory to the dynamics of qubit systems, with the goal of investigating the lower bound of minimum gate times. In practice, we not only need to reach the desired unitary gates but we need to do so in a reasonable time (below the typical decoherence time). Therefore, we employ the recently introduced lower bound to estimate the minimum gate time and resort to numerical gate optimization in order to study the tightness of the obtained bound and our findings verify the relationship between the internal Hamiltonian and the minimum evolution time remarkably well. Finally, we discuss both challenges and ways forward for obtaining the same efficacy under realistic conditions.

An innovative methodology for quickly modeling the spatial-temporal evolution of domino accidents triggered by fire

Past accident analyses indicate that fire escalation is responsible for most of the domino effects that happened in the process industries. The evolution of domino accidents triggered by fire is different from domino accidents triggered by other primary scenarios, since the escalation caused by heat radiation is delayed with respect to the start of the fire. In this study, a methodology involving a Domino Evolution Graph (DEG) model and a Minimum Evolution Time (MET) algorithm is proposed to model the spatial-temporal evolution of domino accidents. Synergistic effects and parallel effects of the spatial evolution, as well as superimposed effects of the temporal evolution possibly occurring in complex domino evolution processes, are considered in this study. A case study demonstrates that the methodology is able to not only capture the spatial-temporal dimension but also to overcome the limitation of the “probit model” w.r.t only able to estimate the damage probability of the first level propagation. Besides, different from simulation or Bayesian approaches, our methodology can quickly provide evolution graphs (paths), the evolution time and the corresponding probability given a primary scenario. Therefore our approach can also be applied to domino risk assessment within an industrial park level and provide support for the allocation decision of safety and security resources.

The roles of drift and control field constraints upon quantum control speed limits

In this work we derive a lower bound for the minimum time required to implement a target unitary transformation through a classical time-dependent field in a closed quantum system. The bound depends on the target gate, the strength of the internal Hamiltonian and the highest permitted control field amplitude. These findings reveal some properties of the reachable set of operations, explicitly analyzed for a single qubit. Moreover, for fully controllable systems, we identify a lower bound for the time at which all unitary gates become reachable. We use numerical gate optimization in order to study the tightness of the obtained bounds. It is shown that in the single qubit case our analytical findings describe the relationship between the highest control field amplitude and the minimum evolution time remarkably well. Finally, we discuss both challenges and ways forward for obtaining tighter bounds for higher dimensional systems, offering a discussion about the mathematical form and the physical meaning of the bound.

Quantum speed limit for a relativistic electron in the noncommutative phase space

The influence of the noncommutativity on the average speed of a relativistic electron interacting with a uniform magnetic field within the minimum evolution time is investigated. We find that it is possible for the wave packet of the electron to travel faster than the speed of light in vacuum because of the noncommutativity. It is a clear signature of violating Lorentz invariance in the noncommutative relativistic quantum mechanical region.

Quantum speed limit for a relativistic electron in a uniform magnetic field

We analyze the influence of relativistic effects on the minimum evolution time between two orthogonal states of a quantum system. Defining the initial state as an homogeneous superposition between two Hamiltonian eigenstates of an electron in a uniform magnetic field, we obtain a relation between the minimum evolution time and the displacement of the mean radial position of the electron wavepacket. The quantum speed limit time is calculated for an electron dynamics described by Dirac and Schroedinger-Pauli equations considering different parameters, such as the strength of magnetic field and the linear momentum of the electron in the axial direction. We highlight that when the electron undergoes a region with extremely strong magnetic field the relativistic and non-relativistic dynamics differ substantially, so that the description given by Schroedinger-Pauli equation enables the electron traveling faster than c, which is prohibited by Einstein's theory of relativity. This approach allows a connection between the abstract Hilbert space and the space-time coordinates, besides the identification of the most appropriate quantum dynamics used to describe the electron motion.

Quantum speed limit and optimal evolution time in a two-level system

Quantum mechanics establishes a fundamental bound for the minimum evolution time between two states of a given system. Known as the quantum speed limit (QSL), it is a useful tool in the context of quantum control, where the speed of some control protocol is usually intended to be as large as possible. While QSL expressions for time-independent Hamiltonians have been well studied, the time-dependent regime has remained somewhat unexplored, albeit being usually the relevant problem to be compared with when studying systems controlled by external fields. In this paper we explore the relation between optimal times found in quantum control and the QSL bound, in the (relevant) time-dependent regime, by discussing the ubiquitous two-level Landau-Zener–type Hamiltonian.

Quantum speed limit with forbidden speed intervals

Quantum mechanics imposes fundamental constraints known as quantum speed limits (QSLs) on the information processing speed of all quantum systems. Every QSL known to date comes from the restriction imposed on the evolution time between two quantum states through the value of a single system observable such as the mean energy relative to its ground state. So far these restrictions only place upper bounds on the information processing speed of a quantum system. Here I report QSLs each with permissible information processing speeds separated by forbidden speed intervals. They are found by a systematic and efficient procedure that takes the values of several compatible system observables into account simultaneously. This procedure generalizes almost all existing QSL proofs; the QSLs show a novel first-order phase transition in the minimum evolution time.

Nutritional Status After Total Gastrectomy for Gastric Cancer.

BackgroundGastric cancer is one of the most frequent causes of death secondary to cancer in the world. Surgery is the only potentially curative treatment but its clinical consequences are significant. The objective of this study is to evaluate the nutritional state of patients with a total gastrectomy secondary to gastric adenocarcinoma.MethodsWe designed a descriptive study with a transversal cut in our institution. We included 22 patients which had a minimum evolution time of six months after total gastrectomy secondary to gastric cancer surgery was performed. Neither of them had metastasis. The nutritional analysis included only biochemical data. Descriptive statistics were used for statistical analysis.ResultsEight females and 14 males were included in the study. Median age was 57 years (34 - 69 years). The 74% of the patients were underweight and none of them was overweight. The average body mass index (BMI) was 16.88 kg/m2. Eleven patients suffered from mild anemia (10.5 - 12 g/dl) and 5 from moderate anemia (9 - 10.5 g/dl). Only two patients presented severe anemia (less than 9 g/dl). The 58% presented hypoproteinaemia and hypoalbuminaemia. The main post-surgery complication was nausea (46%). Seventy-eight percent of the patients had loss of appetite. Twenty-one patients were able to walk without help and leave their homes.ConclusionsThe incidence of anemia in these patients was very high. In most of the patients, albumin and proteins levels were affected too. So malnutrition was a relevant consequence of a total gastrectomy.