scholarly journals Fast-forwarding quantum evolution

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 577
Author(s):  
Shouzhen Gu ◽  
Rolando D. Somma ◽  
Burak Şahinoğlu
Keyword(s):  
Positive Semidefinite ◽  
Quantum Circuit ◽  
Quantum Systems ◽  
Spin Systems ◽  
Quantum Evolution ◽  
Diagonal Form ◽  
Initial State ◽  
Local Spin ◽  
Low Energies ◽  
Asymptotic Complexity

We investigate the problem of fast-forwarding quantum evolution, whereby the dynamics of certain quantum systems can be simulated with gate complexity that is sublinear in the evolution time. We provide a definition of fast-forwarding that considers the model of quantum computation, the Hamiltonians that induce the evolution, and the properties of the initial states. Our definition accounts for any asymptotic complexity improvement of the general case and we use it to demonstrate fast-forwarding in several quantum systems. In particular, we show that some local spin systems whose Hamiltonians can be taken into block diagonal form using an efficient quantum circuit, such as those that are permutation-invariant, can be exponentially fast-forwarded. We also show that certain classes of positive semidefinite local spin systems, also known as frustration-free, can be polynomially fast-forwarded, provided the initial state is supported on a subspace of sufficiently low energies. Last, we show that all quadratic fermionic systems and number-conserving quadratic bosonic systems can be exponentially fast-forwarded in a model where quantum gates are exponentials of specific fermionic or bosonic operators, respectively. Our results extend the classes of physical Hamiltonians that were previously known to be fast-forwarded, while not necessarily requiring methods that diagonalize the Hamiltonians efficiently. We further develop a connection between fast-forwarding and precise energy measurements that also accounts for polynomial improvements.

scholarly journals Quantum speed limit time in the presence of disturbance

2020 ◽  
pp. 2150009
Author(s):  
S. Haseli ◽  
S. Salimi ◽  
H. Dolatkhah ◽  
A. S. Khorashad
Keyword(s):  
Quantum Theory ◽  
Quantum System ◽  
Open Quantum System ◽  
Quantum Systems ◽  
Quantum Evolution ◽  
Speed Limit ◽  
Initial State ◽  
Limit Time ◽  
Maximal Speed ◽  
Disturbed Environment

Quantum theory sets a bound on the minimal time it takes for a system to evolve from initial state to target state. This bound is called the quantum speed limit (QSL) time. The quantum speed limit time is used to quantify the maximal speed of the quantum evolution. The quantum evolution will be faster if the quantum speed limit time decreases. In this work, we study the quantum speed limit time for an open quantum system in the presence of disturbance in an environment. We use the model which is provided by Ban [Phys. Rev. A 99, 012116 (2019)]. In this model, two quantum systems [Formula: see text] and [Formula: see text] interact with environment sequentially. At first, quantum system [Formula: see text] interacts with the environment [Formula: see text] as an auxiliary system, then quantum system [Formula: see text] starts its interaction with disturbed environment immediately. In this work, we consider the dephasing coupling with two types of environment that has different spectral density: Ohmic and Lorentzian. We observe that, non-Markovian effects will appear in the dynamics of the second quantum system [Formula: see text] due to the interaction of the first quantum system [Formula: see text] with the environment. Given the fact that the quantum speed limit time reduces due to the non-Markovian feature of quantum evolution, we show that disturbance effects will reduce the quantum speed limit time for the dynamics of the second quantum system [Formula: see text].

scholarly journals Convergence Rates for Quantum Evolution and Entropic Continuity Bounds in Infinite Dimensions

2019 ◽  
Vol 374 (2) ◽  
pp. 823-871 ◽  
Author(s):  
Simon Becker ◽  
Nilanjana Datta
Keyword(s):  
Convergence Rates ◽  
Lipschitz Continuity ◽  
Open Quantum Systems ◽  
High Energy ◽  
Quantum Systems ◽  
Quantum Evolution ◽  
Infinite Dimensions ◽  
Quantum Brownian Motion ◽  
Infinite Dimensional ◽  
Energy Constrained

Abstract By extending the concept of energy-constrained diamond norms, we obtain continuity bounds on the dynamics of both closed and open quantum systems in infinite dimensions, which are stronger than previously known bounds. We extensively discuss applications of our theory to quantum speed limits, attenuator and amplifier channels, the quantum Boltzmann equation, and quantum Brownian motion. Next, we obtain explicit log-Lipschitz continuity bounds for entropies of infinite-dimensional quantum systems, and classical capacities of infinite-dimensional quantum channels under energy-constraints. These bounds are determined by the high energy spectrum of the underlying Hamiltonian and can be evaluated using Weyl’s law.

scholarly journals Ontology in Quantum Mechanics

2021 ◽  
Author(s):  
Gerard ’t Hooft
Keyword(s):  
Hilbert Space ◽  
General Relativity ◽  
Black Hole ◽  
Quantum Mechanics ◽  
Evolution Equations ◽  
Black Hole Physics ◽  
Special Kind ◽  
Quantum Evolution ◽  
The Standard Model ◽  
Low Energies

It is suspected that the quantum evolution equations describing the micro-world as we know it are of a special kind that allows transformations to a special set of basis states in Hilbert space, such that, in this basis, the evolution is given by elements of the permutation group. This would restore an ontological interpretation. It is shown how, at low energies per particle degree of freedom, almost any quantum system allows for such a transformation. This contradicts Bell’s theorem, and we emphasise why some of the assumptions made by Bell to prove his theorem cannot hold for the models studied here. We speculate how an approach of this kind may become helpful in isolating the most likely version of the Standard Model, combined with General Relativity. A link is suggested with black hole physics.

scholarly journals Local Spin and Open Quantum Systems: Clarifying Misconceptions, Unifying Approaches

2020 ◽  
Author(s):  
Angel Martín Pendás ◽  
Evelio Francisco
Keyword(s):  
Quantum Control ◽  
Open Systems ◽  
Open Quantum Systems ◽  
Real Space ◽  
Quantum Systems ◽  
Spin Coupling ◽  
Molecular Systems ◽  
Open Quantum ◽  
Local Spin

<p>We now show that Clark and Davidson local spins operators are perfectly defined subsystem operators if a fragment is taken as an <i>open quantum system</i> (OQS). Open systems have become essential in quantum control and quantum computation, but have not received much attention in Chemistry. We have already shown (<i>J. Chem. Theory Comput</i>. <b>2018</b>, <i>15</i>, 1079) how real space OQSs can be defined in molecular systems and how they offer new insights relating quantum mechanical entaglement and chemical bonding. The OQS account of local spin that we offer yields a rigorous, yet easily accessible way to rationalize local spin values. A fragment is found in a mixed state direct sum of sectors characterized by different number of electrons that occur with different probabilities. The local spin is then a weighted sum of otherwise standard <i>S</i>(<i>S</i>+1) values. With OQS glasses, it is obvious that atomic or fragment spins should not vanish. Our approach thus casts doubts on any procedure used to annihilate them, like those used by Mayer and coworkers. OQS local spins allow for a fruitful use of models. One can propose easily sector probabilities for localized, covalent, ionic, zwitterionic, etc. situations, and examine their ideal local spins. We have mapped all 2c-2e cases, and shown how to do that in general multielectron cases. The role of electron correlation is also studied by tuning the Hubbard U/t parameter for H chains. Correlation induced localization changes the spin-coupling patterns even qualitatively, and show how the limiting antiferromagnet arises.</p>

scholarly journals Probing Many-Body Systems Near Spectral Degeneracies

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1796
Author(s):  
Klaus Ziegler
Keyword(s):  
Decay Rate ◽  
Correlation Matrix ◽  
Time Correlation ◽  
General Concept ◽  
Quantum Systems ◽  
Quantum Evolution ◽  
Many Body ◽  
Space Localization ◽  
Many Body Systems ◽  
Random Times

The diagonal elements of the time correlation matrix are used to probe closed quantum systems that are measured at random times. This enables us to extract two distinct parts of the quantum evolution, a recurrent part and an exponentially decaying part. This separation is strongly affected when spectral degeneracies occur, for instance, in the presence of spontaneous symmetry breaking. Moreover, the slowest decay rate is determined by the smallest energy level spacing, and this decay rate diverges at the spectral degeneracies. Probing the quantum evolution with the diagonal elements of the time correlation matrix is discussed as a general concept and tested in the case of a bosonic Josephson junction. It reveals for the latter characteristic properties at the transition to Hilbert-space localization.

scholarly journals Validation of quantum adiabaticity through non-inertial frames and its trapped-ion realization

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Chang-Kang Hu ◽  
Jin-Ming Cui ◽  
Alan C. Santos ◽  
Yun-Feng Huang ◽  
Chuan-Feng Li ◽  
...  
Keyword(s):  
Quantum Dynamics ◽  
Adiabatic Approximation ◽  
Inertial Frame ◽  
Quantum Systems ◽  
Resonance Phenomenon ◽  
Quantum Evolution ◽  
Adiabatic Condition ◽  
Quantum Bit ◽  
Adiabatic Conditions ◽  
Inertial Frames

AbstractValidity conditions for the adiabatic approximation are useful tools to understand and predict the quantum dynamics. Remarkably, the resonance phenomenon in oscillating quantum systems has challenged the adiabatic theorem. In this scenario, inconsistencies in the application of quantitative adiabatic conditions have led to a sequence of new approaches for adiabaticity. Here, by adopting a different strategy, we introduce a validation mechanism for the adiabatic approximation by driving the quantum system to a non-inertial reference frame. More specifically, we begin by considering several relevant adiabatic approximation conditions previously derived and show that all of them fail by introducing a suitable oscillating Hamiltonian for a single quantum bit (qubit). Then, by evaluating the adiabatic condition in a rotated non-inertial frame, we show that all of these conditions, including the standard adiabatic condition, can correctly describe the adiabatic dynamics in the original frame, either far from resonance or at a resonant point. Moreover, we prove that this validation mechanism can be extended for general multi-particle quantum systems, establishing the conditions for the equivalence of the adiabatic behavior as described in inertial or non-inertial frames. In order to experimentally investigate our method, we consider a hyperfine qubit through a single trapped Ytterbium ion 171Yb+, where the ion hyperfine energy levels are used as degrees of freedom of a two-level system. By monitoring the quantum evolution, we explicitly show the consistency of the adiabatic conditions in the non-inertial frame.

TEMPORAL QUANTUM CHAOS

1999 ◽  
Vol 13 (18) ◽  
pp. 2361-2369 ◽  
Author(s):  
R. AURICH ◽  
F. STEINER
Keyword(s):  
Quantum Chaos ◽  
Chaotic Systems ◽  
Quantum Systems ◽  
Time Behavior ◽  
Classical Dynamics ◽  
Long Time Behavior ◽  
Initial State ◽  
Numerical Tests ◽  
Weyl Sum ◽  
Long Time

We study the long-time behavior of bound quantum systems whose classical dynamics is chaotic and put forward two conjectures. Conjecture A states that the autocorrelation function C(t)=<Ψ(0)|Ψ(t)> of a delocalized initial state |Ψ(0)> shows characteristic fluctuations, which we identify with a universal signature of temporal quantum chaos. For example, for the (appropriately normalized) value distribution of S~|C(t)| we predict the distribution P(S)=(π/2)Se-πS2/4. Conjecture B gives the best possible upper bound for a generalized Weyl sum and is related to the extremely large recurrence times in temporal quantum chaos. Numerical tests carried out for numerous chaotic systems confirm nicely the two conjectures and thus provide strong evidence for temporal quantum chaos.

Quantum circuits for calculating the squared sum of the inner product of quantum states and its application

2019 ◽  
Vol 17 (05) ◽  
pp. 1950043
Author(s):  
Panchi Li ◽  
Jiahui Guo ◽  
Bing Wang ◽  
Mengqi Hao
Keyword(s):  
Quantum Circuit ◽  
Quantum States ◽  
Experimental Results ◽  
Quantum Circuits ◽  
Inner Product ◽  
Superposition State ◽  
Initial State ◽  
Control Rules ◽  
Control Qubit ◽  
Classical Computer

In this paper, we propose a quantum circuit for calculating the squared sum of the inner product of quantum states. The circuit is designed by the multi-qubits controlled-swapping gates, in which the initial state of each control qubit is [Formula: see text] and they are in the equilibrium superposition state after passing through some Hadamard gates. Then, according to the control rules, each basis state in the superposition state controls the corresponding quantum states pair to swap. Finally, the Hadamard gates are applied to the control qubits again, and the squared sum of the inner product of many pairs of quantum states can be obtained simultaneously by measuring only one control qubit. We investigate the application of this method in quantum images matching on a classical computer, and the experimental results verify the correctness of the proposed method.

scholarly journals Generation of Quantum Correlations in Bipartite Gaussian Open Quantum Systems

2018 ◽  
Vol 173 ◽  
pp. 01006 ◽  
Author(s):  
Aurelian Isar
Keyword(s):  
Open Systems ◽  
Thermal Environment ◽  
Open Quantum Systems ◽  
Quantum Correlations ◽  
Quantum Systems ◽  
Thermal Bath ◽  
Initial State ◽  
Entanglement Generation ◽  
Strength Of Interaction ◽  
Zero Values

We describe the generation of quantum correlations (entanglement, discord and steering) in a system composed of two coupled non-resonant bosonic modes immersed in a common thermal reservoir, in the framework of the theory of open systems. We show that for separable initial squeezed thermal states entanglement generation may take place, for definite values of squeezing parameter, average photon numbers, temperature of the thermal bath, dissipation constant and strength of interaction between the two bosonic modes. We also show that for initial uni-modal squeezed states Gaussian discord can be generated for all non-zero values of the strength of interaction between the modes. Likewise, for an initial separable state, a generation of Gaussian steering may take place temporarily, for definite values of the parameters characterizing the initial state and the thermal environment, and the strength of coupling between the two modes.

scholarly journals QUANTUM DISCORD IN THE GROUND STATE OF SPIN CHAINS

2012 ◽  
Vol 27 (01n03) ◽  
pp. 1345030 ◽  
Author(s):  
MARCELO S. SARANDY ◽  
THIAGO R. DE OLIVEIRA ◽  
LUIGI AMICO
Keyword(s):  
Ground State ◽  
Quantum Discord ◽  
Quantum Phase Transitions ◽  
Spatial Dimension ◽  
Quantum Systems ◽  
Quantum Spin ◽  
Spin Systems ◽  
Quantum Spin Systems ◽  
Quantum Spin Chain ◽  
Quantum Critical Points

The ground state of a quantum spin chain is a natural playground for investigating correlations. Nevertheless, not all correlations are genuinely of quantum nature. Here we review the recent progress to quantify the "quantumness" of the correlations throughout the phase diagram of quantum spin systems. Focusing to one spatial dimension, we discuss the behavior of quantum discord (QD) close to quantum phase transitions (QPT). In contrast to the two-spin entanglement, pairwise discord is effectively long-ranged in critical regimes. Besides the features of QPT, QD is especially feasible to explore the factorization phenomenon, giving rise to nontrivial ground classical states in quantum systems. The effects of spontaneous symmetry breaking are also discussed as well as the identification of quantum critical points through correlation witnesses.

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