State Of Quantum System Research Articles

Toward Atomic-Resolution Quantum Measurements with Coherently Shaped Free Electrons.

Free electrons provide a powerful tool for probing material properties at atomic resolution. Recent advances in ultrafast electron microscopy enable the manipulation of free-electron wave functions using laser pulses. It would be of great importance if one could combine the spatial resolution of electron microscopes with the ability of laser pulses to probe coherent phenomena in quantum systems. To this end, we propose a novel concept that leverages free electrons that are coherently shaped by laser pulses to measure quantum coherence in materials. We develop the quantum theory of interactions between shaped electrons and arbitrary qubit states in materials, and show how the postinteraction electron energy spectrum enables measuring the qubit state (on the Bloch sphere) and the decoherence or relaxation times (T_{2}/T_{1}). Finally, we describe how such electrons can detect and quantify superradiance from multiple qubits. Our scheme can be implemented in ultrafast transmission electron microscopes (UTEM), opening the way toward the full characterization of the state of quantum systems at atomic resolution.

Probability Representation of Quantum States.

The review of new formulation of conventional quantum mechanics where the quantum states are identified with probability distributions is presented. The invertible map of density operators and wave functions onto the probability distributions describing the quantum states in quantum mechanics is constructed both for systems with continuous variables and systems with discrete variables by using the Born’s rule and recently suggested method of dequantizer–quantizer operators. Examples of discussed probability representations of qubits (spin-, two-level atoms), harmonic oscillator and free particle are studied in detail. Schrödinger and von Neumann equations, as well as equations for the evolution of open systems, are written in the form of linear classical–like equations for the probability distributions determining the quantum system states. Relations to phase–space representation of quantum states (Wigner functions) with quantum tomography and classical mechanics are elucidated.

Quantum k-uniform states for heterogeneous systems from irredundant mixed orthogonal arrays

Quantum multipartite entangled states play significant roles in quantum information processing. By using difference schemes and orthogonal partitions, we construct a series of infinite classes of irredundant mixed orthogonal arrays (IrMOAs) and thus provide positive answers to two open problems. The first is the extension of the method for constructing homogeneous systems from orthogonal arrays to heterogeneous multipartite systems with different individual levels. The second is the existence of k-uniform states in heterogeneous quantum systems. We present explicit constructions of two- and three-uniform states for arbitrary heterogeneous multipartite systems with coprime individual levels and characterize the entangled states in heterogeneous systems consisting of subsystems with nonprime power dimensions as well. Moreover, we obtain infinite classes of k-uniform states for heterogeneous multipartite systems for any $$k\ge 2$$ . The non-existence of a class of IrMOAs is also proved.

Gaussian states of continuous-variable quantum systems provide universal and versatile reservoir computing

Quantum reservoir computing aims at harnessing the rich dynamics of quantum systems for machine-learning purposes. It can be used for online time series processing while having a remarkably low training cost. Here, we establish the potential of continuous-variable Gaussian states of linear dynamical systems for quantum reservoir computing. We prove that Gaussian resources are enough for universal reservoir computing. We find that encoding the input into Gaussian states is both a source and a means to tune the nonlinearity of the overall input-output map. We further show that the full potential of the proposed model can be reached by encoding to quantum fluctuations, such as squeezed vacuum, instead of classical fields or thermal fluctuations. Our results introduce a research paradigm for reservoir computing harnessing quantum systems and engineered Gaussian quantum states.

Dephasing-assisted entanglement in a system of strongly coupled qubits.

Creation of entangled states of quantum systems with low decoherence rates is a cornerstone in practical implementation of quantum computations. Processes of separate dephasing in each qubit in experimentally feasible systems is commonly accepted to destroy entanglement. In this work, we consider a system of two strongly coupled qubits that interact with dephasing reservoirs. We demonstrate that interaction with dephasing reservoirs can contribute to the formation of a long-lived mixed entangled state with nonzero concurrence. The weight of the subradiant state in this mixed state tends toward unity if the dephasing rate is much larger than the radiative rate and less than the coupling constant between qubits. The lifetime of this state is proportional to the exponent of the ratio of the coupling constant to environmental temperature and can be, by orders of magnitude, larger than the system's characteristic dephasing and dissipation times. Therefore, high dephasing, along with strong coupling, contributes to the creation of an entangled state with a long lifetime. This result paves the way for creation of long-lived entangled states.

Operational Resource Theory of Imaginarity.

Wave-particle duality is one of the basic features of quantum mechanics, giving rise to the use of complex numbers in describing states of quantum systems and their dynamics and interaction. Since the inception of quantum theory, it has been debated whether complex numbers are essential or whether an alternative consistent formulation is possible using real numbers only. Here, we attack this long-standing problem theoretically and experimentally, using the powerful tools of quantum resource theories. We show that, under reasonable assumptions, quantum states are easier to create and manipulate if they only have real elements. This gives an operational meaning to the resource theory of imaginarity. We identify and answer several important questions, which include the state-conversion problem for all qubit states and all pure states of any dimension and the approximate imaginarity distillation for all quantum states. As an application, we show that imaginarity plays a crucial role in state discrimination, that is, there exist real quantum states that can be perfectly distinguished via local operations and classical communication but that cannot be distinguished with any nonzero probability if one of the parties has no access to imaginarity. We confirm this phenomenon experimentally with linear optics, discriminating different two-photon quantum states by local projective measurements. Our results prove that complex numbers are an indispensable part of quantum mechanics.

First-detection time of a quantum state under random probing

We solve for the statistics of the first detection of a quantum system in a particular desired state, when the system is subject to a projective measurement at independent identically distributed random time intervals. We present formulas for the probability of detection in the $n\mathrm{th}$ attempt. We calculate as well the mean and mean square, both of the number of the first successful detection attempt and the time until first detection. We present explicit results for a particle initially localized at a site on a ring of size $L$, probed at some arbitrary given site, in the case when the detection intervals are distributed exponentially. We prove that, for all interval distributions and finite-dimensional Hamiltonians, the mean detection time is equal to the mean attempt number times the mean time interval between attempts. We further prove that for the return problem when the initial and target state are identical, the total detection probability is unity and the mean attempts until detection is an integer, which is the size of the Hilbert space (symmetrized about the target state). We study an interpolation between the fixed time interval case to an exponential distribution of time intervals via the Gamma distribution with constant mean and varying width. The mean arrival time as a function of the mean interval changes qualitatively as we tune the interarrival time distribution from very narrow ($\ensuremath{\delta}$ peaked) to exponential, as resonances are wiped out by the randomness of the sampling.

A quantum algorithm for the direct estimation of the steady state of open quantum systems

Simulating the dynamics and the non-equilibrium steady state of an open quantum system are hard computational tasks on conventional computers. For the simulation of the time evolution, several efficient quantum algorithms have recently been developed. However, computing the non-equilibrium steady state as the long-time limit of the system dynamics is often not a viable solution, because of exceedingly long transient features or strong quantum correlations in the dynamics. Here, we develop an efficient quantum algorithm for the direct estimation of averaged expectation values of observables on the non-equilibrium steady state, thus bypassing the time integration of the master equation. The algorithm encodes the vectorized representation of the density matrix on a quantum register, and makes use of quantum phase estimation to approximate the eigenvector associated to the zero eigenvalue of the generator of the system dynamics. We show that the output state of the algorithm allows to estimate expectation values of observables on the steady state. Away from critical points, where the Liouvillian gap scales as a power law of the system size, the quantum algorithm performs with exponential advantage compared to exact diagonalization.

Quantum Solver of Contracted Eigenvalue Equations for Scalable Molecular Simulations on Quantum Computing Devices.

The accurate computation of ground and excited states of many-fermion quantum systems is one of the most consequential, contemporary challenges in the physical and computational sciences whose solution stands to benefit significantly from the advent of quantum computing devices. Existing methodologies using phase estimation or variational algorithms have potential drawbacks such as deep circuits requiring substantial error correction or nontrivial high-dimensional classical optimization. Here, we introduce a quantum solver of contracted eigenvalue equations, the quantum analog of classical methods for the energies and reduced density matrices of ground and excited states. The solver does not require deep circuits or difficult classical optimization and achieves an exponential speed-up over its classical counterpart. We demonstrate the algorithm though computations on both a quantum simulator and two IBM quantum processing units.

Floquet theory for temporal correlations and spectra in time-periodic open quantum systems: Application to squeezed parametric oscillation beyond the rotating-wave approximation

Open quantum systems can display periodic dynamics at the classical level either due to external periodic modulations or to self-pulsing phenomena typically following a Hopf bifurcation. In both cases, the quantum fluctuations around classical solutions do not reach a quantum-statistical stationary state, which prevents adopting the simple and reliable methods used for stationary quantum systems. Here we put forward a general and efficient method to compute two-time correlations and corresponding spectral densities of time-periodic open quantum systems within the usual linearized (Gaussian) approximation for their dynamics. Using Floquet theory we show how the quantum Langevin equations for the fluctuations can be efficiently integrated by partitioning the time domain into one-period duration intervals, and relating the properties of each period to the first one. Spectral densities, like squeezing spectra, are computed similarly, now in a two-dimensional temporal domain that is treated as a chessboard with one-period x one-period cells. This technique avoids cumulative numerical errors as well as efficiently saves computational time. As an illustration of the method, we analyze the quantum fluctuations of a damped parametrically-driven oscillator (degenerate parametric oscillator) below threshold and far away from rotating-wave approximation conditions, which is a relevant scenario for modern low-frequency quantum oscillators. Our method reveals that the squeezing properties of such devices are quite robust against the amplitude of the modulation or the low quality of the oscillator, although optimal squeezing can appear for parameters that are far from the ones predicted within the rotating-wave approximation.

Topology Protects Robust Global Cycles in Stochastic Systems

Living systems can exhibit time-scales much longer that those of the underlying components, as well as emergent dynamical and collective behavior. How such robust global behavior is subserved by stochastic constituents remains unclear. Here, we present biologically-plausible motifs from which two-dimensional stochastic networks can be constructed. The motifs represent out-of-equilibrium cycles on the microscopic scale, which support macroscopic edge currents in configuration space. This behavior is qualitatively different from previous proposals for topological states in stochastic networks and other classical systems, and can be understood using the framework of non-Hermitian physics. Topological properties of the system are seen in the emergence of exceptional points or the non-zero vorticity and doubled periodicity of edge states. Our framework enables a wealth of dynamical phenomena such as a global clock, dynamical growth and de-growth, as well as synchronization, similar to observations that are quite prevalent in biology. Our models suggest new insights into the theoretical framework of non-Hermitian physics, and pave the way for the prediction of new states in both classical and quantum systems.

Nonequilibrium states in quantum materials under time-period driving

The topology of quantum materials is the frontier research in condensed matter physics. In contrast with the conventional classification of materials by using the local symmetry breaking criterion, the states of quantum systems are classified according to the topology of wave functions. The potential applications of topological states may lead the traditional microelectronics to break through and accelerate the significant improvement in topological electronics. Most of the recent studies focus on the topological states of quantum systems under equilibrium conditions without external perturbations. The topological states of quantum systems far from the equilibrium under time-periodic driving have attracted wide attention. Here we first introduce the framework of Floquet engineering under the frame of the Floquet theorem. The nonequilibrium topological states of massless and massive Dirac fermions are discussed including the mechanism of phase transition. Light field driven electronic transition term in the quantum material gains extra time-dependent phase. Thereby the manipulation of effective transition term of the electron is realized to regulate the non-equilibrium topological states. We also mention how the photoinduced coherent phonon affects the nonequilibrium topological states of quantum systems from the perspective of atom manufacturing. Furthermore, research outlook on the nonequilibrium topological states is given. This review provides some clues to the design of physical properties and transport behaviors of quantum materials out of equilibrium.

Cryogenic Low-Noise Amplifiers: Noise Performance and Power Dissipation

Cryogenically cooled low-noise amplifiers (LNAs) have had a profound impact on experimental science. For instance, these amplifiers allow us to communicate with distant spacecraft, probe the history and composition of the universe through radio astronomy, study basic phenomena through low-temperature physics research, and read out the state of quantum systems as required for quantum computing. These devices-which can achieve noise performance within an order of magnitude of the fundamental limits imposed by quantum mechanics-find use from low frequencies through several hundreds of gigahertz. Without cryogenic LNAs, whole branches of experimental science simply could not exist.

Ultrafast manipulation of the weakly bound helium dimer

Controlling the interactions between atoms with external fields opened up new branches in physics ranging from strongly correlated atomic systems to ideal Bose and Fermi gases and Efimov physics. Such control usually prepares samples that are stationary or evolve adiabatically in time. On the other hand, in molecular physics external ultrashort laser fields are employed to create anisotropic potentials that launch ultrafast rotational wave packets and align molecules in free space. Here we combine these two regimes of ultrafast times and low energies. We apply a short laser pulse to the helium dimer, a weakly bound and highly delocalized single bound state quantum system. The laser field locally tunes the interaction between two helium atoms, imparting an angular momentum of $2\hbar$ and evoking an initially confined dissociative wave packet. We record a movie of the density and phase of this wave packet as it evolves from the inside out. At large internuclear distances, where the interaction between the two helium atoms is negligible, the wave packet is essentially free. This work paves the way for future tomography of wave packet dynamics and provides the technique for studying exotic and otherwise hardly accessible quantum systems such as halo and Efimov states.

THE DARK MATTER AND ENERGY IN THE DE SITTER WORLD

It is shown that dark matter and energy are cosmological quantum effects. De Sitter world is considered as a cosmological model. It is shown that in the de Sitter world, gravity and anti-gravity are different states of the Wigner elementary quantum system. It has been proven that in the Minkowski world, which is the limiting case of the de Sitter world, antigravity can be excluded. Moreover, it is shown that the Wigner - Inönü limit of the de Sitter model to the Minkowski world plays the role of Bohr's correspondence principle in quantum mechanics. A plan for further research is proposed.

An Algorithm for Constructing Irreducible Decompositions of Permutation Representations of Wreath Products of Finite Groups

We describe an algorithm for decomposing permutation representations of wreath products of finite groups into irreducible components. The algorithm is based on the construction of a complete set of mutually orthogonal projections to irreducible invariant subspaces of the Hilbert space of the representation under consideration. In constructive models of quantum mechanics, the invariant subspaces of representations of wreath products describe the states of multicomponent quantum systems. The suggested algorithm uses methods of computer algebra and computational group theory. The C implementation of the algorithm is capable of constructing irreducible decompositions of representations of wreath products of high dimensions and ranks. Examples of calculations are given. Bibliography: 15 titles.

Floquet states in dissipative open quantum systems

We theoretically investigate basic properties of nonequilibrium steady states of periodically-driven open quantum systems based on the full solution of the Maxwell–Bloch equation. In a resonant driving condition, we find that the transverse relaxation, also known as decoherence, significantly destructs the formation of Floquet states while the longitudinal relaxation does not directly affect it. Furthermore, by evaluating the quasienergy spectrum of the nonequilibrium steady states, we demonstrate that Rabi splitting can be observed as long as the decoherence time is as short as one third of the Rabi-cycle. Moreover, we find that Floquet states can be formed even under significant dissipation when the decoherence time is substantially shorter than the cycle of driving, once the driving field strength becomes strong enough. In an off-resonant condition, we demonstrate that the Floquet states can be realized even in weak field regimes because the system is not excited and the decoherence mechanism is not activated. Once the field strength becomes strong enough, the system can be excited by multi-photon absorption and the decoherence process becomes active. As a result, the Floquet states are significantly disturbed by the environment even in the off-resonant condition. Thus, we show here that the suppression of energy transfer from light to matter is a key condition for the realization of Floquet states in both on- and off-resonant conditions not only because it prevents material damage but also because it contributes to preserving coherence.

Discrimination of thermal baths by single-qubit probes

Non-equilibrium states of quantum systems in contact with thermal baths help telling environments with different temperatures or different statistics apart. We extend these studies to a more generic problem that consists in discriminating between two baths with disparate constituents at unequal temperatures. Notably there exist temperature regimes in which the presence of coherence in the initial state preparation is beneficial for the discrimination capability. We also find that non-equilibrium states are not universally optimal, and detail the conditions in which it becomes convenient to wait for complete thermalisation of the probe. These concepts are illustrated in a linear optical simulation.

USE OF THE WHIRLIGIG PRINCIPLE FOR STABILIZING THE INITIAL STATES OF SOME CLASSIC AND QUANTUM SYSTEMS

It is shown that the whirligig principle can be used for stabilization of the initial states of some classical and quantum systems. This feature of the whirligig principle is demonstrated by simple examples. The most important result of this work is the proof of the fact that the stabilization of the excited states of quantum systems can be realized by acting not on the quantum system itself, but by acting on the states into which the system must go. Potentially, this result can be used to stabilize excited nuclear systems.

Fate of fractional quantum Hall states in open quantum systems: Characterization of correlated topological states for the full Liouvillian

Despite previous extensive analysis of open quantum systems described by the Lindblad equation, it is unclear whether correlated topological states, such as fractional quantum Hall states, are maintained even in the presence of the jump term. In this paper, we introduce the pseudo-spin Chern number of the Liouvillian which is computed by twisting the boundary conditions only for one of the subspaces of the doubled Hilbert space. The existence of such a topological invariant elucidates that the topological properties remain unchanged even in the presence of the jump term which does not close the gap of the effective non-Hermitian Hamiltonian (obtained by neglecting the jump term). In other words, the topological properties are encoded into an effective non-Hermitian Hamiltonian rather than the full Liouvillian. This is particularly useful when the jump term can be written as a strictly block-upper (-lower) triangular matrix in the doubled Hilbert space, in which case the presence or absence of the jump term does not affect the spectrum of the Liouvillian. With the pseudo-spin Chern number, we address the characterization of fractional quantum Hall states with two-body loss but without gain, elucidating that the topology of the non-Hermitian fractional quantum Hall states is preserved even in the presence of the jump term. This numerical result also supports the use of the non-Hermitian Hamiltonian which significantly reduces the numerical cost. Similar topological invariants can be extended to treat correlated topological states for other spatial dimensions and symmetry (e.g., one-dimensional open quantum systems with inversion symmetry), indicating the high versatility of our approach.