We investigate the physics of projected d-wave pairing states using their fermionic projected entangled pair state (fPEPS) representation. First, we approximate a d-wave Bardeen-Cooper-Schrieffer state using the Gaussian fPEPS. Next, we translate the resulting state into fPEPS tensors and implement the Gutzwiller projection which removes double occupancy by modifying the local tensor elements. The tensor network representation of the projected d-wave pairing state allows us to evaluate physical quantities in the thermodynamic limit without employing the Gutzwiller approximation. Despite having very few variational parameters, such physically motivated tensor network states are shown to exhibit competitive energies for the doped t-J model. We expect that such construction offers useful initial states and guidance for variational tensor network calculations.

Gauge fields are a central concept in fundamental theories of physics, and responsible for mediating long-range interactions between elementary particles. Recently, it has been proposed that dynamical gauge fields can be naturally engineered by photons in composite, neutral quantum gas--cavity systems using suitable atom-photon interactions. Here we comprehensively investigate nonequilibrium dynamical phases appearing in a two-leg bosonic lattice model with leg-dependent, dynamical complex tunnelings mediated by cavity-assisted two-photon Raman processes. The system constitutes a minimal dynamical flux-lattice model. We study fixed points of the equations of motion and their stability, the resultant dynamical phase diagram, and the corresponding phase transitions and bifurcations. Notably, the phase diagram features a plethora of nonequilibrium dynamical phases including limit-cycle and chaotic phases. In the end, we relate regular periodic dynamics (i.e., limit-cycle phases) of the system to time crystals.

A brief (subjective) description of the state of the art of the many-worlds interpretation of quantum mechanics (MWI) is presented. It is argued that the MWI is the only interpretation which removes action at a distance and randomness from quantum theory. Limitations of the MWI regarding questions of probability which can be legitimately asked are specified. The ontological picture of the MWI as a theory of the universal wave function decomposed into a superposition of world wave functions, the important parts of which are defined in three-dimensional space, is presented from the point of view of our particular branch. Some speculations about misconceptions, which apparently prevent the MWI to be in the consensus, are mentioned.

We develop a formalism for constructing particle-number-conserving Gaussian fermionic projected entangled pair states [U(1)-GfPEPS] and show that these states can describe ground states of band insulators and gapless fermions with band touching points. When using them as variational Ans\"{a}tze for two Dirac fermion systems ($\pi$-flux model on the square lattice and $[0,\pi]$-flux model on the kagome lattice), we find that the U(1)-GfPEPS, even with a relatively small bond dimension, can accurately approximate the Dirac Fermi sea ground states. By applying Gutzwiller projectors on top of these U(1)-GfPEPS, we obtain PEPS representation of U(1)-Dirac spin liquid states for spin-1/2 systems. With state-of-the-art tensor network numerics, the critical exponent in the spin-spin correlation function of the Gutzwiller-projected $\pi$-flux state is estimated to be $\eta \approx 1.7$.

Strongly correlated solids are extremely complex and fascinating quantum systems, where new states continue to emerge and where interaction with light may trigger interplay between them. In this interplay, sub-laser-cycle electron response is particularly attractive as a tool for ultrafast manipulation of matter at PHz scale. Here we introduce a new type of non-linear multidimensional spectroscopy, which allows us to unravel the sub-cycle dynamics of strongly correlated systems interacting with few-cycle infrared pulses and the complex interplay between different correlated states evolving on the sub-femtosecond time-scale. For the two-dimensional Hubbard model under the influence of ultra-short, intense electric field transients, we demonstrate that our approach can resolve pathways of charge and energy flow between localized and delocalized many-body states on the sub-cycle timescale and follow the creation of a highly correlated state surviving after the end of the laser pulse. Our findings open a way to a regime of imaging and manipulating strongly correlated materials at optical rates, beyond the multi-cycle approach employed in Floquet engineering of quantum systems.

A fault-tolerant quantum computer will be supported by a classical decoding system interfacing with quantum hardware to perform quantum error correction. It is important that the decoder can keep pace with the quantum clock speed, within the limitations on communication that are imposed by the physical architecture. To this end we propose a local `pre-decoder', which makes greedy corrections to reduce the amount of syndrome data sent to a standard matching decoder. We study these classical overheads for the surface code under a phenomenological phase-flip noise model with imperfect measurements. We find substantial improvements in the runtime of the global decoder and the communication bandwidth by using the pre-decoder. For instance, to achieve a logical failure probability of $f = 10^{-15}$ using qubits with physical error rate $p = 10^{-3}$ and a distance $d=22$ code, we find that the bandwidth cost is reduced by a factor of $1000$, and the time taken by a matching decoder is sped up by a factor of $200$. To achieve this target failure probability, the pre-decoding approach requires a $50\%$ increase in the qubit count compared with the optimal decoder.

Zhuang and Shapiro have recently discussed how quantum illumination can be used to increase the mean value range delay. In this paper it is shown how multiple entangled photon quantum illumination helps to reduce the integration time when evaluating range delay. The analysis is conveyed in the setting of three entangled photon states discrete quantum illumination models, but it is argued the extension of the main result to the setting of continuous quantum illumination models.

We present an oscillator modeling of the relativistic spin-0 charges moving in the quantum states with minimum coupling of electromagnetic fields. Rather than perturbative approach to spinless regime, we put into operation directly under integer dependent levels for anharmonicity. In this way, the charged particle of rest mass energy kept as 280 MeV. Within the familiar Pekeris-like approximation, we have also improved the deep approximation to the orders of third and fourth near equilibrium of $7.5\,{\rm fm}$. Moreover, we have founded a closer agreement of high order approximation and given potential which has width range of $0.43\,{\rm fm^{-1}}$. Although equality between scalar and vector potentials give output in the solvable form, the improved approximation provides the spatial-independent rest mass as a "pure oscillator" without external field. In the absence of scalar distribution, minimal coupling might also leads to an oscillation at equilibrium distances, so we have considered an adding of extra-energy giving shifted Morse potential in the depth range 80 to 100 MeV. As a result of the shift, it has been concluded that the potential depth of the charged particle affects the relativistic energy levels where we have found about 200 MeV being for particles and nearly -10 MeV being for anti-particles. Besides negative energy states, the typical probability picture showing spin-zero charge distribution has been followed by the wavefunctions as ($n=0$ $\ell=0$) and ($n=1$, $\ell=1$) corresponding to relativistic energies. By taking into account a deep approximation to Klein-Gordon anharmonicity with $V_{v}(r)\neq 0$ and $V_{s}(r)=0$, one can introduced approximate-solvable relativistic oscillatory model.

The small size and excellent integrability of silicon metal-oxide-semiconductor (SiMOS) quantum dot spin qubits make them an attractive system for mass-manufacturable, scaled-up quantum processors. Furthermore, classical control electronics can be integrated on-chip, in-between the qubits, if an architecture with sparse arrays of qubits is chosen. In such an architecture qubits are either transported across the chip via shuttling, or coupled via mediating quantum systems over short-to-intermediate distances. This paper investigates the charge and spin characteristics of an elongated quantum dot -- a so-called jellybean quantum dot -- for the prospects of acting as a qubit-qubit coupler. Charge transport, charge sensing and magneto-spectroscopy measurements are performed on a SiMOS quantum dot device at mK temperature, and compared to Hartree-Fock multi-electron simulations. At low electron occupancies where disorder effects and strong electron-electron interaction dominate over the electrostatic confinement potential, the data reveals the formation of three coupled dots, akin to a tunable, artificial molecule. One dot is formed centrally under the gate and two are formed at the edges. At high electron occupancies, these dots merge into one large dot with well-defined spin states, verifying that jellybean dots have the potential to be used as qubit couplers in future quantum computing architectures.

In an N-party quantum network, non-classical correlations can arise when locally measuring across k-party entangled states (k<N) that are independently distributed. Such correlations are said to embody quantum network nonlocality. In this paper, we show that bipartite entanglement (i.e. k=2) is sufficient for generating all forms of quantum network nonlocality when allowing for post-selection, a feature that might not arise when using more general non-signaling devices. We then demonstrate that network nonlocality fails to emerge in quantum networks limited strictly to pure stabilizer states and Clifford gates. This work sheds new light on the distinction between non-genuine and genuine network nonlocality by showing that all known approaches for generating the latter require some form of non-Clifford operation.

While the quantum metrological advantages of performing non-Gaussian operations on two-mode squeezed vacuum (TMSV) states have been extensively explored, similar studies in the context of two-mode squeezed thermal (TMST) states are severely lacking. In this paper, we explore the potential advantages of performing non-Gaussian operations on TMST state for phase estimation using parity detection based Mach-Zehnder interferometry. To this end, we consider the realistic model of photon subtraction, addition, and catalysis. We first provide a derivation of the unified Wigner function of the photon subtracted, photon added and photon catalyzed TMST state, which to the best of our knowledge is not available in the existing literature. This Wigner function is then used to obtain the expression for the phase sensitivity. Our results show that performing non-Gaussian operations on TMST states can enhance the phase sensitivity for significant ranges of squeezing and transmissivity parameters. We also observe that incremental advantage provided by performing these non-Gaussian operations on the TMST state is considerably higher than that of performing these operations on the TMSV state. Because of the probabilistic nature of these operations, it is of utmost importance to take their success probability into account. We identify the photon catalysis operation performed using a high transmissivity beam splitter as the optimal non-Gaussian operation when the success probability is taken into account. This is in contrast to the TMSV case, where we observe photon addition to be the most optimal. These results will be of high relevance for any future phase estimation experiments involving TMST states. Further, the derived Wigner function of the non-Gaussian TMST states will be useful for state characterization and its application in various quantum information protocols.

In this work, the non-relativistic wave equation via the Schr\"{o}dinger wave equation under the influence of the Aharonov-Bohm flux field Subject to physical potentials of various kinds is investigated. These potentials are modified Coulomb potential, modified harmonic oscillator potential, the Kratzer-Feus potential, and the Mie-type potential which have wide applications in different branches of physics and chemistry. We solve the Schrodinger wave equation using the Nikiforov-Uvarov (NU) method and obtain the energy profiles and the wave function of the non-relativistic particle, and analyze the effects of potential and the quantum flux on them. We show that each non-relativistic energy level gets modified in comparison to the known results obtained in the literature.

We prove that all states (mixed or pure) of qubit-qutrit ($2\times 3$) systems have entanglement-preserving unitary (EPU) equivalence to a compact subset of true-generalized X (TGX) states called EPU-minimal TGX states which we give explicitly. Thus, for any spectrum-entanglement combination achievable by general states, there exists an EPU-minimal TGX state of the same spectrum and entanglement. We use I-concurrence to measure entanglement and give an explicit formula for it for all $2\times 3$ minimal TGX states (a more general set than EPU-minimal TGX states) whether mixed or pure, yielding its minimum average value over all decompositions. We also give a computable I-concurrence formula for a more general family called minimal super-generalized X (SGX) states, and give optimal decompositions for minimal SGX states and all of their subsets.

Schrieffer-Wolff transformation (SWT) has been extensively used in quantum many-body physics to calculate the low energy effective Hamiltonian. It provides a perturbative method to comprehend the renormalization effects of strong correlations in the quantum many-body models. The generator for Schrieffer-Wolff transformation is calculated usually by heuristic methods. Recently, a systematic and elegant method for the calculation of this extremely significant transformation has been reported [1]. Given the huge significance of SWT for many areas including quantum condensed matter physics, quantum optics and quantum cavity electrodynamics, it is imperative to develop quantum algorithm for carrying out SWT on quantum computer. In this paper, we put forward this quantum algorithm and demonstrate it for single impurity Anderson model (SIAM), thereby arriving at Kondo model as effective Hamiltonian. We implement our quantum algorithm in QisKit and carry out SWT for SIAM on IBM Quantum computers. To the best of our knowledge, this work is the first of its kind to obtain Kondo model from Anderson impurity model using a quantum algorithm.

The separability problem is one of the basic and emergent problems in the present and future quantum information processing. The latter focuses on information and computing based on quantum mechanics and uses quantum bits as its basic information units. In this paper, we present an overview of the progress in the separability problem in bipartite systems, more specifically in two quantum bits systems from the criterion based on the inequalities of Bell in $1964$ to the recent criteria of separability in 2018.

Entanglement as a vital resource for information processing can be described by special properties of the quantum state.

Using the well-known Weyl basis we propose a new Bloch decomposition of the quantum state and study its separability problem.

This decomposition enables us to find an alternative characterization of the separability based on the correlation matrix.

We shaw that the criterion is effective in detecting entanglement for the isotropic states, Bell-diagonal states and some PPT entangled states.

We also use the Weyl operators to construct an detecting operator for quantum teleportation.

Hole-based spin qubits in strained planar germanium quantum wells have received considerable attention due to their favourable properties and remarkable experimental progress. The sizeable spin-orbit interaction in this structure allows for efficient electric qubit operations. However, it also couples the qubit to electrical noise. In this work we perform simulations of a heterostructure hosting these hole spin qubits. We solve the effective mass equations for a realistic heterostructure, provide a set of analytical basis wave functions, and compute the effective g-factor of the heavy-hole ground-state. Our investigations reveal a strong impact of highly excited light hole states located outside the quantum well on the g-factor. Consequently, contrary to recent predictions, we find that sweet spots in out-of-plane magnetic fields are shifted to impractically large electric fields. However, for magnetic fields close to in-plane alignment, sweet spots at low electric fields are recovered. This work will be helpful in understanding and improving coherence of germanium hole spin qubits.

We theoretically investigate the real-time transient responses of a two-dimensional (2D) electron gas with anisotropic Rashba spin-orbit coupling (SOC) to laser pulses. Through explicitly monitoring the time-dependent photocurrents and spin polarization under different linear polarizations of the laser pulse, we find that the transient breaking of the mirror symmetry in combination with the anisotropy of the Rashba SOC results in significant distinction between the charge-mediated and the spin-mediated contributions to the photocurrents. Such distinction is obtained by analyzing the dependence of the symmetry-breaking induced (transverse) components of the photocurrents on the linear polarization angle of the laser pulse. This suggests a possibility of inferring spin-mediated processes in photocurrents without the use of circularly polarized lights. Moreover, the interplay between transient symmetry breaking and the anisotropy of the Rashba SOC also leads to transiently nonzero spin polarization components that are otherwise zero in the steady-state limit and the linear response regime. Especially, the out-of-plane spin polarization component can be induced or turned off by controlling the relative orientation of the linear polarization with respect to the symmetry axis of the 2D electronic system, without involving material-intrinsic magnetization effects. Our findings demonstrate the efficacy of a particular coordination between the polarization of the ultrafast laser pulses and the spatial symmetry of the electronic materials in directing the real-time charge and the spin responses that are fundamental to the development of ultrafast spintronics in solid states.

We investigate the performance of the Lipkin-Meshkov-Glick quantum battery based on shortcuts to adiabaticity (STA). We mainly consider the situation where the coupling strength of any two sites in the quantum battery is a sinusoidal function with respect to time. The charging efficiency of the quantum battery can be greatly enhanced via STA. We also analyze the influences of parameters, including particle number, anisotropic parameter, the amplitude and frequency of the driving fields. It is found that an efficient charging process and thus high charging advantages can be achieved by adjusting these parameters properly. Moreover, we calculate the energy fluctuation, von Neumann entropy and energy cost during charging. The STA can make the stored energy and the von Neumann entropy change periodically during the charging process and reduce the energy fluctuation, and the minimal energy fluctuation always occurs in the proximity of minima of the von Neumann entropy.

A prerequisite to the successful development of quantum computers and simulators is precise understanding of physical processes occurring therein, which can be achieved by measuring the quantum states they produce. However, the resources required for traditional quantum-state estimation scale exponentially with the system size, highlighting the need for alternative approaches. Here we demonstrate an efficient method for complete characterization of complex multi-qubit quantum states. Using a variational version of the matrix product state ansatz, we perform the full tomography of quantum states produced in a 20-qubit trapped-ion Ising-type quantum simulator, using the data acquired in only 27 bases with 1000 measurements in each basis. We observe superior state reconstruction quality and faster convergence compared to the methods based on neural network quantum state representations: restricted Boltzmann machines and feedforward neural networks with autoregressive architecture. Our results pave the way towards efficient experimental characterization of complex states produced by the dynamics of many-body quantum systems.