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We list three fundamental features of relativistic quantum mechanics equations (RQMEs). 1) A free particle has positive kinetic energy (PKE) and negative kinetic energy (NKE) branches. 2) For Dirac equation, the probability current of particles with PKE is opposite to that of NKE. 3) In each RQME, when potential takes minus sign, the eigen values also take minus sign.
A fundamental postulation is that the features RQMEs should remain in low momentum motion. However, Schrödinger equation does not hold the above three feature. Or these features are lost in low momentum approximation.
Starting from RQMEs and taking low momentum approximation, we derive NKE Schrödinger equation beside familiar Schrödinger equation which is of PKE. With the help of NKE Schrödinger equation, the lost formulas are recovered. The negative branch, the feature 1) above, is retained by NKE Schrödinger equation. In the region where the potential is greater than the energy of a particle, the particle is of NKE. NKE should be treated on an equal footing as PKE.
Klein-Gordon equation is decoupled to be two: PKE one and NKE. In this way, the feature 2) is held by decoupled Klein-Gordon equations. The so-called difficulty of negative probability of Klein-Gordon equation is solved, for the correct expression for the probability current of this equation is given. 
A (PKE) NKE particle can have stationary motion only when it is subject to an attractive (repulsive) potential, which is guaranteed by Virial theorem. 
Two NKE electrons in a potential can constitute a stable system, a new kind of possible mechanism for electron paring. 
The whole discussion stems from RQMEs with no any new postulation. 
We suggest some experiments which may verify that there are indeed NKE electrons.


Quantum 2020

Particles’ negative kinetic energy and possible experimental verification

experiment verifying the nke electron

nke schrodinger equation

low momentum approximation of rqmes

negative kinetic energy (nke)

relativistic quantum mechanics equations (rqmes)

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CAP Virtual Congress 2021

technical paper

The Institute of Physics and IOP Publishing, in partnership with the Chinese Physical Society (CPS) and the University of Science and Technology of China (USTC) are proud to have brought together the international quantum science community online for this inaugural conference.


Early career and leading researchers from universities, industry and government worldwide came together to share, learn and collaborate on the latest research and emerging areas of high interest across quantum science and technology. The broad themes covered by Quantum 2020 included:

Quantum communication;
Quantum computing and quantum simulation;
Quantum sensing, metrology and imaging;
Quantum information theory, software and algorithms;
Quantum foundations;
Quantum technology in industry.
The four-day event featured talks from world-renowned scientists, interactive poster sessions and two exciting panel discussions on the themes of Quantum Technology in Industry and Quantum Technology Programmes Around the World.


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Conventional optical synthesis, the manipulation of the phase and amplitude of spectral components to produce an optical pulse in different temporal modes, is revolutionizing ultrafast optical science and metrology. These technologies rely on the Fourier transform of light fields between time and frequency domains in one-dimensional space. However, within this treatment it is impossible to incorporate the quantum correlation among photons. Here we expand the Fourier synthesis into high dimensional space to deal with the quantum correlation, and carry out an experimental demonstration by manipulating the two-photon probability distribution of a biphoton in two-dimensional time and frequency space. As a potential application, we show manipulation of a heralded single-photon wave packet, which is never explained by the conventional one-dimensional Fourier optics. Our approach opens up a new pathway to tailor the temporal characteristics of a biphoton wave packet with high dimensional quantum-mechanical treatment [1-4].

[1] R-B Jin, et al, arXiv: 2002.08197

[2] R-B Jin, et al, Phys. Rev. Appl. 11.034067(2019)

[3] R-B Jin, et al, Phys. Rev.Appl. 10, 034011 (2018)

[4] R-B Jin, et al, Opt. Express 26, 21153 (2018)

Quantum optical synthesis in 2D time-frequency space 


Quantum simulators are widely seen as one of the most promising near-term applications of quantum technologies. However, it remains unclear to what extent a noisy device can output reliable results in the presence of unavoidable imperfections. Here we propose a framework to characterize the performance of quantum simulators by linking the robustness of measured quantum expectation values to the spectral properties of the output observable, which in turn can be associated with its macroscopic or microscopic character in Hilbert space. We show that, under general assumptions and on average over all states, imperfect devices are able to reproduce the dynamics of macroscopic observables accurately, while the relative error in the expectation value of microscopic observables is much larger on average. We experimentally demonstrate the universality of these features in a state-of-the-art quantum simulator and show that the predicted behavior is generic for a highly accurate device, without assuming any knowledge about the nature of the imperfections.

Quantifying the sensitivity to errors in analog quantum simulation

Various noise models have been developed to describe the propagation and effect of the noise from imperfect implementation of hardware. Usually, parameters characterizing such noise are treated as deterministic numbers regressed from test data. Instead, we use a Bayesian approach to infer the distributions of parameters by regarding error mitigation as a stochastic inverse problem. We will also compare the performance of our methodology with other error mitigation methods on the real device.

Characterizing Noise in Quantum Computing

Preparing the ground state of a Hamiltonian is a problem of great significance in physics with deep implications in combinatorial optimization. While the quantum adiabatic algorithm (QAA) is known to return the ground state for sufficiently long preparation times, the decoherence times of noisy, intermediate-scale quantum devices render the QAA infeasible. Variational approaches such as the quantum approximate optimization algorithm sparked intensive research interest, however, optimization of a multiparameter cost function requires billions of measurements already for a moderate number of qubits and can be prone to noise-induced barren plateaus, thus forsaking any practical quantum advantage. In our work, we aim at combining the strengths of the adiabatic and the variational approaches for fast and high-fidelity ground state preparation by keeping the number of measurements as low as possible, benchmarking our algorithm for a spin-1/2 transverse and longitudinal Ising chain (ZZXZ model) with N=100 sites. Our preliminary results already show a promising significant increase in the overlap with the ground state from 5.7% to 17.4% when compared to naive QAA for fixed total evolution time.

Faster adiabatic ground state preparation with few measurements in the NISQ era

The Green's function plays a crucial role when studying the nature of quantum many-body systems, especially strongly correlated systems. Although the development of quantum computers in the near future may enable us to compute energy spectra of classically intractable systems, methods to simulate the Green's function with near-term quantum algorithms have not been proposed yet. Here, we propose two methods to calculate the Green's function of a given Hamiltonian on near-term quantum computers. The first one makes use of a variational dynamics simulation of quantum systems and computes the dynamics of the Green's function in real time directly. The second one utilizes the Lehmann representation of the Green's function and a method which calculates excited states of the Hamiltonian. Both methods require shallow quantum circuits and are compatible with near-term quantum computers. We numerically simulated the Green's function of the Fermi-Hubbard model and demonstrated the validity of our proposals.

Calculation of the Green's function on near-term quantum computers

Quantum computers can be used for supervised learning by treating parameterised quantum circuits as models that map data inputs to predictions. While a lot of work has been done to investigate practical implications of this approach, many important theoretical properties of these models remain unknown. Here we investigate how the strategy with which data is encoded into the model influences the expressive power of parametrised quantum circuits as function approximators. We show that one can naturally write a quantum model as a partial Fourier series in the data, where the accessible frequencies are determined by the nature of the data encoding gates in the circuit. By repeating simple data encoding gates multiple times, quantum models can access increasingly rich frequency spectra. We show that there exist quantum models which can realise all possible sets of Fourier coefficients, and therefore, if the accessible frequency spectrum is asymptotically rich enough, such models are universal function approximators.

What Functions can Quantum Models Learn?

Designing feasible and qualitative methods for estimation of topological invariants, such as the Chern number, is of great significance for experimental realization of topological quantum matter.We present two key results in this direction. We first show that for two-band systems supported on Bravais lattices with 2n-fold rotation symmetry, the Chern number (mod 2n) of one of the energy bands can be inferred from the spin polarization of the band wavefunction at the high-symmetry crystal momenta in the Brillouin zone. We leverage this result to design an experimental scheme for ultracold bosonic gases that uses Bloch oscillations and Zeeman spectroscopy for validation of the topological phases with Chern number ±2 on a triangular lattice. As part of the latter result, we present the first experimental scheme to our knowledge for simulating spin-orbit coupling on a triangular optical lattice. Our results highlight Bloch oscillations as a robust tool for detection of topological order, and also open doors to new experiments based on spin-orbit coupled systems beyond square lattices.

Detection of Topological Order in Ultracold Atoms

We present multi-layer, mechanically-compliant photonic crystal slabs for use in cavity optomechanical experiments. The slabs have mechanical frequencies in the range of several hundred kilohertz and demonstrate reflectance of close to unity at telecom wavelengths [1]. An optomechanical system consisting of a mechanical resonator array in an optical cavity has been proposed as a method to reach the elusive single-photon strong coupling regime in optomechanics [2]. A critical requirement of such a system is to have highly reflective and uniform mechanical resonators of well-defined spacing. In this work we present our progress in this direction. We demonstrate devices fabricated in an AlGaAs heterostructure consisting of sub-μm spaced, near-identical mechanical resonators on top of a distributed Bragg reflector. We pattern these resonators with photonic crystal structures for engineering their out-of-plane reflectivity. We characterize the mechanical and optical properties of the slabs. The presented devices can be combined with micro-mirrors on an external chip forming a fully integrated chip-based realization of a multi-element optomechanical system. Additonally, two photonic crystal slabs with sub-μm gap can exhibit so-called photonic bound states in the continuum (BICs). Such photonic BICs can be exploited for surpassing the performance of conventional Fabry-Perot-based optomechanical microcavities [3].
References:
[1] S. K. Manjeshwar et al., Appl. Phys. Lett. 116, 264001 (2020)
[2] A. Xuereb et al., Phys. Rev. Lett. 109, 223601 (2012)
[3] J. M. Fitzgerald et al., arXiv:2007.07883 [quant-ph]

Multi-layer suspended photonic crystal membranes in AlGaAs heterostructures for integrated cavity optomechanics

Einstein’s Equivalence Principle (EEP) is a cornerstone in the development
of General Relativity. Its validity implies that gravity is a geometrical
phenomena. Several experiments have proven that EEP is valid in the
classical regime. Nevertheless, its validity for quantum systems is still
undergoing experimental tests. In this work we study, following two
different approaches, the quantum free fall of quantum particles. Our
results suggest that EEP is violated in the quantum regime, but naturally
emerges as the energy/mass approaches macroscopic values. We first show
that the transient current density of a suddenly released beam of quantum
particles depends explicitly on the particle’s mass (thus contradicting
the universality of free fall), but such dependence disappear as the mass
increases (indicating the emerge of the EEP). We also consider the problem
of a quantum particle bouncing above a mirror in the presence of the
Earth’s gravitational field. By means of a simple method based on Fourier
analysis, we show that the classical probability distribution (which is
mass independent) emerges from its quantum-mechanical analogue in the
limit of large quantum numbers (high energy regime), thus also supporting
the emergence of the EEP from quantum mechanics.

On the validity of Einstein's Equivalence Principle in Quantum Mechanics

Tensor network theory and quantum simulation are respectively the key classical and quantum methods in understanding many-body quantum physics. Here we show hybridization of these two seemingly independent methods, inheriting both their distinct advantageous features of efficient representations of many-body wave functions. We introduce the framework of hybrid tensor networks with building blocks consisting of measurable quantum states and classically contractable tensors. As an example, we demonstrate efficient quantum simulation with hybrid tree tensor networks that use quantum hardware whose size is significantly smaller than the one of the target system. We numerically test our method for finding the ground state of 1D and 2D spin systems of up to 8×8 and 4×3 qubits with operations only acting on 8+1 and 4+1 qubits, respectively. Our approach paves the way to the near-term quantum simulation of large practical problems with intermediate size quantum hardware, with potential applications in quantum chemistry, quantum many-body physics, quantum field theory, and quantum gravity thought experiments.

Particles’ negative kinetic energy and possible experimental verification

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