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The Hamiltonian of a quantum system often have some symmetry in various fields of physics, e.g., high energy physics and condensed matter physics, and it is demanding to compute the spectrum of the Hamiltonian that resides in each symmetry sector. For this purpose, we can utilize the variational quantum eigensolver (VQE), which is a promising algorithm to compute eigenstates and their energies of a given quantum system that can be performed on a near-term quantum computer, to compute energy eigenstates possessing such symmetry by adding a penalty term in its cost function. 
The systematic analysis of such penalty terms, however, has been lacking and a heuristic way to set the penalty is adopted so far. In this work, we investigate two types of penalty terms for the VQE that have been previously proposed. We discover a convenient formula to set the penalty for one of the two types, which rigorously guarantees the resulting eigenstates by the VQE have desired symmetry. Meanwhile, we prove that the other type of penalty does not work well in a rigorous sense and gives completely wrong results in some cases. We also provide numerical simulations to validate our analysis.
Our results lay the theoretical foundation for the VQE with the penalty that applies to general quantum systems, and contribute to further application of a near-term quantum computer.

Quantum 2020

Penalty methods for variational quantum eigensolver

near-term quantum computers

penalty terms

energy spectrum

variational quantum eigensolver (vqe)

symmetry

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poster

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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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. 

We show that for the two widely used configurations of the double-$\Lambda$ atom-light coupling scheme, one where the control fields are applied in the same $\Lambda$-subsystem and another where they applied in different $\Lambda$-subsystems, the forward propagation of the probe and signal fields is described by the same set of equations. We then use optimal control theory to find the spatially-dependent optimal control fields which maximize the conversion efficiency from the probe to the signal field, for a given optical density. The present work is expected to find application in the implementation of efficient frequency and orbital angular momentum conversion devices for quantum information processing, as well as to be useful to many other applications using the double-$\Lambda$ atom-light coupling scheme.

Optimal conversion efficiency in the forward double-Λ atom-light coupling system

We investigate whether a trade-off relation between the diagonal elements of the mean square error matrix exists for the two-parameter unitary models with mutually commuting generators. We show that the error trade-off relation which exists in our models of a finite dimension system is a generic phenomenon in the sense that it occurs with a finite volume in the spate space. We analyze a qutrit system to show that there can be an error trade-off relation given by the SLD and RLD Cramer-Rao bounds that intersect each other. First, we analyze an example of the reference state showing the non-trivial trade-off relation numerically, and find that its eigenvalues must be in a certain range to exhibit the trade-off relation. For another example, one-parameter family of reference states, we analytically show that the non-trivial relation always exists and that the range where the trade-off relation exists is up to about a half of the possible range.

Error trade-off relations for two-parameter unitary model with commuting generators

Stimulated Raman adiabatic passage (STIRAP) is one of the most successful quantum control methods for coherent population transfer between two energy levels of a quantum system. A major advantage of STIRAP is its robustness against moderate variations of experimental parameters, while a drawback is that adiabatic transfer requires long times, leading to reduced efficiency when undesirable interactions with the environment are present leading to dephasing and dissipation. The efficiency of STIRAP can be increased when it is combined with shortcuts to adiabaticity techniques. One successful protocol that can be implemented is the superadiabatic STIRAP (SA-STIRAP), where the prototype Λ-type three-level system is driven by three laser pulses, forming a closed-loop configuration [1]. In this work we assess the efficiency of STIRAP and SA-STIRAP, in the presence of noise and dissipation. For the dissipation, we use the typical decay from the excited state, while for noise we use classical Ornstein-Ulhenbeck noise processes with exponential correlation functions leading to dephasing [2]. The performance of the two control protocols are compared for different system parameters.
1. L. Giannelli and E. Arimondo, Phys. Rev. A 89, 033419 (2014).
2. K. Blekos, D. Stefanatos, and E. Paspalakis, Phys. Rev. A 102, 023715 (2020).

Stimulated Raman adiabatic passage shortcuts with dissipation and dephasing

The study of hybrid semiconductor quantum dot (SQD) and metal nanoparticle (MNP) structures has attracted significant interest in recent years, as the hybrid structures have enhanced optical response in comparison to their constituents [1]. A problem that has been studied is the controlled exciton dynamics of the SQD in the presence of the MNP (see Refs. [2,3] and references therein). Insofar, the study of the controlled exciton dynamics in hybrid SQD-MNP structures is limited to symmetric SQDs. Asymmetric SQDs possess permanent dipole moments which may strongly affect their interaction with light. In this work we study the controlled exciton dynamics of hybrid asymmetric SQD-MNP structures and pay special attention to the case that the asymmetric SQD has permanent electric dipoles that take values comparable to the induced electric dipoles. We analyze the exciton dynamics for different electromagnetic pulse durations and different distances between the SQD and the MNP and present cases where high efficiency excitonic population inversion is succeeded. 
1. B. Szychowski, M. Pelton, and M. C. Daniel, Nanophot. 8, 517 (2019). 
2. E. Paspalakis, S. Evangelou, and A. F. Terzis, Phys. Rev. B 87, 235302 (2013).
3. Y. Qi et al, J. Phys. D: Appl. Phys. 52 425101 (2019).

Control of excitonic population dynamics in a coupled asymmetric semiconductor quantum dot - metal nanoparticle structure

Geometry structure optimizations and NBO-analysis of the electron density distributionfor hemi- (hp) and dicarbahemiporphyrazine (dchp) complexes with Ca(II), Ni(II) and Zn(II) were performed at PBE0/pcseg-2 level of theory. The Time Dependent DFT spectra were calculated for this molecules

Features of the electron density distribution in the complexes of hemi- and dicarbahemiporphyrazine with Ca(II), Ni(II) and Zn(II)

The power of a quantum circuit is determined through the number of two-qubit entangling gates that can be performed within the coherence time of the system. In the absence of parallel quantum gate operations, this would make the quantum simulators limited to shallow circuits. Here, we propose a protocol to parallelize the
implementation of two-qubit entangling gates between multiple users which are spatially separated and use a commonly sheared spin chain data-bus. Our protocol works through inducing effective interaction between each pair of qubits without disturbing the others, therefore, it increases the rate of gate operations without creating crosstalk. This is achieved by tuning the Hamiltonian parameters appropriately, described in the form of two different strategies. The tuning of the parameters makes different bilocalized eigenstates responsible for the realization of the entangling gates between different pairs of distant qubits. Remarkably, the performance of our protocol is robust against increasing the length of the data-bus and the number of users. Moreover, we show that
this protocol can accomplish two-way communication and standout the decoherence effects.

Parallel entangling gate operations in spin chins

The preparation of a high-quality single-photon source at the mid-infrared (MIR) wavelength range (approximately 2-20 µm) is of great importance for the next-generation technology of quantum sensing, imaging, and communications. The current research on single-photon sources mainly focuses on the near-infrared band. The high-brightness, spectrally pure, and easy-to-operate quantum photon source at the MIR range remains an unsettled problem. To solve this problem, we design a scheme based on a machine learning framework to optimize the poling period of LN crystal at the MIR range. Calculation results show that the spectral purity of the heralded single photons can over 0.999 for such a custom poled LN (cpLN). This high-quality source could be very useful for applications in quantum sensing, imaging, and communications at the MIR band.

Mid-infrared spectrally pure photons generation from LN optimized by machine learning

The mid-infrared (MIR) wavelength range (approximately 2-20 μm) is of great interest to a variety of applications. However, the advantages of the MIR range have not been fully exploited using quantum technology. It is still lack of high-quality quantum sources for the MIR range. In this work, we theoretically study the preparation of pure-state single-photon source from 23 nonlinear optical crystals, including birefringent crystals CMTC, LIIO3, AAS, HGS, CGA, TAS, AGS, AGSE, GASE, LIS, LISE, LGS, and LGSE; periodic poling crystals LT, LN, KTP, KN, CSP, ZGP, BATIO3, MGBAF4, OP-ZNSE, and PMN-0.38PT. Calculation results show that these crystals satisfy three kinds of group-velocity-matching (GVM) conditions. The down-converted photons wavelength range is from 1298 to 7384 nm for the GVM1 condition, from 2312 to 11650 nm for the GVM2 condition, and from 1658 to 9380 nm for the GVM3 condition. The spectral purities for three kinds of GVM conditions are around 0.97, 0.97, and 0.82, respectively. We also calculate their performance in the Hong-Ou-Mandel interference from independent sources, and it can also achieve visibility as high as 97%. This study may provide high-quality heralded single-photon sources and entangled photon sources for quantum sensing, imaging, and communications at the MIR wavelength range.

Mid-infrared spectrally-pure single-photon states generation from 23 nonlinear optical crystals

We theoretically investigate the preparation of spectrally-uncorrelated biphotons from a spontaneous parametric down-conversion process using doped PPLN crystals, including MgO, ZnO, and In2O3 doped PPLN with a doping ratio from 0 to 7 mol%. Calculation results show that these crystals satisfy three kinds of group-velocity-matching (GVM) conditions at mid-infrared (MIR) wavelengths. Under the GVM1, GVM2, and GVM3 conditions, the wavelengths are at around 2.5μm, 4.0μm, and 3.2μm, and the corresponding spectral purities are around 0.97, 0.97, and 0.82, respectively. We also calculate the thermal properties of the doped PPLN crystals and their performance in Hong-Ou-Mandel interference. It can be concluded that the doping ratio can be utilized as a degree of freedom to manipulate the biphoton state. The spectrally uncorrelated biphotons can be used to prepare pure single-photon source and entangled photon source, which may have promising applications for quantum-enhanced sensing, imaging, and communications at the MIR range.

Mid-infrared spectrally-uncorrelated biphotons generation from doped PPLN

The orbital angular momentum (OAM) is an important degree of freedom for photons because the OAM state can be utilized as a high dimensional information carrier for large-capacity quantum communications. How to recognizing a single -photon-level OAM state with high accuracy in a noisy environment is a very important problem in this scenario. In this research, we use a convolutional neural 
network (CNN) technique to recognize the Laguerre-Gaussian (LG) modes at the single-photon level. Simulation and experimental results show that with the help of deep learning techniques, recognizing accuracy can be greatly improved. This study may shed new light on the OAM based quantum sensing and quantum communications in the future.

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Penalty methods for variational quantum eigensolver

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