Variational quantum simulation of thermal statistical states on a superconducting quantum processer

Quantum computers promise to solve finite-temperature properties of quantum many-body systems,which is generally challenging for classical computers due to high computational complexities.Here,we report experimental preparations of Gibbs states and excited states of Heisenberg X X and X X Z models by using a 5-qubit programmable superconducting processor.In the experiments,we apply a hybrid quantum–classical algorithm to generate finite temperature states with classical probability models and variational quantum circuits.We reveal that the Hamiltonians can be fully diagonalized with optimized quantum circuits,which enable us to prepare excited states at arbitrary energy density.We demonstrate that the approach has a self-verifying feature and can estimate fundamental thermal observables with a small statistical error.Based on numerical results,we further show that the time complexity of our approach scales polynomially in the number of qubits,revealing its potential in solving large-scale problems.

Variational quantum simulation of the quantum critical regime

The quantum critical regime marks a zone in the phase diagram where quantum fluctuation around the critical point plays a significant role at finite temperatures.While it is of great physical interest,simulation of the quantum critical regime can be difficult on a classical computer due to its intrinsic complexity.Herein,we propose a variational approach,which minimizes the variational free energy,to simulate and locate the quantum critical regime on a quantum computer.The variational quantum algorithm adopts an ansatz by performing an unitary operator on a product of a single-qubit mixed state,in which the entropy can be analytically obtained from the initial state,and thus the free energy can be accessed conveniently.With numeral simulation,using the one-dimensional Kitaev model as a demonstration we show that the quantum critical regime can be identified by accurately evaluating the temperature crossover line.Moreover,the dependencies of both the correlation length and the phase coherence time with temperature are evaluated for the thermal states.Our work suggests a practical way as well as a first step for investigating quantum critical systems at finite temperatures on quantum devices with few qubits.

A concise review of Rydberg atom based quantum computation and quantum simulation

Quantum information processing based on Rydberg atoms emerged as a promising direction two decades ago.Recent experimental and theoretical progresses have shined exciting light on this avenue.In this concise review,we will briefly introduce the basics of Rydberg atoms and their recent applications in associated areas of neutral atom quantum computation and simulation.We shall also include related discussions on quantum optics with Rydberg atomic ensembles,which are increasingly used to explore quantum computation and quantum simulation with photons.

Review of quantum simulation based on Rydberg many-body system

Quantum simulation has been developed extensively over the past decades,widely applied to different models to explore dynamics in the quantum regime.Rydberg atoms have strong dipole-dipole interactions and interact with each other over a long distance,which makes it straightforward to build many-body interacting quantum systems to simulate specific models.Additionally,neutral atoms are easily manipulated due to their weak interactions.These advantages make Rydberg many-body system an ideal platform to implement quantum simulations.This paper reviews several quantum simulations for different models based on Rydberg many-body systems,including quantum Ising models in one dimension and two dimensions mainly for quantum magnetism,XY model for excitation transport,SSH model for symmetry-protected topological phases,and critical self-organized behaviors in many-body systems.Besides,some challenges and promising directions of quantum simulations based on Rydberg many-body system are discussed in this paper.

Quantum simulation and quantum computation of noisy-intermediate scale

In the past years, great progresses have been made on quantum computation and quantum simulation. Increasing the number of qubits in the quantum processors is expected to be one of the main motivations in the next years, while noises in manipulation of quantum states may still be inevitable even the precision will improve. For research in this direction, it is necessary to review the available results about noisy multiqubit quantum computation and quantum simulation. The review focuses on multiqubit state generations, quantum computational advantage, and simulating physics of quantum many-body systems. Perspectives of near term noisy intermediate-quantum processors will be discussed.

Quantum simulation of τ-anti-pseudo-Hermitian two-level systems

Different from the Hermitian case, non-Hermitian(NH) systems have novel properties and strongly relate to open and dissipative quantum systems. In this work, we investigate how to simulate τ-anti-pseudo-Hermitian systems in a Hermitian quantum device using linear combinations of unitaries and duality quantum algorithm. Specifying the τ to time-reversal(T) and parity-time-reversal(PT) operators, we construct the two NH two-level systems, design quantum circuits including three qubits, and decide the quantum gates explicitly in detail. We also calculate the success probabilities of the simulation.Experimental implementation can be expected in small quantum simulator.

Low-temperature environments for quantum computation and quantum simulation

This review summarizes the requirement of low temperature conditions in existing experimental approaches to quantum computation and quantum simulation.

Quantum simulations with nuclear magnetic resonance system

Thanks to the quantum simulation,more and more problems in quantum mechanics which were previously inaccessible are now open to us.Capitalizing on the state-of-the-art techniques on quantum coherent control developed in past few decades,e.g.,the high-precision quantum gate manipulating,the time-reversal harnessing,the high-fidelity state preparation and tomography,the nuclear magnetic resonance(NMR) system offers a unique platform for quantum simulation of many-body physics and high-energy physics.Here,we review the recent experimental progress and discuss the prospects for quantum simulation realized on NMR systems.

Quantum simulation of lattice gauge theories on superconducting circuits:Quantum phase transition and quench dynamics

Recently,quantum simulation of low-dimensional lattice gauge theories(LGTs)has attracted many interests,which may improve our understanding of strongly correlated quantum many-body systems.Here,we propose an implementation to approximate Z;LGT on superconducting quantum circuits,where the effective theory is a mixture of a LGT and a gauge-broken term.By using matrix product state based methods,both the ground state properties and quench dynamics are systematically investigated.With an increase of the transverse(electric)field,the system displays a quantum phase transition from a disordered phase to a translational symmetry breaking phase.In the ordered phase,an approximate Gauss law of the Z;LGT emerges in the ground state.Moreover,to shed light on the experiments,we also study the quench dynamics,where there is a dynamical signature of the spontaneous translational symmetry breaking.The spreading of the single particle of matter degree is diffusive under the weak transverse field,while it is ballistic with small velocity for the strong field.Furthermore,due to the emergent Gauss law under the strong transverse field,the matter degree can also exhibit confinement dynamics which leads to a strong suppression of the nearest-neighbor hopping.Our results pave the way for simulating the LGT on superconducting circuits,including the quantum phase transition and quench dynamics.

Impact of Temperature Variation on Performance of Carbon Nanotube Field-Effect Transistor-Based on Chaotic Oscillator:A Quantum Simulation Study

We evaluate the impact of temperature on the output behavior of a carbon nanotube field effect transistor （CNFET） based chaotic generator. The sources cause the variations in both current-voltage characteristics of the CNFET device and an overall chaotic circuit is pointed out. To verify the effect of temperature variation on the output dynamics of the chaotic circuit, a simulation is performed by employing the CNFET compact model of Wong et al. in HSPICE with a temperature range from -100℃ to 100℃. The obtained results with time series, frequency spectra, and bifurcation diagram from the simulation demonstrate that temperature plays a significant role in the output dynamics of the CNFET-based chaotic circuit. Thus, temperature-related issues should be taken into account while designing a high-quality chaotic generator with high stability.

Quantum Simulation of 2p-πElectronic Hamiltonian in Molecular Ethylene by Using an NMR Quantum Computer

Classical simulation of a quantum system is a hard problem. It’s known that these problems can be solved efficiently by using quantum computers. This study demonstrates the simulation of the molecular Hamiltonian of 2p-π electrons of ethylene in order to calculate the ground state energy. The ground state energy is estimated by an iterative phase estimation algorithm. The ground state is prepared by the adiabatic state preparation and the implementation of the procedure is carried out by numerical simulation of two-qubit NMR quantum simulator. The readout scheme of the simulator is performed by extracting binary bits via NMR interferometer.

Quantum simulation of Hofstadter butterfly with synthetic gauge fields on two-dimensional superconducting-qubit lattices

Motivated by recent realizations of two-dimensional(2D)superconducting-qubit lattices,we propose a protocol to simulate Hofstadter butterfly with synthetic gauge fields in superconducting circuits.Based on the existing 2D superconducting-qubit lattices,we construct a generalized Hofstadter model on zigzag lattices,which has a fractal energy spectrum similar to the original Hofstadter butterfly.By periodically modulating the resonant frequencies of qubits,we engineer a synthetic gauge field to mimic the generalized Hofstadter Hamiltonian.A spectroscopic method is used to demonstrate the Hofstadter butterfly from the time evolutions of experimental observables.We numerically simulate the dynamics of the system with realistic parameters,and the results show a butterfly spectrum clearly.Our proposal provides a promising way to realize the Hofstadter butterfly on the latest 2D superconducting-qubit lattices and will stimulate the quantum simulation of novel properties induced by magnetic fields in superconducting circuits.

Quantum simulation of a general anti-PT-symmetric Hamiltonian with a trapped ion qubit

Non-Hermitian systems satisfying parity-time(PT)symmetry have aroused considerable interest owing to their exotic features.Anti-PT symmetry is an important counterpart of the symmetry,and has been studied in various classical systems.Although a Hamiltonian with anti-PT symmetry only differs from its PT-symmetric counterpart in a global phase,the information and energy exchange between systems and environment are different under them.It is also suggested theoretically that anti-PT symmetry is a useful concept in the context of quantum information storage with qubits coupled to a bosonic bath.So far,the observation of anti-PT symmetry in individual quantum systems remains elusive.Here,we implement an anti-PT-symmetric Hamiltonian of a single qubit in a single trapped ion by a designed microwave and optical control-pulse sequence.We characterize the anti-PT phase transition by mapping out the eigenvalues at different ratios between coupling strengths and dissipation rates.The full information of the quantum state is also obtained by quantum state tomography.Our work allows quantum simulation of genuine open-system feature of an anti-PT-symmetric system,which paves the way for utilizing non-Hermitian properties for quantum information processing.

Efficient quantum simulation of open quantum dynamics at various Hamiltonians and spectral densities

Simulation of open quantum dynamics for various Hamiltonians and spectral densities are ubiquitous for studying various quantum systems.On a quantum computer,only log2N qubits are required for the simulation of an N-dimensional quantum system,hence simulation in a quantum computer can greatly reduce the computational complexity compared with classical methods.Recently,a quantum simulation approach was proposed for studying photosynthetic light harvesting[npj Quantum Inf.4,52(2018)].In this paper,we apply the approach to simulate the open quantum dynamics of various photosynthetic systems.We show that for Drude—Lorentz spectral density,the dimerized geometries with strong couplings within the donor and acceptor clusters respectively exhibit significantly improved efficiency.We also demonstrate that the overall energy transfer can be optimized when the energy gap between the donor and acceptor clusters matches the optimum of the spectral density.The effects of different types of baths,e.g.,Ohmic,sub-Ohmic,and super-Ohmic spectral densities are also studied.The present investigations demonstrate that the proposed approach is universal for simulating the exact quantum dynamics of photosynthetic systems.

Quantum simulation of molecular interaction and dynamics at surfaces

The interaction between molecules and solid surfaces plays important roles in various applications, including catalysis, sensors, nanoelectronies, and solar cells. Surprisingly, a full understanding of molecule-surface interaction at the quantum mechanical level has not been achieved even for very simple molecules, such as water. In this mini-review, we report recent progresses and current status of studies on interaction between representative molecules and surfaces. Taking water/metal, DNA bases/carbon nanotube, and organic dye molecule/oxide as examples, we focus on the understanding on the microstructure, electronic property, and electron-ion dynamics involved in these systems obtained from first-principles quantum mechanical calculations. We find that a quantum mechanical description of molecule surface interaction is essential for understanding interface phenomenon at the microscopic level, such as wetting. New theoretical developments, including van der Waals density functional and quantum nuclei treatment, improve further our understanding of surface interactions.

Quantum computation and simulation with vibrational modes of trapped ions

Vibrational degrees of freedom in trapped-ion systems have recently been gaining attention as a quantum resource,beyond the role as a mediator for entangling quantum operations on internal degrees of freedom,because of the large available Hilbert space.The vibrational modes can be represented as quantum harmonic oscillators and thus offer a Hilbert space with infinite dimensions.Here we review recent theoretical and experimental progress in the coherent manipulation of the vibrational modes,including bosonic encoding schemes in quantum information,reliable and efficient measurement techniques,and quantum operations that allow various quantum simulations and quantum computation algorithms.We describe experiments using the vibrational modes,including the preparation of non-classical states,molecular vibronic sampling,and applications in quantum thermodynamics.We finally discuss the potential prospects and challenges of trapped-ion vibrational-mode quantum information processing.

Quantum computation and simulation with superconducting qubits

Superconducting circuits based on Josephson junctions are regarded as one of the most promising technologies for the implementation of scalable quantum computers.This review presents the basic principles of superconducting qubits and shows the progress of quantum computing and quantum simulation based on superconducting qubits in recent years.The experimental realization of gate operations,readout,error correction codes,as well as some quantum algorithms are summarized,followed by an introduction of quantum simulation.And then some important applications in fields including condensed matter physics,quantum annealing,and quantum chemistry are discussed.

Security Simulation of Continuous-Variable Quantum Key Distribution over Air-to-Water Channel Using Monte Carlo Method

Considering the ocean water＇s optical attenuation and the roughness of the sea surface, we analyze the security of continuous-variable （CV） quantum key distribution （QKD） based Mr-to-water channel. The effects of the absorp- tion and scattering on the transmittance of underwater quantum channel and the maximum secure transmission distance are studied. Considering the roughness of the sea surface, we simulate the performance bounds of CV QKD with different wind speeds using the Monte Carlo method. The results show that even if the secret key rate gradually reduces as the wind speed increases, the maximum transmission distance will not be affected obviously. Compared to the works regarding short-distance underwater optical communication, our research represents a significant step towards establishing secure communication between air platform and submarine vehicle.

Quantum transport simulation of the two-dimensional GaSb transistors

Owing to the high carrier mobility,two-dimensional(2D)gallium antimonite(GaSb)is a promising channel material for field-effect transistors(FETs)in the post-silicon era.We investigated the ballistic performance of the 2D GaSb metal-oxide-semiconductor FETs with a 10 nm-gate-length by the ab initio quantum transport simulation.Because of the wider bandgap and better gate-control ability,the performance of the 10-nm monolayer(ML)GaSb FETs is generally superior to the bilayer counterparts,including the three-to-four orders of magnitude larger on-current.Via hydrogenation,the delaytime and power consumption can be further enhanced with magnitude up to 35%and 57%,respectively,thanks to the expanded bandgap.The 10-nm ML GaSb FETs can almost meet the International Technology Roadmap for Semiconductors(ITRS)for high-performance demands in terms of the on-state current,intrinsic delay time,and power-delay product.

Selected topics of quantum computing for nuclear physics

Nuclear physics,whose underling theory is described by quantum gauge field coupled with matter,is fundamentally important and yet is formidably challenge for simulation with classical computers.Quantum computing provides a perhaps transformative approach for studying and understanding nuclear physics.With rapid scaling-up of quantum processors as well as advances on quantum algorithms,the digital quantum simulation approach for simulating quantum gauge fields and nuclear physics has gained lots of attention.In this review,we aim to summarize recent efforts on solving nuclear physics with quantum computers.We first discuss a formulation of nuclear physics in the language of quantum computing.In particular,we review how quantum gauge fields(both Abelian and non-Abelian)and their coupling to matter field can be mapped and studied on a quantum computer.We then introduce related quantum algorithms for solving static properties and real-time evolution for quantum systems,and show their applications for a broad range of problems in nuclear physics,including simulation of lattice gauge field,solving nucleon and nuclear structures,quantum advantage for simulating scattering in quantum field theory,non-equilibrium dynamics,and so on.Finally,a short outlook on future work is given.