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 control for time-dependent noise by inverse geometric optimization

Quantum systems are exceedingly difficult to engineer because they are sensitive to various types of noises.In particular,timedependent noises are frequently encountered in experiments but how to overcome them remains a challenging problem.In this work,we propose a flexible robust control technique to resist time-dependent noises based on inverse geometric optimization working in the filter-function formalism.The basic idea is to parameterize the control filter function geometrically and minimize its overlap with the noise spectral density.This then effectively reduces the noise susceptibility of the controlled system evolution.We show that the proposed method can produce high-quality robust pulses for realizing desired quantum evolutions under realistic noise models.Also,we demonstrate this method in examples including dynamical decoupling and quantum sensing protocols to enhance their performances.

Experimental quantum simulation of a topologically protected Hadamard gate via braiding Fibonacci anyons

Topological quantum computation(TQC)is one of the most striking architectures that can realize fault-tolerant quantum computers.In TQC,the logical space and the quantum gates are topologically protected,i.e.,robust against local disturbances.The topological protection,however,requires complicated lattice models and hard-to-manipulate dynamics;even the simplest system that can realize universal TQC-the Fibonacci anyon system—lacks a physical realization,let alone braiding the non-Abelian anyons.Here,we propose a disk model that can simulate the Fibonacci anyon system and construct the topologically protected logical spaces with the Fibonacci anyons.Via braiding the Fibonacci anyons,we can implement universal quantum gates on the logical space.Our disk model merely requires two physical qubits to realize three Fibonacci anyons at the boundary.By 15 sequential braiding operations,we construct a topologically protected Hadamard gate,which is to date the least-resource requirement for TQC.To showcase,we implement a topological Hadamard gate with two nuclear spin qubits,which reaches 97.18%fidelity by randomized benchmarking.We further prove by experiment that the logical space and Hadamard gate are topologically protected:local disturbances due to thermal fluctuations result in a global phase only.As a platform-independent proposal,our work is a proof of principle of TQC and paves the way toward fault-tolerant quantum computation.

Hardware-efficient quantum principal component analysis for medical image recognition

Principal component analysis(PCA)is a widely used tool in machine learning algorithms,but it can be computationally expensive.In 2014,Lloyd,Mohseni&Rebentrost proposed a quantum PCA(qPCA)algorithm[Nat.Phys.10,631(2014)]that has not yet been experimentally demonstrated due to challenges in preparing multiple quantum state copies and implementing quantum phase estimations.In this study,we presented a hardware-efficient approach for qPCA,utilizing an iterative approach that effectively resets the relevant qubits in a nuclear magnetic resonance(NMR)quantum processor.Additionally,we introduced a quantum scattering circuit that efficiently determines the eigenvalues and eigenvectors(principal components).As an important application of PCA,we focused on classifying thoracic CT images from COVID-19 patients and achieved high accuracy in image classification using the qPCA circuit implemented on the NMR system.Our experiment highlights the potential of near-term quantum devices to accelerate qPCA,opening up new avenues for practical applications of quantum machine learning algorithms.

Experimental demonstration of nonlinear quantum metrology with optimal quantum state

Nonlinear quantum metrology may exhibit better precision scalings. For example, the uncertainty of an estimated phase may scale as △φ∝ 1/N2 under quadratic phase accumulation, which is 1/N times smal-ler than the linear counterpart, where N is probe number. Here, we experimentally demonstrate the non-linear quantum metrology by using a spin-I（I 〉 1/2） nuclear magnetic resonance （NMR） ensemble that can be mapped into a system ofN = 2I spin-1/2 particles and the quadratic interaction can be utilized for the quadratic phase accumulation. Our experimental results show that the phase uncertainty can scale as △φ∝1/（N2-1） by optimizing the input states, when N is an odd number. In addition, the interferomet-tic measurement with quadratic interaction provides a new way for estimating the quadrupolar coupling strength in an NMR system. Our system may be further extended to exotic nonlinear quantum metrology with higher order many-body interactions.

Testing a quantum error-correcting code on various platforms

Quantum error correction plays an important role in fault-tolerant quantum information processing.It is usually difficult to experimentally realize quantum error correction,as it requires multiple qubits and quantum gates with high fidelity.Here we propose a simple quantum error-correcting code for the detected amplitude damping channel.The code requires only two qubits.We implement the encoding,the channel,and the recovery on an optical platform,the IBM Q System,and a nuclear magnetic resonance system.For all of these systems,the error correction advantage appears when the damping rate exceeds some threshold.We compare the features of these quantum information processing systems used and demonstrate the advantage of quantum error correction on current quantum computing platforms.

Floquet-engineered quantum state transfer in spin chains

Quantum state transfer between two distant parties is at the heart of quantum computation and quantum communication.Among the various protocols,the counterdiabatic driving(CD)method,by suppressing the unwanted transitions with an auxiliary Hamiltonian Hcd(t),offers a fast and robust strategy to transfer quantum states.However,Hcd(t)term often takes a complicated form in higherdimensional systems and is difficult to realize in experiment.Recently,the Floquet-engineered method was proposed to emulate the dynamics induced by Hcd(t)without the need for complex interactions in multi-qubit systems,which can accelerate the adiabatic process through the fast-oscillating control in the original Hamiltonian H0(t).Here,we apply this method in the Heisenberg spin chains,with only control of the two marginal couplings,to achieve the fast,high-fidelity,and robust quantum state transfer.Then we report an experimental implementation of our scheme using a nuclear magnetic resonance simulator.The experimental results demonstrate the feasibility of this method in complex many-body system and thus provide a new alternative to realize the high-fidelity quantum state manipulation in practice.

Experimental cryptographic verification for near-term quantum cloud computing

An important task for quantum cloud computing is to make sure that there is a real quantum computer running,instead of classical simulation.Here we explore the applicability of a cryptographic verification scheme for verifying quantum cloud computing.We provided a theoretical extension and implemented the scheme on a 5-qubit NMR quantum processor in the laboratory and a 5-qubit and 16-qubit processors of the IBM quantum cloud.We found that the experimental results of the NMR processor can be verified by the scheme with about 1.4%error,after noise compensation by standard techniques.However,the fidelity of the IBM quantum cloud is currently too low to pass the test(about 42%error).This verification scheme shall become practical when servers claim to offer quantum-computing resources that can achieve quantum supremacy.