arXiv subjects

Chenfeng Cao

Publications and source records attributed to Chenfeng Cao.

30 records · Page 2Linked to original sources

arXiv2022

Quantum Approximate Optimization Algorithm with Adaptive Bias Fields

The quantum approximate optimization algorithm (QAOA) transforms a simple many-qubit wavefunction into one which encodes a solution to a difficult classical optimization problem. It does this by optimizing the schedule according to which two unitary operators are alternately applied to the qubits. In this paper, the QAOA is modified by updating the operators themselves to include local fields, using information from the measured wavefunction at the end of one iteration step to improve the operators at later steps. It is shown by numerical simulation on MaxCut problems that, for a fixed accuracy, this procedure decreases the runtime of QAOA very substantially. This improvement appears to increase with the problem size. Our method requires essentially the same number of quantum gates per optimization step as the standard QAOA, and no additional measurements. This modified algorithm enhances the prospects for quantum advantage for certain optimization problems.

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arXiv2022

Quantum imaginary time evolution steered by reinforcement learning

The quantum imaginary time evolution is a powerful algorithm for preparing the ground and thermal states on near-term quantum devices. However, algorithmic errors induced by Trotterization and local approximation severely hinder its performance. Here we propose a deep reinforcement learning-based method to steer the evolution and mitigate these errors. In our scheme, the well-trained agent can find the subtle evolution path where most algorithmic errors cancel out, enhancing the fidelity significantly. We verified the method's validity with the transverse-field Ising model and the Sherrington-Kirkpatrick model. Numerical calculations and experiments on a nuclear magnetic resonance quantum computer illustrate the efficacy. The philosophy of our method, eliminating errors with errors, sheds light on error reduction on near-term quantum devices.

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arXiv2022

Supervised learning in Hamiltonian reconstruction from local measurements on eigenstates

Reconstructing a system Hamiltonian through measurements on its eigenstates is an important inverse problem in quantum physics. Recently, it was shown that generic many-body local Hamiltonians can be recovered by local measurements without knowing the values of the correlation functions. In this work, we discuss this problem in more depth for different systems and apply the supervised learning method via neural networks to solve it. For low-lying eigenstates, the inverse problem is well-posed, neural networks turn out to be efficient and scalable even with a shallow network and a small data set. For middle-lying eigenstates, the problem is ill-posed, we present a modified method based on transfer learning accordingly. Neural networks can also efficiently generate appropriate initial points for numerical optimization based on the BFGS method.

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arXiv2021

All-optical neural network quantum state tomography

Quantum state tomography (QST) is a crucial ingredient for almost all aspects of experimental quantum information processing. As an analog of the "imaging" technique in the quantum settings, QST is born to be a data science problem, where machine learning techniques, noticeably neural networks, have been applied extensively. In this work, we build an integrated all-optical setup for neural network QST, based on an all-optical neural network (AONN). Our AONN is equipped with built-in nonlinear activation function, which is based on electromagnetically induced transparency. Experiment results demonstrate the validity and efficiency of the all-optical setup, indicating that AONN can mitigate the state-preparation-and-measurement error and predict the phase parameter in the quantum state accurately. Given that optical setups are highly desired for future quantum networks, our all-optical setup of integrated AONN-QST may shed light on replenishing the all-optical quantum network with the last brick.

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arXiv2021

Noise-Assisted Quantum Autoencoder

Quantum autoencoder is an efficient variational quantum algorithm for quantum data compression. However, previous quantum autoencoders fail to compress and recover high-rank mixed states. In this work, we discuss the fundamental properties and limitations of the standard quantum autoencoder model in more depth, and provide an information-theoretic solution to its recovering fidelity. Based on this understanding, we present a noise-assisted quantum autoencoder algorithm to go beyond the limitations, our model can achieve high recovering fidelity for general input states. Appropriate noise channels are used to make the input mixedness and output mixedness consistent, the noise setup is determined by measurement results of the trash system. Compared with the original quantum autoencoder model, the measurement information is fully used in our algorithm. In addition to the circuit model, we design a (noise-assisted) adiabatic model of quantum autoencoder that can be implemented on quantum annealers. We verified the validity of our methods through compressing the thermal states of transverse field Ising model and Werner states. For pure state ensemble compression, we also introduce a projected quantum autoencoder algorithm.

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arXiv2021

Simulating noisy variational quantum eigensolver with local noise models

Variational quantum eigensolver (VQE) is promising to show quantum advantage on near-term noisy-intermediate-scale quantum (NISQ) computers. One central problem of VQE is the effect of noise, especially the physical noise on realistic quantum computers. We study systematically the effect of noise for the VQE algorithm, by performing numerical simulations with various local noise models, including the amplitude damping, dephasing, and depolarizing noise. We show that the ground state energy will deviate from the exact value as the noise probability increase and normally noise will accumulate as the circuit depth increase. We build a noise model to capture the noise in a real quantum computer. Our numerical simulation is consistent with the quantum experiment results on IBM Quantum computers through Cloud. Our work sheds new light on the practical research of noisy VQE. The deep understanding of the noise effect of VQE may help to develop quantum error mitigation techniques on near team quantum computers.

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arXiv2021

A variational quantum algorithm for Hamiltonian diagonalization

Hamiltonian diagonalization is at the heart of understanding physical properties and practical applications of quantum systems. It is highly desired to design quantum algorithms that can speedup Hamiltonian diagonalization, especially those can be implemented on near-term quantum devices. In this work, we propose a variational algorithm for Hamiltonians diagonalization (VQHD) of quantum systems, which explores the important physical properties, such as temperature, locality and correlation, of the system. The key idea is that the thermal states of the system encode the information of eigenvalues and eigenstates of the system Hamiltonian. To obtain the full spectrum of the Hamiltonian, we use a quantum imaginary time evolution algorithm with high temperature, which prepares a thermal state with a small correlation length. With Trotterization, this then allows us to implement each step of imaginary time evolution by a local unitary transformation on only a small number of sites. Diagonalizing these thermal states hence leads to a full knowledge of the Hamiltonian eigensystem. We apply our algorithm to diagonalize local Hamiltonians and return results with high precision. Our VQHD algorithm sheds new light on the applications of near-term quantum computers.

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arXiv2021

Speedup of the Quantum Adiabatic Algorithm using Delocalization Catalysis

We propose a method to speed up the quantum adiabatic algorithm using catalysis by many-body delocalization. This is applied to random-field antiferromagnetic Ising spin models. The algorithm is catalyzed in such a way that the evolution approximates a Heisenberg model in the middle of its course, and the model is in a delocalized phase. We show numerically that we can speed up the standard algorithm for finding the ground state of the random-field Ising model using this idea. We also demonstrate that the speedup is due to gap amplification, even though the underlying model is not frustration-free. The crossover to speedup occurs at roughly the value of the interaction which is known to be the critical one for the delocalization transition. We also calculate the participation ratio and entanglement entropy as a function of time: their time dependencies indicate that the system is exploring more states and that they are more entangled than when there is no catalyst. Together, all these pieces of evidence demonstrate that the speedup is related to delocalization. Even though only relatively small systems can be investigated, the evidence suggests that the scaling of the method with system size is favorable. Our method is illustrated by experimental results from a small online IBM quantum computer, showing how to verify the method in future as such machines improve. The cost of the catalytic method compared to the standard algorithm is only a constant factor.

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arXiv2021

SpinQ Gemini: a desktop quantum computer for education and research

SpinQ Gemini is a commercial desktop quantum computer designed and manufactured by SpinQ Technology. It is an integrated hardware-software system. The first generation product with two qubits was launched in January 2020. The hardware is based on NMR spectrometer, with permanent magnets providing $\sim 1$ T magnetic field. SpinQ Gemini operates under room temperature ($0$-$30^{\circ}$C), highlighting its lightweight (55 kg with a volume of $70\times 40 \times 80$ cm$^3$), cost-effective (under $50$k USD), and maintenance-free. SpinQ Gemini aims to provide real-device experience for quantum computing education for K-12 and at the college level. It also features quantum control design capabilities that benefit the researchers studying quantum control and quantum noise. Since its first launch, SpinQ Gemini has been shipped to institutions in Canada, Taiwan and Mainland China. This paper introduces the system of design of SpinQ Gemini, from hardware to software. We also demonstrate examples for performing quantum computing tasks on SpinQ Gemini, including one task for a variational quantum eigensolver of a two-qubit Heisenberg model. The next generations of SpinQ quantum computing devices will adopt models of more qubits, advanced control functions for researchers with comparable cost, as well as simplified models for much lower cost (under $5$k USD) for K-12 education. We believe that low-cost portable quantum computer products will facilitate hands-on experience for teaching quantum computing at all levels, well-prepare younger generations of students and researchers for the future of quantum technologies.

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arXiv2020

Simulating Noisy Quantum Circuits with Matrix Product Density Operators

Simulating quantum circuits with classical computers requires resources growing exponentially in terms of system size. Real quantum computer with noise, however, may be simulated polynomially with various methods considering different noise models. In this work, we simulate random quantum circuits in 1D with Matrix Product Density Operators (MPDO), for different noise models such as dephasing, depolarizing, and amplitude damping. We show that the method based on Matrix Product States (MPS) fails to approximate the noisy output quantum states for any of the noise models considered, while the MPDO method approximates them well. Compared with the method of Matrix Product Operators (MPO), the MPDO method reflects a clear physical picture of noise (with inner indices taking care of the noise simulation) and quantum entanglement (with bond indices taking care of two-qubit gate simulation). Consequently, in case of weak system noise, the resource cost of MPDO will be significantly less than that of the MPO due to a relatively small inner dimension needed for the simulation. In case of strong system noise, a relatively small bond dimension may be sufficient to simulate the noisy circuits, indicating a regime that the noise is large enough for an `easy' classical simulation. Moreover, we propose a more effective tensor updates scheme with optimal truncations for both the inner and the bond dimensions, performed after each layer of the circuit, which enjoys a canonical form of the MPDO for improving simulation accuracy. With truncated inner dimension to a maximum value $κ$ and bond dimension to a maximum value $χ$, the cost of our simulation scales as $\sim NDκ^3χ^3$, for an $N$-qubit circuit with depth $D$.

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arXiv2020

Phase Analysis on the Error Scaling of Entangled Qubits in a 53-Qubit System

We have studied carefully the behaviors of entangled qubits on the IBM Rochester with various connectivities and under a "noisy" environment. A phase trajectory analysis based on our measurements of the GHZ-like states is performed. Our results point to an important fact that entangled qubits are "protected" against environmental noise by a scaling property that impacts only the weighting of their amplitudes. The reproducibility of most measurements has been confirmed within a reasonably short gate operation time. But there still are a few combinations of qubits that show significant entanglement evolution in the form of transitions between quantum states. The phase trajectory of an entangled evolution, and the impact of the sudden death of GHZ-like states and the revival of newly excited states are analyzed in details. All observed trajectories of entangled qubits arise under the influences of the newly excited states in a "noisy" intermediate-scale quantum (NISQ) computer.

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arXiv2020

Upper bounds for relative entropy of entanglement based on active learning

Quantifying entanglement for multipartite quantum state is a crucial task in many aspects of quantum information theory. Among all the entanglement measures, relative entropy of entanglement $E_{R}$ is an outstanding quantity due to its clear geometric meaning, easy compatibility with different system sizes, and various applications in many other related quantity calculations. Lower bounds of $E_R$ were previously found based on distance to the set of positive partial transpose states. We propose a method to calculate upper bounds of $E_R$ based on active learning, a subfield in machine learning, to generate an approximation of the set of separable states. We apply our method to calculate $E_R$ for composite systems of various sizes, and compare with the previous known lower bounds, obtaining promising results. Our method adds a reliable tool for entanglement measure calculation and deepens our understanding for the structure of separable states.

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