arXiv subjects

Yu-Chun Wu

Publications and source records attributed to Yu-Chun Wu.

At least 55 records · Page 3Linked to original sources

arXiv2023

Efficient and Error-Resilient Data Access Protocols for a Limited-Sized Quantum Random Access Memory

Quantum Random Access Memory (QRAM) is a critical component for loading classical data into quantum computers. While constructing a practical QRAM presents several challenges, including the impracticality of an infinitely large QRAM size and a fully error-correction implementation, it is essential to consider a practical case where the QRAM has a limited size. In this work, we focus on the access of larger data sizes without keeping on increasing the size of the QRAM. Firstly, we address the challenge of word length, as real-world datasets typically have larger word lengths than the single-bit data that most previous studies have focused on. We propose a novel protocol for loading data with larger word lengths $k$ without increasing the number of QRAM levels $n$. By exploiting the parallelism in the data query process, our protocol achieves a time complexity of $O(n+k)$ and improves error scaling performance compared to existing approaches. Secondly, we provide a data-loading method for general-sized data access tasks when the number of data items exceeds $2^n$, which outperforms the existing hybrid QRAM+QROM architecture. Our method contributes to the development of time and error-optimized data access protocols for QRAM devices, reducing the qubit count and error requirements for QRAM implementation, and making it easier to construct practical QRAM devices with a limited number of physical qubits.

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arXiv2023

Predicting RNA Secondary Structure on Universal Quantum Computer

It is the first step for understanding how RNA structure folds from base sequences that to know how its secondary structure is formed. Traditional energy-based algorithms are short of precision, particularly for non-nested sequences, while learning-based algorithms face challenges in obtaining high-quality training data. Recently, quantum annealer has rapidly predicted the folding of the secondary structure, highlighting that quantum computing is a promising solution to this problem. However, gate model algorithms for universal quantum computing are not available. In this paper, gate-based quantum algorithms will be presented, which are highly flexible and can be applied to various physical devices. Mapped all possible secondary structure to the state of a quadratic Hamiltonian, the whole folding process is described as a quadratic unconstrained binary optimization model. Then the model can be solved through quantum approximation optimization algorithm. We demonstrate the performance with both numerical simulation and experimental realization. Throughout our benchmark dataset, simulation results suggest that our quantum approach is comparable in accuracy to classical methods. For non-nested sequences, our quantum approach outperforms classical energy-based methods. Experimental results also indicate our method is robust in current noisy devices. It is the first instance of universal quantum algorithms being employed to tackle RNA folding problems, and our work provides a valuable model for utilizing universal quantum computers in solving RNA folding problems.

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arXiv2023

An Improved QFT-Based Quantum Comparator and Extended Modular Arithmetic Using One Ancilla Qubit

Quantum comparators and modular arithmetic are fundamental in many quantum algorithms. Current research mainly focuses on operations between two quantum states. However, various applications, such as integer factorization, optimization, option pricing, and risk analysis, commonly require one of the inputs to be classical. It requires many ancillary qubits, especially when subsequent computations are involved. In this paper, we propose a quantum-classical comparator based on the quantum Fourier transform (QFT). Then we extend it to compare two quantum integers and modular arithmetic. Proposed operators only require one ancilla qubit, which is optimal for qubit resources. We analyze limitations in the current modular addition circuit and develop it to process arbitrary quantum states in the entire $n$-qubit space. The proposed algorithms reduce computing resources and make them valuable for Noisy Intermediate-Scale Quantum (NISQ) computers.

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arXiv2023

Concatenation of the Gottesman-Kitaev-Preskill code with the XZZX surface code

Bosonic codes provide an alternative option for quantum error correction. An important category of bosonic codes called the Gottesman-Kitaev-Preskill (GKP) code has aroused much interest recently. Theoretically, the error correction ability of GKP code is limited since it can only correct small shift errors in position and momentum quadratures. A natural approach to promote the GKP error correction for large-scale, fault-tolerant quantum computation is concatenating encoded GKP states with a stabilizer code. The performance of the XZZX surface-GKP code, i.e., the single-mode GKP code concatenated with the XZZX surface code is investigated in this paper under two different noise models. Firstly, in the code-capacity noise model, the asymmetric rectangular GKP code with parameter $λ$ is introduced. Using the minimum weight perfect matching decoder combined with the continuous-variable GKP information, the optimal threshold of the XZZX-surface GKP code reaches $σ\approx0.67$ when $λ=2.1$, compared with the threshold $σ\approx0.60$ of the standard surface-GKP code. Secondly, we analyze the shift errors of two-qubit gates in the actual implementation and build the full circuit-level noise model. By setting the appropriate bias parameters, the logical error rate is reduced by several times in some cases. These results indicate the XZZX surface-GKP codes are more suitable for asymmetric concatenation under the general noise models. We also estimate the overhead of the XZZX-surface GKP code which uses about 291 GKP states with the noise parameter 18.5 dB ($κ/g \approx 0.71\%$) to encode a logical qubit with the error rate $2.53\times10^{-7}$, compared with the qubit-based surface code using 3041 qubits to achieve almost the same logical error rate.

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arXiv2023

Simulation of chemical reaction dynamics based on quantum computing

The molecular energies of chemical systems have been successfully calculated on quantum computers, however, more attention has been paid to the dynamic process of chemical reactions in practical application, especially in catalyst design, material synthesis. Due to the limited the capabilities of the noisy intermediate scale quantum (NISQ) devices, directly simulating the reaction dynamics and determining reaction pathway still remain a challenge. Here we develop the ab initio molecular dynamics based on quantum computing to simulate reaction dynamics by extending correlated sampling approach. And, we use this approach to calculate Hessian matrix and evaluate computation resources. We test the performance of our approach by simulating hydrogen exchange reaction and bimolecular nucleophilic substitution SN2 reaction. Our results suggest that it is reliable to characterize the molecular structure, property, and reactivity, which is another important expansion of the application of quantum computing

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arXiv2023

Scalable Program Implementation and Simulation of the Large-Scale Quantum Algorithm: $1024\times 1024$ Quantum Linear Solver and Beyond

Program implementation and simulation are essential for research in the field of quantum algorithms. However, complex and large-scale quantum algorithms can pose challenges for existing quantum programming languages and simulators. Here, we present a scalable program implementation of the quantum walk on a sparse matrix and the quantum linear solver based on the quantum walk. Our implementation is based on a practical scenario in which the sparse matrix is stored in the compressed-sparse-column format in quantum random access memory. All necessary modules are implemented unitarily and are ensured to be decomposed at the quantum gate level, including implementing a quantum binary search and a modification of the original algorithm. The program is validated using a highly efficient quantum circuit simulator which is based on the register level and sparse state representation. With only a single core, we simulate the quantum walk on a 16384-dimensional matrix with 582 qubits in 1.1 minutes per step, as well as a quantum linear solver up to 1024 dimensions and 212245 steps in 70 hours. Our work narrows the gap between the simulation of a quantum algorithm and its classical counterparts, where the asymptotic complexity of our quantum linear solver simulation approximates a classical linear solver. These program implementation and simulation techniques have the potential to expand the boundary of numerical research for large-scale quantum algorithms, with implications for the development of error-correction-era quantum computing solutions.

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arXiv2023

Quantum memory error correction computation based on Chamon model

Quantum error correction codes play a central role in the realisation of fault-tolerant quantum computing. Chamon model is a 3D generalization of the toric code. The error correction computation on this model has not been explored so far. In this work, the Chamon model is turned to a non-CSS error correction code. Logical qubits are built by the construct of logical Pauli operators. The property of logical operators reveals the expressions of code distance. According to the topological properties of Chamon models, an error elimination algorithm is proposed. Based on the error elimination algorithm, we propose a global randomized error correction algorithm to decode Chamon models in every single-qubit depolarized channel. This decoding algorithm is improved by adding the pretreatment process, termed the probabilistic greedy local algorithm, which adapts to different kinds of high-dimensional models. The estimated threshold error rate for numerical experiment can be raised to $4.92\%$.

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arXiv2023

Mitigating Barren Plateaus with Transfer-learning-inspired Parameter Initializations

Variational quantum algorithms (VQAs) are widely applied in the noisy intermediate-scale quantum era and are expected to demonstrate quantum advantage. However, training VQAs faces difficulties, one of which is the so-called barren plateaus (BP) phenomenon, where gradients of cost functions vanish exponentially with the number of qubits. In this paper, inspired by transfer learning, where knowledge of pre-solved tasks could be further used in a different but related work with training efficiency improved, we report a parameter initialization method to mitigate BP. In the method, a small-sized task is solved with a VQA. Then the ansatz and its optimum parameters are transferred to tasks with larger sizes. Numerical simulations show that this method could mitigate BP and improve training efficiency. A brief discussion on how this method can work well is also provided. This work provides a reference for mitigating BP, and therefore, VQAs could be applied to more practical problems.

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arXiv2022

ChemiQ: A Chemistry Simulator for Quantum Computer

Quantum computing, an innovative computing system carrying prominent processing rate, is meant to be the solutions to problems in many fields. Among these realms, the most intuitive application is to help chemical researchers correctly de-scribe strong correlation and complex systems, which are the great challenge in current chemistry simulation. In this paper, we will present a standalone quantum simulation tool for chemistry, ChemiQ, which is designed to assist people carry out chemical research or molecular calculation on real or virtual quantum computers. Under the idea of modular programming in C++ language, the software is designed as a full-stack tool without third-party physics or chemistry application packages. It provides services as follow: visually construct molecular structure, quickly simulate ground-state energy, scan molecular potential energy curve by distance or angle, study chemical reaction, and return calculation results graphically after analysis.

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arXiv2022

A unified framework of transformations based on the Jordan-Wigner transformation

Quantum simulation of chemical Hamiltonians enables the efficient calculation of chemical properties. Mapping is one of the essential steps in simulating fermionic systems on quantum computers. In this work, a unified framework of transformations mapping fermionic systems to qubit systems is presented, and many existing transformations, such as Jordan-Wigner, Bravyi-Kitaev, and parity transformations, are included in this framework. Based on this framework, the Multilayer Segmented Parity (MSP) transformation is proposed. The MSP transformation is a general mapping with an adjustable parameter vector, which can be viewed as a generalization of the above-mentioned mappings. Furthermore, the MSP transformation can adjust flexibly when dealing with different systems. Applying these mappings to the electronic structure Hamiltonians of various molecules, the MSP transformation is found to perform better on the number of Pauli operators and gates needed in the circuit of Hamiltonian simulation. The MSP transformation will reduce the qubit gate requirement for Hamiltonian simulation on noisy intermediate-scale quantum devices,and it will provide a much wider choice of mappings for researchers.

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arXiv2022

Quantum Algorithm for Solving a Quadratic Nonlinear System of Equations

Solving a quadratic nonlinear system of equations (QNSE) is a fundamental, but important, task in nonlinear science. We propose an efficient quantum algorithm for solving $n$-dimensional QNSE. Our algorithm embeds QNSE into a finite-dimensional system of linear equations using the homotopy perturbation method and a linearization technique; then we solve the linear equations with a quantum linear system solver and obtain a state which is $ε$-close to the normalized exact solution of the QNSE with success probability $Ω(1)$. The complexity of our algorithm is $O({\rm polylog}(n/ε))$, which provides an exponential improvement over the optimal classical algorithm in dimension $n$, and the dependence on $ε$ is almost optimal. Therefore, our algorithm exponentially accelerates the solution of QNSE and has wide applications in all kinds of nonlinear problems, contributing to the research progress of nonlinear science.

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arXiv2022

The Exclusivity Principle Determines the Correlation Monogamy

Adopting the graph-theoretic approach to the correlation experiments, we analyze the origin of monogamy and prove that it can be recognized as a consequence of the exclusivity principle(EP). We provide an operational criterion for monogamy: if the fractional packing number of the graph corresponding to the union of event sets of several physical experiments does not exceed the sum of independence numbers of each individual experiment graph, then these experiments are monogamous. As applications of this observation, several examples are provided, including the monogamy for experiments of Clauser-Horne-Shimony-Holt (CHSH) type, Klyachko-Can-Binicioğlu-Shumovsky (KCBS) type, and for the first time, we give some monogamy relations of Svetlichny's genuine nonlocality. We also give the necessary and sufficient conditions for several experiments to be monogamous: several experiments are monogamous if and only if the Lovász number of the union exclusive graph is less than or equal to the sum of independence numbers of each exclusive graph.

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arXiv2022

Shortcuts to Quantum Approximate Optimization Algorithm

The Quantum Approximate Optimization Algorithm (QAOA) is a quantum-classical hybrid algorithm intending to find the ground state of a target Hamiltonian. Theoretically, QAOA can obtain the approximate solution if the quantum circuit is deep enough. Actually, the performance of QAOA decreases practically if the quantum circuit is deep since near-term devices are not noise-free and the errors caused by noise accumulate as the quantum circuit increases. In order to reduce the depth of quantum circuits, we propose a new ansatz dubbed as "Shortcuts to QAOA" (S-QAOA), S-QAOA provides shortcuts to the ground state of target Hamiltonian by including more two-body interactions and releasing the parameter freedoms. To be specific, besides the existing ZZ interaction in the QAOA ansatz, other two-body interactions are introduced in the S-QAOA ansatz such that the approximate solutions could be obtained with smaller circuit depth. Considering the MaxCut problem and Sherrington-Kirkpatrick (SK) model, numerically computation shows the YY interaction has the best performance. The reason for this might arise from the counterdiabatic effect generated by YY interaction. On top of this, we release the freedom of parameters of two-body interactions, which a priori do not necessarily have to be fully identical, and numerical results show that it is worth paying the extra cost of having more parameter freedom since one has a greater improvement on success rate.

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arXiv2021

Quantum error correction with the color-Gottesman-Kitaev-Preskill code

The Gottesman-Kitaev-Preskill (GKP) code is an important type of bosonic quantum error-correcting code. Since the GKP code only protects against small shift errors in $\hat{p}$ and $\hat{q}$ quadratures, it is necessary to concatenate the GKP code with a stabilizer code for the larger error correction. In this paper, we consider the concatenation of the single-mode GKP code with the two-dimension (2D) color code (color-GKP code) on the square-octagon lattice. We use the Steane type scheme with a maximum-likelihood estimation (ME-Steane scheme) for GKP error correction and show its advantage for the concatenation. In our main work, the minimum-weight perfect matching (MWPM) algorithm is applied to decode the color-GKP code. Complemented with the continuous-variable information from the GKP code, the threshold of 2D color code is improved. If only data GKP qubits are noisy, the threshold reaches $σ\approx 0.59$ $(\bar{p}\approx13.3\%)$ compared with $\bar{p}=10.2\%$ of the normal 2D color code. If measurements are also noisy, we introduce the generalized Restriction Decoder on the three-dimension space-time graph for decoding. The threshold reaches $σ\approx 0.46$ when measurements in the GKP error correction are noiseless, and $σ\approx 0.24$ when all measurements are noisy. Lastly, the good performance of the generalized Restriction Decoder is also shown on the normal 2D color code giving the threshold at $3.1\%$ under the phenomenological error model.

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arXiv2021

Quantum homotopy perturbation method for nonlinear dissipative ordinary differential equations

While quantum computing provides an exponential advantage in solving linear differential equations, there are relatively few quantum algorithms for solving nonlinear differential equations. In our work, based on the homotopy perturbation method, we propose a quantum algorithm for solving $n$-dimensional nonlinear dissipative ordinary differential equations (ODEs). Our algorithm first converts the original nonlinear ODEs into the other nonlinear ODEs which can be embedded into finite-dimensional linear ODEs. Then we solve the embedded linear ODEs with quantum linear ODEs algorithm and obtain a state $ε$-close to the normalized exact solution of the original nonlinear ODEs with success probability $Ω(1)$. The complexity of our algorithm is $O(gηT{\rm poly}(\log(nT/ε)))$, where $η$, $g$ measure the decay of the solution. Our algorithm provides exponential improvement over the best classical algorithms or previous quantum algorithms in $n$ or $ε$.

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arXiv2021

Quantum Newton's method for solving system of nonlinear algebraic equations

While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving $N$-dimensional system of nonlinear equations based on Newton's method. In QNM, we solve the system of linear equations in each iteration of Newton's method with quantum linear system solver. We use a specific quantum data structure and $l_{\infty}$ tomography with sample error $ε_s$ to implement the classical-quantum data conversion process between the two iterations of QNM, thereby constructing the whole process of QNM. The complexity of QNM in each iteration is $O(\log^4N/ε_s^2)$. Through numerical simulation, we find that when $ε_s>>1/\sqrt{N}$, QNM is still effective, so the complexity of QNM is sublinear with $N$, which provides quantum advantage compared with the optimal classical algorithm.

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arXiv2021

Quantum advantages of communication complexity from Bell nonlocality

Communication games are crucial tools for investigating the limitations of physical theories. The communication complexity (CC) problem is a typical example, for which several distributed parties attempt to jointly calculate a given function with limited classical communications. In this work, we present a method to construct CC problems from Bell tests in a graph-theoretic way. Starting from an experimental compatibility graph and the corresponding Bell test function, a target function which encodes the information of each edge can be constructed, then using this target function we could construct an CC function for which by pre-sharing entangled states, the success probability will exceed that for arbitrary classical strategy. The non-signaling protocol based on Popescu-Rohrlich box is also discussed, and the success probability in this case would reach one.

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arXiv2021

Quantum Quantitative Trading: High-Frequency Statistical Arbitrage Algorithm

Quantitative trading is an integral part of financial markets with high calculation speed requirements, while no quantum algorithms have been introduced into this field yet. We propose quantum algorithms for high-frequency statistical arbitrage trading in this work by utilizing variable time condition number estimation and quantum linear regression.The algorithm complexity has been reduced from the classical benchmark O(N^2d) to O(sqrt(d)(kappa)^2(log(1/epsilon))^2 )). It shows quantum advantage, where N is the length of trading data, and d is the number of stocks, kappa is the condition number and epsilon is the desired precision. Moreover, two tool algorithms for condition number estimation and cointegration test are developed.

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