In quantum computing, state preparation techniques for loading classical data into quantum states can be resource-intensive and error-prone, especially on Noisy Intermediate-Scale Quantum (NISQ) devices. This work applies variational learning to compress quantum circuits for state preparation, transforming resource-heavy techniques into hardware-efficient ansatzes suitable for current quantum architectures. This approach enhances the efficiency of state preparation, broadening the applicability of quantum algorithms. We demonstrate significant reductions in circuit size and depth compared to the explicit circuit of the FF-QRAM state preparation. Additionally, we show that the learned ansatzes perform better in noisy environments, with significant fidelity improvements over the explicit state preparation technique under analysis.
In quantum computing, state preparation techniques for loading classical data into quantum states can be resource-intensive and error-prone, especially on Noisy Intermediate-Scale Quantum (NISQ) devices. This work applies variational learning to compress quantum circuits for state preparation, transforming resource-heavy techniques into hardware-efficient ansatzes suitable for current quantum architectures. This approach enhances the efficiency of state preparation, broadening the applicability of quantum algorithms. We demonstrate significant reductions in circuit size and depth compared to the explicit circuit of the FF-QRAM state preparation. Additionally, we show that the learned ansatzes perform better in noisy environments, with significant fidelity improvements over the explicit state preparation technique under analysis.
Quantum state preparation, a crucial subroutine in quantum computing, involves generating a target quantum state from initialized qubits. Arbitrary state preparation algorithms can be broadly categorized into arithmetic decomposition (AD) and variational quantum state preparation (VQSP). AD employs a predefined procedure to decompose the target state into a series of gates, whereas VQSP iteratively tunes ansatz parameters to approximate target state. VQSP is particularly apt for Noisy-Intermediate Scale Quantum (NISQ) machines due to its shorter circuits. However, achieving noise-robust parameter optimization still remains challenging. We present RobustState, a novel VQSP training methodology that combines high robustness with high training efficiency. The core idea involves utilizing measurement outcomes from real machines to perform back-propagation through classical simulators, thus incorporating real quantum noise into gradient calculations. RobustState serves as a versatile, plug-and-play technique applicable for training parameters from scratch or fine-tuning existing parameters to enhance fidelity on target machines. It is adaptable to various ansatzes at both gate and pulse levels and can even benefit other variational algorithms, such as variational unitary synthesis. Comprehensive evaluation of RobustState on state preparation tasks for 4 distinct quantum algorithms using 10 real quantum machines demonstrates a coherent error reduction of up to 7.1 × and state fidelity improvement of up to 96\% and 81\% for 4-Q and 5-Q states, respectively. On average, RobustState improves fidelity by 50\% and 72\% for 4-Q and 5-Q states compared to baseline approaches.
Variational quantum algorithms (VQAs) have shown strong evidence to gain provable computational advantages in diverse fields such as finance, machine learning, and chemistry. However, the heuristic ansatz exploited in modern VQAs is incapable of balancing the trade-off between expressivity and trainability, which may lead to degraded performance when executed on noisy intermediate-scale quantum (NISQ) machines. To address this issue, here, we demonstrate the first proof-of-principle experiment of applying an efficient automatic ansatz design technique, i.e., quantum architecture search (QAS), to enhance VQAs on an 8-qubit superconducting quantum processor. In particular, we apply QAS to tailor the hardware-efficient ansatz toward classification tasks. Compared with heuristic ansätze, the ansatz designed by QAS improves the test accuracy from 31% to 98%. We further explain this superior performance by visualizing the loss landscape and analyzing effective parameters of all ansätze. Our work provides concrete guidance for developing variable ansätze to tackle various large-scale quantum learning problems with advantages.
A significant hurdle in the noisy intermediate-scale quantum (NISQ) era is identifying functional quantum circuits. These circuits must also adhere to the constraints imposed by current quantum hardware limitations. Variational quantum algorithms (VQAs), a class of quantum-classical optimization algorithms, were developed to address these challenges in the currently available quantum devices. However, the overall performance of VQAs depends on the initialization strategy of the variational circuit, the structure of the circuit (also known as ansatz), and the configuration of the cost function. Focusing on the structure of the circuit, in this thesis, we improve the performance of VQAs by automating the search for an optimal structure for the variational circuits using reinforcement learning (RL). Within the thesis, the optimality of a circuit is determined by evaluating its depth, the overall count of gates and parameters, and its accuracy in solving the given problem. The task of automating the search for optimal quantum circuits is known as quantum architecture search (QAS). The majority of research in QAS is primarily focused on a noiseless scenario. Yet, the impact of noise on the QAS remains inadequately explored. In this thesis, we tackle the issue by introducing a tensor-based quantum circuit encoding, restrictions on environment dynamics to explore the search space of possible circuits efficiently, an episode halting scheme to steer the agent to find shorter circuits, a double deep Q-network (DDQN) with an ε-greedy policy for better stability. The numerical experiments on noiseless and noisy quantum hardware show that in dealing with various VQAs, our RL-based QAS outperforms existing QAS. Meanwhile, the methods we propose in the thesis can be readily adapted to address a wide range of other VQAs.
The development of practical quantum algorithms hinges critically on the ability to efficiently manage and compress quantum states. Noisy Intermediate-Scale Quantum (NISQ) computers, characterized by limited qubit counts and inherent noise, exacerbate this challenge. This paper proposes a novel quantum state compression technique utilizing tensor decomposition and variational quantum algorithms to minimize qubit requirements while mitigating error accumulation. The core idea involves transforming a complex quantum state into a lower-rank tensor representation, subsequently optimized using a variational quantum algorithm. This approach aims to capture the essential information within the original state, reducing computational overhead and enhancing the feasibility of running quantum algorithms on NISQ devices. We outline the theoretical framework, detailing the mathematical formulation of the compression process, including the tensor representation, variational optimization, and error correction strategies. The paper explores the key parameters influencing the compression ratio and error rates, ultimately demonstrating the potential of this technique to unlock the computational power of NISQ computers.
Gate-based quantum algorithms are typically implemented by circuits consisting of many single-qubit and multi-qubit gates operating on a quantum input state, followed by measurements of the output state. For certain quantum subroutines, such as initial state preparation and quantum Fourier transforms, explicit decompositions of the circuit in terms of single-qubit and two-qubit maximally entangling gates may exist. However, they often lead to large-depth circuits that are challenging for noisy intermediate-scale quantum (NISQ) hardware. Additionally, exact decompositions might only exist for some modular quantum circuits. Therefore, it is essential to find gate combinations that approximate these circuits to high fidelity with potentially low depth. Gradient-based optimization has been used to find such approximate decompositions. Still, these traditional optimizers often run into problems of slow convergence requiring many iterations, and performing poorly in the presence of noise, a factor that is especially relevant for NISQ hardware. Here we present iteratively preconditioned gradient descent (IPG) for optimizing quantum circuits and demonstrate performance speedups for state preparation and implementation of quantum algorithmic subroutines. IPG is a noise-resilient, higher-order algorithm that has shown promising gains in convergence speed for classical optimizations, converging locally at a linear rate for convex problems and superlinearly when the solution is unique. Specifically, we show an improvement in fidelity by a factor of 104for preparing a 4-qubit W state and a maximally entangled 5-qubit GHZ state with compared to other commonly used classical optimizers tuning the same ansatz. Such faster convergence with promise for noise-resilience could provide advantages for quantum algorithms on NISQ hardware, especially since the cost of running each iteration on a quantum computer is substantially higher than the classical optimizer step.
Quantum computing holds immense potential for solving complex problems. However, current Noisy Intermediate-Scale Quantum (NISQ) devices are limited by high error rates and restricted qubit counts. Variational Quantum Algorithms (VQAs) have emerged as promising approaches for utilizing NISQ hardware, particularly in applications like protein structure prediction. Nonetheless, their practical implementation re-mains challenging due to the large number of gates required in quantum circuits. In this paper, we employ two methods: quantum circuit cutting, which makes circuits more hardware-friendly, and Initial-State-Dependent Optimization (ISDO), which dynamically prunes unnecessary gates to optimize the ansatz for protein structure prediction. Together, these techniques reduce circuit gate count, enhancing fidelity and improving the practi-cality of real-world quantum applications.