We propose a variational approach for preparing entangled quantum states on quantum computers. The methodology involves training a unitary operation to match with a target unitary using the Fubini-Study distance as a cost function. We employ various gradient-based optimization techniques to enhance performance, including Adam and quantum natural gradient. Our investigation showcases the versatility of different ansatzes featuring a hypergraph structure, enabling the preparation of diverse entanglement target states such as GHZ, W, and absolutely maximally entangled states. Remarkably, the circuit depth scales efficiently with the number of layers and does not depend on the number of qubits. Moreover, we explore the impacts of barren plateaus, readout noise, and error mitigation techniques on the proposed approach. Through our analysis, we demonstrate the effectiveness of the variational algorithm in maximizing the efficiency of quantum state preparation, leveraging low-depth quantum circuits.
We propose a variational approach for preparing entangled quantum states on quantum computers. The methodology involves training a unitary operation to match with a target unitary using the Fubini-Study distance as a cost function. We employ various gradient-based optimization techniques to enhance performance, including Adam and quantum natural gradient. Our investigation showcases the versatility of different ansatzes featuring a hypergraph structure, enabling the preparation of diverse entanglement target states such as GHZ, W, and absolutely maximally entangled states. Remarkably, the circuit depth scales efficiently with the number of layers and does not depend on the number of qubits. Moreover, we explore the impacts of barren plateaus, readout noise, and error mitigation techniques on the proposed approach. Through our analysis, we demonstrate the effectiveness of the variational algorithm in maximizing the efficiency of quantum state preparation, leveraging low-depth quantum circuits.
Universal compilation is a training process that compiles a trainable unitary into a target unitary and it serves vast potential applications from quantum dynamic simulations to optimal circuits with deep-compressing, device benchmarking, quantum error mitigation, and so on. Here, we propose a universal compilation-based variational algorithm for the preparation and tomography of quantum states in low-depth quantum circuits. We apply the Fubini-Study distance to be a trainable cost function under various gradient-based optimizers, including the quantum natural gradient approach. We evaluate the performance of various unitary topologies and the trainability of different optimizers for getting high efficiency. In practice, we address different circuit ansatzes in quantum state preparation, including the linear and graph-based ansatzes for preparing different entanglement target states such as representative GHZ and W states. We also discuss the effect of the circuit depth, barren plateau, readout noise in the model, and the error mitigation solution. We next evaluate the reconstructing efficiency in quantum state tomography via various popular circuit ansatzes and reveal the crucial role of the circuit depth in the robust fidelity. The results are comparable with the shadow tomography method, a similar fashion in the field. Our work expresses the adequate capacity of the universal compilation-based variational algorithm to maximize the efficiency in the quantum state preparation and tomography. Further, it promises applications in quantum metrology and sensing and is applicable in the near-term quantum computers for verification of the circuits fidelity and various quantum computing tasks.
Long-range entanglement is an important quantum resource, particularly for topological orders and quantum error correction. In reality, preparing long-range entangled states requires a deep unitary circuit, which poses significant experimental challenges. A promising avenue is offered by replacing some quantum resources with local operations and classical communication (LOCC). With these classical components, one can communicate outcomes of midcircuit measurements in distant subsystems, substantially reducing circuit depth in many important cases. However, to prepare general long-range entangled states, finding LOCC-assisted circuits of a short depth remains an open question. Here, to address this challenge, we propose a quantum-classical hybrid algorithm to find optimal LOCC protocols for preparing ground states of given Hamiltonians. In our algorithm, we introduce an efficient way to estimate parameter gradients and use such gradients for variational optimization. Theoretically, we establish the conditions for the absence of barren plateaus, ensuring trainability at a large system size. Numerically, the algorithm accurately solves the ground state of long-range entangled models, such as the perturbed Greenberger-Horne-Zeilinger state and surface code. Our results demonstrate the advantage of our method over conventional unitary variational circuits: the practical advantage in the accuracy of estimated ground-state energy and the theoretical advantage in creating long-range entanglement.
Universal compilation is a training process that compiles a trainable unitary into a target unitary. It has vast potential applications from depth-circuit compressing to device benchmarking and quantum error mitigation. Here we propose a universal compilation algorithm for quantum state tomography in low-depth quantum circuits. We apply the Fubini-Study distance as a trainable cost function and employ various gradient-based optimizations. We evaluate the performance of various trainable unitary topologies and the trainability of different optimizers for getting high efficiency and reveal the crucial role of the circuit depth in robust fidelity. The results are comparable with the shadow tomography method, a similar fashion in the field. Our work expresses the adequate capability of the universal compilation algorithm to maximize the efficiency in the quantum state tomography. Further, it promises applications in quantum metrology and sensing and is applicable in the near-term quantum computers for various quantum computing tasks.
Quantum computing offers new algorithmic primitives—superposition, entanglement, and interference—that can accelerate or qualitatively change parts of the machine-learning pipeline. This article surveys optimization of neural networks using quantum techniques, focusing on three avenues: (i) quantum-accelerated linear algebra and sampling to speed up gradient and Hessian-vector computations; (ii) hybrid variational algorithms where parameterized quantum circuits (PQCs) act as feature maps or layers within classical networks; and (iii) quantum-aware optimizers such as the quantum natural gradient (QNG) that respect the geometry of quantum states. We synthesize theoretical results with NISQ-era constraints (noise, barren plateaus, trainability), propose design patterns for end-to-end systems, and present an illustrative comparison of convergence between classical SGD and a hybrid QNG setup. The analysis indicates that, for structured data and appropriately shallow, problem-matched ansätze, hybrid methods can improve sample efficiency and generalization while remaining hardware-feasible.
Ubiquitous in quantum computing is the step to encode data into a quantum state. This process is called quantum state preparation, and its complexity for nonstructured data is exponential on the number of qubits. Several works address this problem, for instance, by using variational methods that train a fixed depth circuit with manageable complexity. These methods have their limitations, as the lack of a back-propagation technique and barren plateaus. This work proposes an algorithm to reduce state preparation circuit depth by offloading computational complexity to a classical computer. The initialized quantum state can be exact or an approximation, and we show that the approximation is better on today’s quantum processors than the initialization of the original state. Experimental evaluation demonstrates that the proposed method enables more efficient initialization of probability distributions in a quantum state.
Quantum variational algorithms are one of the most promising applications of near-term quantum computers; however, recent studies have demonstrated that unless the variational quantum circuits are configured in a problem-specific manner, optimization of such circuits will most likely fail.In this paper, we focus on a special family of quantum circuits called the Hamiltonian variational ansatz (HVA), which its takes inspiration from the quantum approximate optimization algorithm and adiabatic quantum computation.Through the study of its entanglement spectrum and energy-gradient statistics, we find that the HVA exhibits favorable structural properties such as mild or entirely absent barren plateaus and a restricted state space that eases their optimization in comparison to the well-studied "hardware-efficient ansatz."We also numerically observe that the optimization landscape of the HVA becomes almost trap free, i.e., there are no suboptimal minima, when the ansatz is overparametrized.We observe a size-dependent "computational phase transition" as the number of layers in the HVA circuit is increased where the optimization crosses over from a hard to an easy region in terms of the quality of the approximations and the speed of convergence to a good solution.In contrast to the analogous transitions observed in the learning of random unitaries, which occur at a number of layers that grows exponentially with the number of qubits, our variational-quantum-eigensolver experiments suggest that the threshold to achieve the overparametrization phenomenon scales at most polynomially in the number of qubits for the transverse-field Ising and XXZ models.Lastly, as a demonstration of its entangling power and effectiveness, we show that the HVA can find accurate approximations to the ground states of a modified Haldane-Shastry Hamiltonian on a ring, which has long-range interactions and has a power-law entanglement scaling.