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.
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 State Preparation Algorithms consist of defining a sequence or unitary operations to load a specific target state on a quantum computer. We can use those algorithms in appli- cations such as quantum machine learning. However, some state preparation algorithms have exponential circuit complexity with the number of qubits on the system. That is the case of amplitude encoding algorithms, which is an encoding type for loading normalized data into the probability amplitudes of the state. To circumvent this overhead in circuits’ complexity, works explore specific properties of quantum states to optimize the circuit’s complexity, such as sparsity or symmetry. Other works explore simplifying the quantum circuit to load an ap- proximate quantum state. It is the case of Quantum Generative Adversarial Networks, which use a specific circuit architecture comprised of alternating blocks of single-qubit rotations and two-qubit entangling controlled gates. But when trained to load random distributions on, we observed the performance deteriorates as the number of qubits increases in terms of relative entropy. In this work, we propose different architectures for the Quantum Generative mod- els based on the state preparation algorithm known as Low-Rank. Through experiments for loading the log-normal distribution, we show error reductions in quantum state initialization.
Quantum state preparation is the process of producing a target quantum state that will be used as the input to a quantum circuit. Many quantum algorithms require an input state where amplitudes, phases, or basis probabilities encode problem data, and the cost of preparing this state can be significant in gate count and circuit depth. This review summarizes common goals, assumptions, and methods for quantum state preparation, with emphasis on preparing states from classical vectors, probability distributions, and feature data used in quantum machine learning. We organize approaches by the information they load and by the resources they require, including gate count, circuit depth, qubit overhead, and classical preprocessing. It also compares exact and approximate preparation procedures, and discusses how precision targets affect cost. The review highlights links between families of methods, typical sources of resource estimates, and criteria that help match a preparation method to a task and hardware constraints.
Any quantum computation begins with some process of state preparation where the prepared state functions as the input value for the computation. For most states, preparation becomes exceedingly more demanding as the number of qubits increases. Moreover, the noise present in the gate operations further complicates the process by contributing to the decoherence of the state. This thesis studies possible approaches to address these problems. For a reader not familiar with the basic principles of quantum computing, Chapter 2 should provide a sufficient summary in order to follow through the rest of the thesis. In Chapter 3 a standard method of state preparation is presented in detail for 2 and 4-qubit cases and then generalized for an arbitrary number of qubits. However in order to present a comprehensive coverage, the necessary gate decompositions for state preparation are first presented and proved. The number of required quantum gates for the preparation of a general state increases exponentially in the number of qubits. Each gate introduces a small error in the computation, the cumulative effect of which can make the decoherence in the final state very severe. Therefore it is perhaps more suitable to prepare a less complex approximation of the target state with fewer gates to obtain better fidelity in the presence of noise. For this purpose, two methods are presented: low-rank state preparation algorithm (LRSP) and a genetic algorithm. LRSP provides a systematic way to generate circuits for approximate state preparation; however, for any given state LRSP can make only very specific approximations, giving us a very limited range of circuits to work with. For this reason our work introduces a genetic algorithm to iterate over the LRSP circuits and to provide a wider range of candidate circuits for approximate state preparation. Using this approach we prepared a range of approximate state preparation circuits for 1000 different Haar-random states and ran them with simulated noise on IBM Qiskit FakeVigo backend. We found that the numerical results matched closely with our theoretical prediction and showed that when run on a noisy quantum computer, the highest fidelity is obtained not for the exact state preparation circuit but for a shorter approximate circuit.
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.
In quantum image processing, a fundamental step is encoding classical image data into quantum states. This can be achieved using methods such as Flexible Representation of Quantum Images (FRQI), Quantum Probability Image Encoding (QPIE), and Novel Enhanced Quantum Representation (NEQR). However, on real quantum hardware, these encodings can quickly lead to circuits with many gates, large circuit depth, and high qubit usage, which is a problem for Noisy Intermediate-Scale Quantum (NISQ) devices. In this work, we investigate whether low-rank state approximation, formulated via Schmidt decomposition, can help reduce this complexity. The method keeps only the most significant parts of a quantum state's entanglement structure, making state preparation more efficient while preserving most of the image information. We compare the three encoding techniques in their original form and with low-rank approximation, evaluating metrics such as circuit depth, CNOT count, MSE, and visual quality of reconstructed images. The results reveal meaningful trade-offs between accuracy and resource efficiency, with the FRQI model achieving a 97 percent reduction in circuit depth while maintaining a near-perfect reconstruction (MSE of about 0.27). This demonstrates the potential of low-rank techniques for advancing practical quantum image processing on near-term hardware.
Numerous quantum algorithms assume that classical data has already been converted into quantum states, a process known as Quantum State Preparation (QSP). However, achieving precise QSP requires a circuit depth that scales exponentially with the number of qubits, posing a significant challenge to realizing quantum advantage. Recent research explores Parameterized Quantum Circuits (PQCs) as an approximate alternative, offering improved scalability with reduced circuit depth. However, the iterative, state-by-state optimization required by this approach creates substantial runtime overhead, which severely limits its practicality.To improve the efficiency of approximate QSP, we introduce a novel two-stage framework that can potentially generate QSP circuits for arbitrary quantum states. In theoffline training stage, our model learns a direct mapping from target states to circuit parameters, thereby bypassing the need foronline, state-by-state optimizationduring theinference stage. Extensive evaluations show that our approach significantly reduces runtime overhead by up to 132×, making a steady step towards efficient neural approximate QSP.