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.
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.
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.
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.
Compiling quantum algorithms for near-term quantum computers (accounting for connectivity and native gate alphabets) is a major challenge that has received significant attention both by industry and academia. Avoiding the exponential overhead of classical simulation of quantum dynamics will allow compilation of larger algorithms, and a strategy for this is to evaluate an algorithm's cost on a quantum computer. To this end, we propose a variational hybrid quantum-classical algorithm called quantum-assisted quantum compiling (QAQC). In QAQC, we use the overlap between a target unitary U and a trainable unitary V as the cost function to be evaluated on the quantum computer. More precisely, to ensure that QAQC scales well with problem size, our cost involves not only the global overlap T r ( V † U ) but also the local overlaps with respect to individual qubits. We introduce novel short-depth quantum circuits to quantify the terms in our cost function, and we prove that our cost cannot be efficiently approximated with a classical algorithm under reasonable complexity assumptions. We present both gradient-free and gradient-based approaches to minimizing this cost. As a demonstration of QAQC, we compile various one-qubit gates on IBM's and Rigetti's quantum computers into their respective native gate alphabets. Furthermore, we successfully simulate QAQC up to a problem size of 9 qubits, and these simulations highlight both the scalability of our cost function as well as the noise resilience of QAQC. Future applications of QAQC include algorithm depth compression, black-box compiling, noise mitigation, and benchmarking.
Abstract Quantum compilation is the process of converting a target unitary operation into a trainable unitary represented by a quantum circuit. It has a wide range of applications, including gate optimization, quantum-assisted compiling, quantum state preparation, and quantum dynamic simulation. Traditional quantum compilation usually optimizes circuits for a single target. However, many quantum systems require simultaneous optimization of multiple targets, such as thermal state preparation, time-dependent dynamic simulation, and others. To address this, we develop a multi-target quantum compilation algorithm to improve the performance and flexibility of simulating multiple quantum systems. Our benchmarks and case studies demonstrate the effectiveness of the algorithm, highlighting the importance of multi-target optimization in advancing quantum computing. This work lays the groundwork for further development and evaluation of multi-target quantum compilation algorithms.
Quantum circuit compilation is a crucial step in the process of executing quantum algorithms on near-term quantum hardware. The challenge lies in translating high-level quantum algorithms, often expressed using universal gate sets, into efficient, gate-level circuits that minimize gate count and circuit depth, thereby reducing error rates and improving execution times. Traditional compilation methods often rely on hand-crafted heuristics or limited search algorithms, failing to fully explore the exponentially large search space of possible circuit transformations. This work proposes an adaptive quantum circuit compilation framework leveraging Bayesian optimization. The system dynamically explores the space of potential circuit transformations, learning to identify optimal compilation strategies through a probabilistic modeling approach. The core claim is that Bayesian optimization can effectively adaptively compile quantum circuits, optimizing for performance and minimizing gate count. The system incorporates a compiler that utilizes Bayesian optimization to explore the vast space of possible quantum circuit transformations, learning to identify the most efficient compilation strategies. The results demonstrate the potential of this approach to significantly reduce the complexity of quantum circuits while maintaining algorithm fidelity.
Despite advances in the development of quantum computers, the practical application of quantum algorithms requiring deep circuit depths or high-fidelity transformations remains outside the current range of the so-called noisy intermediate-scale quantum devices. Now and beyond, quantum circuit compilation (QCC) is a crucial component of any quantum algorithm execution. Besides translating a circuit into hardware-specific gates, it can optimize circuit depth and adapt to noise. Variational quantum circuit compilation (VQCC) optimizes the parameters of an ansatz according to the goal of reproducing a given unitary transformation. In this work, we present a VQCC-objective function called the quantum Wasserstein compilation (QWC) cost function based on the quantum Wasserstein distance of order 1. We show that the QWC cost function upper bounds the average infidelity of two circuits. An estimation method based on measurements of local Pauli-observable is utilized in a generative adversarial network to learn a given quantum circuit. We demonstrate the efficacy of the QWC cost function by compiling hardware efficient ansatz (HEA) as both the target and the ansatz and comparing to cost functions such as the Loschmidt echo test (LET) and the Hilbert-Schmidt test (HST). Finally, our experiments demonstrate that QWC as a cost function is the least affected by barren plateaus when compared to LET and HST for deep enough circuits.