Related papers: Noise-tolerant learnability of shallow quantum cir…
Random unitaries are a central object of study in quantum information, with applications to quantum computation, quantum many-body physics, and quantum cryptography. Recent work has constructed unitary designs and pseudorandom unitaries…
Motivated by realistic hardware considerations of the pre-fault-tolerant era, we comprehensively study the impact of uncorrected noise on quantum circuits. We first show that any noise `truncates' most quantum circuits to effectively…
We consider the learnability of the quantum neural network (QNN) built on the variational hybrid quantum-classical scheme, which remains largely unknown due to the non-convex optimization landscape, the measurement error, and the…
In this work, we initiate the study of learning quantum processes from quantum statistical queries. We focus on two fundamental learning tasks in this new access model: shadow tomography of quantum processes and process tomography with…
The existence of pseudorandom unitaries (PRUs) -- efficient quantum circuits that are computationally indistinguishable from Haar-random unitaries -- has been a central open question, with significant implications for cryptography,…
Advancements in quantum computing have spurred significant interest in harnessing its potential for speedups over classical systems. However, noise remains a major obstacle to achieving reliable quantum algorithms. In this work, we present…
Efficiently characterizing large quantum states and processes is a central yet notoriously challenging task in quantum information science, as conventional tomography methods typically require resources that grow exponentially with system…
We show that concrete hardness assumptions about learning or cloning the output state of a random quantum circuit can be used as the foundation for secure quantum cryptography. In particular, under these assumptions we construct secure…
The computational power of real-world quantum computers is limited by errors. When using quantum computers to perform algorithms which cannot be efficiently simulated classically, it is important to quantify the accuracy with which the…
We present the first computationally-efficient algorithm for average-case learning of shallow quantum circuits with many-qubit gates. Specifically, we provide a quasi-polynomial time and sample complexity algorithm for learning unknown…
We prove that random quantum circuits on any geometry, including a 1D line, can form approximate unitary designs over $n$ qubits in $\log n$ depth. In a similar manner, we construct pseudorandom unitaries (PRUs) in 1D circuits in…
Quantifying the complexity of quantum states is a longstanding key problem in various subfields of science, ranging from quantum computing to the black-hole theory. The lower bound on quantum pure state complexity has been shown to grow…
We propose a classical-quantum hybrid algorithm for machine learning on near-term quantum processors, which we call quantum circuit learning. A quantum circuit driven by our framework learns a given task by tuning parameters implemented on…
Extracting information efficiently from quantum systems is a major component of quantum information processing tasks. Randomized measurements, or classical shadows, enable predicting many properties of arbitrary quantum states using few…
Quantum compiling, where a parameterized quantum circuit is trained to learn a target unitary, is an important primitive for quantum computing that can be used as a subroutine to obtain optimal circuits or as a tomographic tool to study the…
Learning problems involving quantum data are natural candidates for demonstrating an advantage in quantum machine learning. Recent results indicate that, for certain tasks and under noiseless conditions, coherent processing of quantum data…
Random quantum circuits have been utilized in the contexts of quantum supremacy demonstrations, variational quantum algorithms for chemistry and machine learning, and blackhole information. The ability of random circuits to approximate any…
In quantum computing the decoherence time of the qubits determines the computation time available and this time is very limited when using current hardware. In this paper we minimize the execution time (the depth) for a class of circuits…
Despite fundamental interests in learning quantum circuits, the existence of a computationally efficient algorithm for learning shallow quantum circuits remains an open question. Because shallow quantum circuits can generate distributions…
There is increasing interest in the development of gate-based quantum circuits for the training of machine learning models. Yet, little is understood concerning the parameters of circuit design, and the effects of noise and other…