相关论文: An infinite hierarchy of multi-copy quantum learni…
Characterizing quantum processes is essential for unlocking the potential of quantum devices. However, standard quantum process tomography is resource-intensive and becomes infeasible on large-scale systems. Despite alternative approaches…
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…
Characterizing a quantum system by learning its state or evolution is a fundamental problem in quantum physics and learning theory with a myriad of applications. Recently, as a new approach to this problem, the task of agnostic state…
Google's recent quantum supremacy experiment heralded a transition point where quantum computing performed a computational task, random circuit sampling, that is beyond the practical reach of modern supercomputers. We examine the…
Recent breakthroughs in generative machine learning, powered by massive computational resources, have demonstrated unprecedented human-like capabilities. While beyond-classical quantum experiments can generate samples from classically…
Multi-class classification problems are fundamental in many varied domains in research and industry. To solve multi-class classification problems, heuristic strategies such as One-vs-One or One-vs-All can be employed. However, these…
Recent work of Bravyi et al. and follow-up work by Bene Watts et al. demonstrates a quantum advantage for shallow circuits: constant-depth quantum circuits can perform a task which constant-depth classical (i.e., AC$^0$) circuits cannot.…
We show that entangled measurements provide an exponential advantage in sample complexity for Pauli channel estimation, which is both a fundamental problem and a practically important subroutine for benchmarking near-term quantum devices.…
This paper reviews recent advances in quantum learning theory for continuous-variable (CV) systems. Quantum learning theory investigates how to extract classical information from quantum systems as efficiently as possible. CV systems are…
In a work by Raz (J. ACM and FOCS 16), it was proved that any algorithm for parity learning on $n$ bits requires either $\Omega(n^2)$ bits of classical memory or an exponential number (in~$n$) of random samples. A line of recent works…
In quantum information theory, the accurate estimation of observables is pivotal for quantum information processing, playing a crucial role in compute and communication protocols. This work introduces a novel technique for estimating such…
We establish connections between state tomography, pseudorandomness, quantum state synthesis, and circuit lower bounds. In particular, let $\mathfrak{C}$ be a family of non-uniform quantum circuits of polynomial size and suppose that there…
In classical computation, a problem can be solved in multiple steps where calculated results of each step can be copied and used repeatedly. While in quantum computation, it is difficult to realize a similar multi-step computation process…
A longstanding goal in quantum information science is to demonstrate quantum computations that cannot be feasibly reproduced on a classical computer. Such demonstrations mark major milestones: they showcase fine control over quantum systems…
Extracting work from a physical system is one of the cornerstones of quantum thermodynamics. The extractable work, as quantified by ergotropy, necessitates a complete description of the quantum system. This is significantly more challenging…
This paper furthers existing evidence that quantum computers are capable of computations beyond classical computers. Specifically, we strengthen the collapse of the polynomial hierarchy to the second level if: (i) Quantum computers with…
We develop a framework for learning properties of quantum states beyond the assumption of independent and identically distributed (i.i.d.) input states. We prove that, given any learning problem (under reasonable assumptions), an algorithm…
Quantum state tomography is a fundamental problem in quantum computing. Given $n$ copies of an unknown $N$-qubit state $\rho \in \mathbb{C}^{d \times d},d=2^N$, the goal is to learn the state up to an accuracy $\epsilon$ in trace distance,…
We identify five selected open problems in the theory of quantum information, which are rather simple to formulate, were well-studied in the literature, but are technically not easy. As these problems enjoy diverse mathematical connections,…
In quantum information transformation and quantum computation, the most critical issues are security and accuracy. These features, therefore, stimulate research on quantum state characterization. A characterization tool, Quantum state…