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The exploration of quantum algorithms that possess quantum advantages is a central topic in quantum computation and quantum information processing. One potential candidate in this area is quantum generative adversarial learning (QuGAL),…
Significant advances in the development of computing devices based on quantum effects and the demonstration of their use to solve various problems have rekindled interest in the nature of the "quantum computational advantage." Although…
Recent work has exposed the idea that interesting quantum-like probability laws, including interference effects, can be manifest in classical systems. Here we propose a model for quantum-like (QL) states and QL bits. We suggest a way that…
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…
Fermions are fundamental particles which obey seemingly bizarre quantum-mechanical principles, yet constitute all the ordinary matter that we inhabit. As such, their study is heavily motivated from both fundamental and practical incentives.…
Understanding the complexity of quantum states and circuits is a central challenge in quantum information science, with broad implications in many-body physics, high-energy physics and quantum learning theory. A common way to model the…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
State preparation is a necessary component of many quantum algorithms. In this work, we combine a method for efficiently representing smooth differentiable probability distributions using matrix product states with recently discovered…
Unsupervised machine learning models build an internal representation of their training data without the need for explicit human guidance or feature engineering. This learned representation provides insights into which features of the data…
Given a quantum circuit, a quantum computer can sample the output distribution exponentially faster in the number of bits than classical computers. A similar exponential separation has yet to be established in generative models through…
We prove that recognizing the phase of matter of an unknown quantum state is quantum computationally hard. More specifically, we show that the quantum computational time of any phase recognition algorithm must grow exponentially in the…
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…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
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 non-structured data is exponential on the number of qubits. Several works address this…
Free fermions are some of the best studied quantum systems. However, little is known about the complexity of learning free-fermion distributions. In this work we establish the hardness of this task in the particle number non-preserving…
The architecture of circuital quantum computers requires computing layers devoted to compiling high-level quantum algorithms into lower-level circuits of quantum gates. The general problem of quantum compiling is to approximate any unitary…
In quantum information technology, crucial information is regularly encoded in different quantum states. To extract information, the identification of one state from the others is inevitable. However, if the states are non-orthogonal and…
Quantum computers may outperform classical computers on machine learning tasks. In recent years, a variety of quantum algorithms promising unparalleled potential to enhance, speed up, or innovate machine learning have been proposed. Yet,…
We consider the efficiency of classically simulating measurement-based quantum computation on surface-code states. We devise a method for calculating the elements of the probability distribution for the classical output of the quantum…
Learning about physical systems from quantum-enhanced experiments, relying on a quantum memory and quantum processing, can outperform learning from experiments in which only classical memory and processing are available. Whereas quantum…