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A quantum system may be purified, i.e., projected into a pure state, faster if one applies feedback operations during the measurement process. However existing results suggest that such an enhancement is only possible when the measurement…
We present a general-purpose quantum error correction primitive based on state purification via the SWAP test, which we refer to as purification quantum error correction (PQEC). This method operates on $N$ noisy copies, requires minimally…
Quantum memory -- the capacity to store and faithfully recover unknown quantum states -- is essential for quantum-enhanced technology. There is thus a pressing need for operationally meaningful means to benchmark candidate memories across…
Quantum reservoir computing (QRC) is an emerging framework for near-term quantum machine learning that offers in-memory processing, platform versatility across analogue and digital systems, and avoids typical trainability challenges such as…
Quantum computing promises the ability to compute properties of quantum systems exponentially faster than classical computers. Quantum advantage is achieved when a practical problem is solved more efficiently on a quantum computer than on a…
Demonstrating quantum advantage with less powerful but more realistic devices is of great importance in modern quantum information science. Recently, a significant quantum speedup was achieved in the problem of learning a hidden parity…
We develop a quantum learning scheme for binary discrimination of coherent states of light. This is a problem of technological relevance for the reading of information stored in a digital memory. In our setting, a coherent light source is…
Recent theoretical results in quantum machine learning have demonstrated a general trade-off between the expressive power of quantum neural networks (QNNs) and their trainability; as a corollary of these results, practical exponential…
We propose a quantum algorithm for the purification of a generic mixed state $\rho$ of a $n$-qudit system by using an ancillary $n$-qudit system. The algorithm is optimal in that (i) the number of ancillary qudits cannot be reduced, (ii)…
Quantum repeater networks that allow long-distance entanglement distribution will be the backbone of distributed quantum information processing. In this paper we explore entanglement distribution using quantum repeaters with optimized…
Certifying that an n-qubit state synthesized in the lab is close to the target state is a fundamental task in quantum information science. However, existing rigorous protocols either require deep quantum circuits or exponentially many…
High-quality long-distance entanglement is essential for both quantum communication and scalable quantum networks. Entanglement purification is to distill high-quality entanglement from low-quality entanglement in a noisy environment and it…
Quantum networks crucially rely on the availability of high-quality entangled pairs of qubits, known as entangled links, distributed across distant nodes. Maintaining the quality of these links is a challenging task due to the presence of…
Understanding the computational complexity of learning efficient classical programs in various learning models has been a fundamental and important question in classical computational learning theory. In this work, we study the…
Quantum computers can offer dramatic improvements over classical devices for data analysis tasks such as prediction and classification. However, less is known about the advantages that quantum computers may bring in the setting of…
We introduce the concept of a physical process that purifies a mixed quantum state, taken from a set of states, and investigate the conditions under which such a purification map exists. Here, a purification of a mixed quantum state is a…
Quantum state preparation is an important subroutine for quantum computing. We show that any $n$-qubit quantum state can be prepared with a $\Theta(n)$-depth circuit using only single- and two-qubit gates, although with a cost of an…
Entanglement purification describes a primitive in quantum information processing, where several copies of noisy quantum states are distilled into few copies of nearly-pure states of high quality via local operations and classical…
The Kullback-Leibler divergence offers an information-theoretic basis for measuring the difference between two given distributions. Its quantum analog, however, fails to play a corresponding role for comparing two density matrices, if the…
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…