Related papers: Dense Quantum Coding and a Lower Bound for 1-way Q…

Quantum error correction promises a viable path to fault-tolerant computations, enabling exponential error suppression when the device's error rates remain below the protocol's threshold. This threshold, however, strongly depends on the…

The training of deep neural networks (DNNs) requires intensive resources both for computation and for storage performance. Thus, DNNs cannot be efficiently applied to mobile phones and embedded devices, which seriously limits their…

We prove that two-way probabilistic and quantum finite automata (2PFA's and 2QFA's) can be considerably more concise than both their one-way versions (1PFA's and 1QFA's), and two-way nondeterministic finite automata (2NFA's). For this…

It is becoming increasingly clear that, if a useful device for quantum computation will ever be built, it will be embodied by a classical computing machine with control over a truly quantum subsystem, this apparatus performing a mixture of…

Superdense coding proved that entanglement-assisted quantum communications can improve the data transmission rates compared to classical systems. It allows sending 2 classical bits between the parties in exchange of 1 quantum bit and a…

We design a quantum method for classical information compression that exploits the hidden subgroup quantum algorithm. We consider sequence data in a database with a priori unknown symmetries of the hidden subgroup type. We prove that data…

The relative power of quantum algorithms, using an adaptive access to quantum devices, versus classical post-processing methods that rely only on an initial quantum data set, remains the subject of active debate. Here, we present evidence…

We develop and implement automated methods for optimizing quantum circuits of the size and type expected in quantum computations that outperform classical computers. We show how to handle continuous gate parameters and report a collection…

Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding…

In this thesis, we are interested in the limits of quantum communication with and without entanglement, and with and without noise assumptions on the communication setup. When a sender and a receiver are connected by a communication line…

The optimal rate of reliable communication over a quantum channel can be enhanced by pre-shared entanglement. Whereas the enhancement may be unbounded in infinite-dimensional settings even when the input power is constrained, a…

We introduce a construction for entanglement-assisted quantum error-correcting codes (EAQECCs) that saturates the classical Singleton bound with less shared entanglement than any known method for code rates below $ \frac{k}{n} = \frac{1}{3}…

We show that the algorithmic complexity of any classical algorithm written in a Turing-complete programming language polynomially bounds the number of quantum bits that are required to run and even symbolically execute the algorithm on a…

In recent years, quantum kernel methods have shown promising applications on near-term quantum devices. However, selecting an appropriate encoding circuit for a given dataset requires costly evaluation of multiple candidates, formulated as…

We show that any classical two-way communication protocol with shared randomness that can approximately simulate the result of applying an arbitrary measurement (held by one party) to a quantum state of $n$ qubits (held by another), up to…

We provide modular circuit-level implementations and resource estimates for several methods of block-encoding a dense $N\times N$ matrix of classical data to precision $\epsilon$; the minimal-depth method achieves a $T$-depth of…

We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…

Quantum computers have the potential to speed up certain computational tasks. A possibility this opens up within the field of machine learning is the use of quantum techniques that may be inefficient to simulate classically but could…

Finding solid and practical quantum advantages via noisy quantum devices without error correction is a critical but challenging problem. Conversely, comprehending the fundamental limitations of the state-of-the-art is equally crucial. In…

Estimation of unknown qubit elementary gates and alignment of reference frames are formally the same problem. Using quantum states made out of $N$ qubits, we show that the theoretical precision limit for both problems, which behaves as…