Related papers: Connecting quantum circuit amplitudes and matrix p…

Primitive polynomials over finite fields are crucial for various domains of computer science, including classical pseudo-random number generation, coding theory and post-quantum cryptography. Nevertheless, the pursuit of an efficient…

Quantum signal processing (QSP) is a framework which was proven to unify and simplify a large number of known quantum algorithms, as well as discovering new ones. QSP allows one to transform a signal embedded in a given unitary using…

The paper deals with some spectral properties of (mostly infinite) quantum and combinatorial graphs. Quantum graphs have been intensively studied lately due to their numerous applications to mesoscopic physics, nanotechnology, optics, and…

Realising a global quantum network requires combining individual strengths of different quantum systems to perform universal tasks, notably using flying and stationary qubits. However, transferring coherently quantum information between…

We introduce the concept of quantum field tomography, the efficient and reliable reconstruction of unknown quantum fields based on data of correlation functions. At the basis of the analysis is the concept of continuous matrix product…

Linear optical circuits of growing complexity are playing an increasing role in emerging photonic quantum technologies. Individual photonic devices are typically described by a unitary matrix containing amplitude and phase information, the…

This paper presents a quantum generalization of the multinomial distribution for the transition probabilities of $m$ identical photons in a $k$-port linear optical interferometer: two multinomial coefficients (one for the input…

Qutrits, the triple level quantum systems in various forms, have been proposed for quantum information processing recently. By the methods presented in this paper a bi-photonic qutrit, which is encoded with the polarizations of two photons…

We present a quantum algorithm for the calculation of scattering amplitudes of massive charged scalar particles in scalar quantum electrodynamics. Our algorithm is based on continuous-variable quantum computing architecture resulting in…

Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…

We consider a class of random quantum circuits where at each step a gate from a universal set is applied to a random pair of qubits, and determine how quickly averages of arbitrary finite-degree polynomials in the matrix elements of the…

Over a decade ago, it was demonstrated that quantum computing has the potential to revolutionize numerical linear algebra by enabling algorithms with complexity superior to what is classically achievable, e.g., the seminal HHL algorithm for…

Realizing the advantages of quantum computation requires access to the full Hilbert space of states of many quantum bits (qubits). Thus, large-scale quantum computation faces the challenge of efficiently generating entanglement between many…

Realizing a large-scale quantum computer requires hardware platforms that can simultaneously achieve universality, scalability, and fault tolerance. As a viable pathway to meeting these requirements, quantum computation based on…

Photonic quantum computing offers a promising platform for quantum information processing, benefiting from the long coherence times of photons and their ease of manipulation. This paper presents a scheme for implementing a deterministic…

We present some basic integer arithmetic quantum circuits, such as adders and multipliers-accumulators of various forms, as well as diagonal operators, which operate on multilevel qudits. The integers to be processed are represented in an…

Quantum technologies promise profound advances in communication security, sensing and computing. The underpinning hardware must be engineered to generate, manipulate and detect quantum phenomena with exceptional performance, whilst being…

The scalability, error correction and practical problem solving are important challenges for quantum computing (QC) as more emphasized by quantum supremacy (QS) experiments. Quantum path computing (QPC), recently introduced for linear optic…

Programmable photonic integrated circuits represent an emerging technology that amalgamates photonics and electronics, paving the way for light-based information processing at high speeds and low power consumption. Considering their wide…

This work investigates the expressive power of quantum circuits in approximating high-dimensional, real-valued functions. We focus on countably-parametric holomorphic maps $u:U\to \mathbb{R}$, where the parameter domain is…