Related papers: Quantum signal processing with continuous variable…
A quantum circuit transformation (QCT) is required when executing a quantum program in a real quantum processing unit (QPU). Through inserting auxiliary SWAP gates, a QCT algorithm transforms a quantum circuit to one that satisfies the…
We formulate a notion of group Fourier transform for a finite dimensional Lie group. The transform provides a unitary map from square integrable functions on the group to square integrable functions on a non-commutative dual space. We then…
Quantum superposition says that any physical system simultaneously exists in all of its possible states, the number of which is exponential in the number of entities composing the system. The strength of presence of each possible state in…
A fundamental task in quantum information science is to transfer an unknown state from particle $A$ to particle $B$ (often in remote space locations) by using a bipartite quantum operation $\mathcal{E}^{AB}$. We suggest the power of…
The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. Quantum kernels exist that, subject to…
Quantum systems with a finite number of states at all times have been a primary element of many physical models in nuclear and elementary particle physics, as well as in condensed matter physics. Today, however, due to a practical demand in…
Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. However, this effort involves repeatedly diagonalizing…
Convolutional neural networks owe much of their success to hard-coding translation equivariance. Quantum convolutional neural networks (QCNNs) have been proposed as near-term quantum analogues, but the relevant notion of translation depends…
This paper introduces quantum circuit methodologies for pointwise multiplication and convolution of complex functions, conceptualized as "processing through encoding". Leveraging known techniques, we describe an approach where multiple…
Fully convolutional networks are robust in performing semantic segmentation, with many applications from signal processing to computer vision. From the fundamental principles of variational quantum algorithms, we propose a feasible pure…
Quantum Process Tomography (QPT) methods aim at identifying, i.e. estimating, a quantum process. QPT is a major quantum information processing tool, since it especially allows one to experimentally characterize the actual behavior of…
Quantum Image Processing (QIP)is an exciting new field showing a lot of promise as a powerful addition to the arsenal of Image Processing techniques. Representing image pixel by pixel using classical information requires an enormous amount…
Quantum Fourier transform (QFT) is a key ingredient of many quantum algorithms where a considerable amount of ancilla qubits and gates are often needed to form a Hilbert space large enough for high-precision results. Qubit recycling reduces…
Quantum sensing harnesses the unique properties of quantum systems to enable precision measurements of physical quantities such as time, magnetic and electric fields, acceleration, and gravitational gradients well beyond the limits of…
The kernel trick in supervised learning signifies transformations of an inner product by a feature map, which then restructures training data in a larger Hilbert space according to an endowed inner product. A quantum feature map corresponds…
In this note we consider a system with a large angular momentum l whose state we can store using some log_2(l) qubits. The problem then is how to carry out spatial rotations of the system in this representation. In other words we are…
The vector fields of the quantum Lie algebra are described for the quantum groups $GL_q(N), SL_q(N)$ and $SO_q(N)$ as pseudodifferential operators on the linear quantum spaces covariant under the corresponding quantum group. Their…
A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum…
The characterization of a unitary gate is experimentally accomplished via Quantum Process Tomography, which combines the outcomes of different projective measurements to reconstruct the underlying operator. The process matrix is typically…
Pricing financial derivatives on quantum computers typically includes quantum arithmetic components which contribute heavily to the quantum resources required by the corresponding circuits. In this manuscript, we introduce a method based on…