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The inverse design of photonic integrated circuits (PICs) presents distinctive computational challenges, including their large memory requirements. Advancements in the two-photon polymerization (2PP) fabrication process introduce additional…
Practical success of quantum learning models hinges on having a suitable structure for the parameterized quantum circuit. Such structure is defined both by the types of gates employed and by the correlations of their parameters. While much…
We study the deterministic complexity of the $2$-Ruling Set problem in the model of Massively Parallel Computation (MPC) with linear and strongly sublinear local memory. Linear MPC: We present a constant-round deterministic algorithm for…
This paper is divided in two parts. In the first part, the inverse spectral problem for tight-binding hamiltonians is studied. This problem is shown to have an infinite number of solutions for properly chosen energies. The space of such…
We obtain, for a subclass of structure functions characterizing a first class Hamiltonian system, recursive relations from which the general form of the local symmetry transformations can be constructed in terms of the independent gauge…
We have fabricated a sub-micron-sized structure consisting of an InAs-based 2DEG, two narrow Nb leads and a gate, where the indirect ballistic transport between the non-oppositely superconducting contacts can be controlled by the voltage…
Recently, deep residual networks have been successfully applied in many computer vision and natural language processing tasks, pushing the state-of-the-art performance with deeper and wider architectures. In this work, we interpret deep…
Reversible logic has become immensely popular research area and its applications have spread in various technologies for their low power consumption. In this paper we proposed an efficient design of random access memory using reversible…
(i) We point out that every local unitary circuit of depth smaller than the linear system size is easily distinguished from a global Haar random unitary if there is a conserved quantity that is a sum of local operators. This is always the…
We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…
We consider the hashing mechanism for constructing binary embeddings, that involves pseudo-random projections followed by nonlinear (sign function) mappings. The pseudo-random projection is described by a matrix, where not all entries are…
Superconducting circuits consisting of a few low-anharmonic transmons coupled to readout and bus resonators can perform basic quantum computations. Since the number of qubits in such circuits is limited to not more than a few tens, the…
Spectrum manipulation is central to photonic systems, where advanced computing and sensing applications often demand highly complex spectral responses to achieve high throughput. Conventional methods for enhancing spectral complexity…
We study the richness of the ensemble of graphical structures (i.e., unlabeled graphs) of the one-dimensional random geometric graph model defined by $n$ nodes randomly scattered in $[0,1]$ that connect if they are within the connection…
In a recursive way and by including a parameter, we introduce a family of deterministic scale-free networks. The resulting networks exhibit small-world effects. We calculate the exact results for the degree exponent, the clustering…
We consider quantum circuits consisting of randomly chosen two-local gates and study the number of gates needed for the distribution over measurement outcomes for typical circuit instances to be anti-concentrated, roughly meaning that the…
Dynamic simulation of materials is a promising application for near-term quantum computers. Current algorithms for Hamiltonian simulation, however, produce circuits that grow in depth with increasing simulation time, limiting feasible…
Transforms using random matrices have been found to have many applications. We are concerned with the projection of a signal onto Gaussian-distributed random orthogonal bases. We also would like to easily invert the process through…
The design of recurrent neural networks (RNNs) to accurately process sequential inputs with long-time dependencies is very challenging on account of the exploding and vanishing gradient problem. To overcome this, we propose a novel RNN…
A new construction is proposed for low density parity check (LDPC) codes using quadratic permutation polynomials over finite integer rings. The associated graphs for the new codes have both algebraic and pseudo-random nature, and the new…