Related papers: Quantum binary field multiplication with subquadra…
We present an algorithm for computing depth-optimal decompositions of logical operations, leveraging a meet-in-the-middle technique to provide a significant speed-up over simple brute force algorithms. As an illustration of our method we…
Quantum computers have the potential to break classical cryptographic systems by efficiently solving problems such as the elliptic curve discrete logarithm problem using Shor's algorithm. While resource estimates for factoring-based…
Optimal construction of quantum operations is a fundamental problem in the realization of quantum computation. We here introduce a newly discovered quantum gate, B, that can implement any arbitrary two-qubit quantum operation with minimal…
Quantum algorithms are a very promising field. However, creating and manipulating these kind of algorithms is a very complex task, specially for software engineers used to work at higher abstraction levels. The work presented here is part…
The intrinsic structure of binary fields poses a challenging complexity problem from both hardware and software point of view. Motivated by applications to modern cryptography, we describe some simple techniques aimed at performing…
Qutrit (or ternary) structures arise naturally in many quantum systems, particularly in certain non-abelian anyon systems. We present efficient circuits for ternary reversible and quantum arithmetics. Our main result is the derivation of…
Solving non-linear Diophantine systems lies at the mathematical core of integer optimization and cryptography. While the general unbounded problem is undecidable, even over bounded integer domains it remains classically intractable in the…
The problem of efficient multiplication of large numbers has been a long-standing challenge in classical computation and has been extensively studied for centuries. It appears that the existing classical algorithms are close to their…
We consider recent works on the simulation of quantum circuits using the formalism of matrix product states and the formalism of contracting tensor networks. We provide simplified direct proofs of many of these results, extending an…
We apply a hybrid evolutionary algorithm to minimize the depth of circuits in quantum computing. More specifically, we evaluate two different variants of the algorithm. In the first approach, we combine the evolutionary algorithm with an…
There are various gate sets that can be used to describe a quantum computation. A particularly popular gate set in the literature on quantum computing consists of arbitrary single-qubit gates and 2-qubit CNOT gates. A CNOT gate is however…
We consider the fundamental problem of constructing fast and small circuits for binary addition. We propose a new algorithm with running time $\mathcal O(n \log_2 n)$ for constructing linear-size $n$-bit adder circuits with a significantly…
The multiplicative depth of a logic network over the gate basis $\{\land, \oplus, \neg\}$ is the largest number of $\land$ gates on any path from a primary input to a primary output in the network. We describe a dynamic programming based…
We present some deterministic schemes to construct universal quantum gates, that is, controlled- NOT, three-qubit Toffoli, and Fredkin gates, between flying photon qubits and stationary electron-spin qubits assisted by quantum dots inside…
Implementing quantum operations in the form of natural Hamiltonian dynamics is desirable, since they almost require no external control or feedback. In this work, we propose a NISQ-friendly quantum-classical hybrid approach to designing a…
Quantum algorithms on near-term quantum processors are typically executed using shallow quantum circuits composed of one- and two-qubit gates. However, as circuit depth and gate number increase, gate imperfections and qubit decoherence…
As the most central and computationally intensive component of deep neural networks, the execution efficiency of matrix multiplication directly determines the training and inference performance of models. Harnessing the parallel processing…
A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…
Qubitization is a modern approach to estimate Hamiltonian eigenvalues without simulating its time evolution. While in this way approximation errors are avoided, its resource and gate requirements are more extensive: qubitization requires…
We present a scalable set of universal gates and multiply controlled gates in a qudit basis through a bijective mapping from N qubits to qudits with D = 2^N levels via rotations in U(2). For each of the universal gates (H, CNOT, and T), as…