Related papers: Constant-Optimized Quantum Circuits for Modular Mu…
We discuss efficient quantum logic circuits which perform two tasks: (i) implementing generic quantum computations and (ii) initializing quantum registers. In contrast to conventional computing, the latter task is nontrivial because the…
This work is a tutorial on Shor's factoring algorithm by means of a worked out example. Some basic concepts of Quantum Mechanics and quantum circuits are reviewed. It is intended for non-specialists which have basic knowledge on…
We design a deterministic subexponential time algorithm that takes as input a multivariate polynomial $f$ computed by a constant-depth circuit over rational numbers, and outputs a list $L$ of circuits (of unbounded depth and possibly with…
Optimizing quantum circuits is challenging due to the very large search space of functionally equivalent circuits and the necessity of applying transformations that temporarily decrease performance to achieve a final performance…
Circuit augmentation schemes are a family of combinatorial algorithms for linear programming that generalize the simplex method. To solve the linear program, they construct a so-called monotone circuit walk: They start at an initial vertex…
Shor's factorisation algorithm is a combination of classical pre- and post-processing and a quantum period finding (QPF) subroutine which allows an exponential speed up over classical factoring algorithms. We consider the stability of this…
Integer factorization has been one of the cornerstone applications of the field of quantum computing since the discovery of an efficient algorithm for factoring by Peter Shor. Unfortunately, factoring via Shor's algorithm is well beyond the…
Implementation of logical entangling gates is an important step towards realizing a quantum computer. We use a gradient-based optimization approach to find single-qubit rotations which can be interleaved between applications of a noisy…
Quantum optimization solvers typically rely on one-variable-to-one-qubit mapping. However, the low qubit count on current quantum computers is a major obstacle in competing against classical methods. Here, we develop a qubit-efficient…
We present a quantum variational algorithm based on a novel circuit that generates all permutations that can be spanned by one- and two-qubits permutation gates. The construction of the circuits follows from group-theoretical results, most…
We consider maximization of stochastic monotone continuous submodular functions (CSF) with a diminishing return property. Existing algorithms only guarantee the performance \textit{in expectation}, and do not bound the probability of…
We first show how to construct an O(n)-depth O(n)-size quantum circuit for addition of two n-bit binary numbers with no ancillary qubits. The exact size is 7n-6, which is smaller than that of any other quantum circuit ever constructed for…
Implementing a quantum circuit on specific hardware with a reduced available gate set is often associated with a substantial increase in the length of the equivalent circuit. This process is also known as transpilation and due to…
Most work in quantum circuit optimization has been performed in isolation from the results of quantum fault-tolerance. Here we present a polynomial-time algorithm for optimizing quantum circuits that takes the actual implementation of…
In this work, we evaluate an evolutionary algorithm (EA) to optimize a given circuit in such a way that it reduces the required communication when executed in the Distributed Quantum Computing (DQC) paradigm. We evaluate our approach for a…
We present QEst, a procedure to systematically generate approximations for quantum circuits to reduce their CNOT gate count. Our approach employs circuit partitioning for scalability with procedures to 1) reduce circuit length using…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
Reversible or information-lossless circuits have applications in digital signal processing, communication, computer graphics and cryptography. They are also a fundamental requirement in the emerging field of quantum computation. We…
We introduce AQCtensor, a novel algorithm to produce short-depth quantum circuits from Matrix Product States (MPS). Our approach is specifically tailored to the preparation of quantum states generated from the time evolution of quantum…
We introduce symmetric arithmetic circuits, i.e. arithmetic circuits with a natural symmetry restriction. In the context of circuits computing polynomials defined on a matrix of variables, such as the determinant or the permanent, the…