Related papers: Integer Factoring with Unoperations
A quantum compiling algorithm is an algorithm for decomposing ("compiling") an arbitrary unitary matrix into a sequence of elementary operations (SEO). Suppose $U_{in}$ is an $\nb$-bit unstructured unitary matrix (a unitary matrix with no…
We reveal a relationship between the prime counting function and an operation performed on a unique subsequence of the primes.
We consider procedures to realize an approximate universal NOT gate in terms of average fidelity and fidelity deviation. The average fidelity indicates the optimality of operation on average, while the fidelity deviation does the…
Recently, it was realized that use of the properties of quantum mechanics might speed up certain computations dramatically. Interest in quantum computation has since been growing. One of the main difficulties of realizing quantum…
Unitary transformations are routinely modeled and implemented in the field of quantum optics. In contrast, nonunitary transformations that can involve loss and gain require a different approach. In this theory work, we present a universal…
Quantum computing tries to exploit entanglement and interference to process information more efficiently than the best known classical solutions. Experiments demonstrating the feasibility of this approach have already been performed.…
Quantum computing is a promising new area of computing with quantum algorithms offering a potential speedup over classical algorithms if fault tolerant quantum computers can be built. One of the first applications of the classical computer…
We study the complexity of securely evaluating arithmetic circuits over finite rings. This question is motivated by natural secure computation tasks. Focusing mainly on the case of two-party protocols with security against malicious…
We consider algorithms for the factorization of linear partial differential operators. We introduce several new theoretical notions in order to simplify such considerations. We define an obstacle and a ring of obstacles to factorizations.…
While the question ``how many CNOT gates are needed to simulate an arbitrary two-qubit operator'' has been conclusively answered -- three are necessary and sufficient -- previous work on this topic assumes that one wants to simulate a given…
Factoring integers is considered as a computationally-hard problem for classical methods, whereas there exists polynomial-time Shor's quantum algorithm for solving this task. However, requirements for running the Shor's algorithm for…
This paper presents a novel way to use the algebra of unit quaternions to express arbitrary roots or fractional powers of single-qubit gates, and to use such fractional powers as generators for algebras that combine these fractional input…
Divisor functions have attracted the attention of number theorists from Dirichlet to the present day. Here we consider associated divisor functions $c_j^{(r)}(n)$ which for non-negative integers $j, r$ count the number of ways of…
Realizing non-unitary transformations on unitary-gate based quantum devices is critically important for simulating a variety of physical problems including open quantum systems and subnormalized quantum states. We present a dilation based…
This is a brief report on a particular use of measurement-based uncomputation. Though not appealing in performance, it may shed light on optimization techniques in various quantum circuits.
The energy efficiency of analog forms of computing makes it one of the most promising candidates to deploy resource-hungry machine learning tasks on resource-constrained system such as mobile or embedded devices. However, it is well known…
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…
We present a quantum algorithm for European option pricing in finance, where the key idea is to work in the unary representation of the asset value. The algorithm needs novel circuitry and is divided in three parts: first, the amplitude…
We show that in quantum computation almost every gate that operates on two or more bits is a universal gate. We discuss various physical considerations bearing on the proper definition of universality for computational components such as…
Twirling operations, which average a quantum state with respect to a unitary subgroup, have become a frequently-employed tool in quantum information processing. We investigate the efficient implementation of twirling operations with minimal…