Related papers: A technical note for a Shor's algorithm by phase e…
We describe an implementation of Shor's quantum algorithm to factor n-bit integers using only 2n+2 qubits. In contrast to previous space-optimized implementations, ours features a purely Toffoli based modular multiplication circuit. The…
Quantum information processing and its associated technologies has reached an interesting and timely stage in their development where many different experiments have been performed establishing the basic building blocks. The challenge…
In this paper, we briefly discuss the methodology for simulating a quantum computer which performs Shor's algorithm on a 7-qubit system to factorise 15. Using this simulation and the overlooked quantum brachistochrone method, we devised a…
Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…
Modular exponentiation (ME) operators are one of the fundamental components of Shor's algorithm, and the place where most of the quantum resources are deployed. I propose a method for constructing the ME operators that relies upon the…
Let N be a (large positive integer, let b > 1 be an integer relatively prime to N, and let r be the order of b modulo N. Finally, let QC be a quantum computer whose input register has the size specified in Shor's original description of his…
It is commonly assumed that Shor's quantum algorithm for the efficient factorization of a large number $N$ requires a pure initial state. Here we demonstrate that a single pure qubit together with a collection of $log_2 N$ qubits in an…
We review some of the features of the ProjectQ software framework and quantify their impact on the resulting circuits. The concise high-level language facilitates implementing even complex algorithms in a very time-efficient manner while,…
Quantum phase estimation plays a central role in quantum simulation as it enables the study of spectral properties of many-body quantum systems. Most variants of the phase estimation algorithm require the application of the global unitary…
We heuristically show that Shor's algorithm for computing general discrete logarithms achieves an expected success probability of approximately 60% to 82% in a single run when modified to enable efficient implementation with the…
It is well-known that Shor's factorization algorithm, Simon's period-finding algorithm, and Deutsch's original XOR algorithm can all be formulated as solutions to a hidden subgroup problem. Here the salient features of the…
We optimize fault-tolerant quantum error correction to reduce the number of syndrome bit measurements. Speeding up error correction will also speed up an encoded quantum computation, and should reduce its effective error rate. We give both…
Combinatorial optimization - a field of research addressing problems that feature strongly in a wealth of scientific and industrial contexts - has been identified as one of the core potential fields of applicability of quantum computers. It…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
We study the universality of scaling of entanglement in Shor's factoring algorithm and in adiabatic quantum algorithms across a quantum phase transition for both the NP-complete Exact Cover problem as well as the Grover's problem. The…
Shor's algorithm is well-known for its capability to address the elliptic curve discrete logarithm problem (ECDLP) in polynomial time. The enhancement of its quantum resources continues to be a crucial focus of research. Nevertheless, the…
This is an expository talk written for the Bourbaki Seminar. After a brief introduction, Section 1 discusses in the categorical language the structure of the classical deterministic computations. Basic notions of complexity icluding the…
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…
In this paper, we use the methods found in quant-ph/0201095 to create a continuous variable analogue of Shor's quantum factoring algorithm. By this we mean a quantum hidden subgroup algorithm that finds the period P of a function F:R-->R…
We present a polynomial quantum algorithm for the Abelian stabilizer problem which includes both factoring and the discrete logarithm. Thus we extend famous Shor's results. Our method is based on a procedure for measuring an eigenvalue of a…