Related papers: Quantum Computing Discrete Logarithms with the Hel…
Prime factorization on quantum processors is typically implemented either via circuit-based approaches such as Shor's algorithm or through Hamiltonian optimization methods based on adiabatic, annealing, or variational techniques. While…
Entanglement has been termed a critical resource for quantum information processing and is thought to be the reason that certain quantum algorithms, such as Shor's factoring algorithm, can achieve exponentially better performance than their…
Algorithms to compute the quantum Fourier transform over a cyclic group are fundamental to many quantum algorithms. This paper describes such an algorithm and gives a proof of its correctness, tightening some claimed performance bounds…
In quantum information processing (QIP), the quantum Fourier transform (QFT) has a plethora of applications [1] [2] [3]: Shor's algorithm and phase estimation are just a few well-known examples. Shor's quantum factorization algorithm, one…
Physical constraints and engineering challenges, including wafer dimensions, classical control cabling, and refrigeration volumes, impose significant limitations on the scalability of quantum computing units. As a result, a modular quantum…
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…
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…
A common starting point of traditional quantum algorithm design is the notion of a universal quantum computer with a scalable number of qubits. This convenient abstraction mirrors classical computations manipulating finite sets of symbols,…
We construct a quantum algorithm that performs function-dependent phase transform and requires no initialization of an ancillary register. The algorithm recovers the initial state of an ancillary register regardless of whether its state is…
Shor's factoring algorithm (SFA), by its ability to efficiently factor large numbers, has the potential to undermine contemporary encryption. At its heart is a process called order finding, which quantum mechanics lets us perform…
Entanglement is essential for quantum computation. However, disentanglement is also necessary. It can be achieved without the need of classical operations (measurements). Two examples are analyzed: the discrete Fourier transform and error…
This is a course on the theory of quantum computing. It consists of 16 lessons, each with a video and written component, covering the basics of quantum information, quantum algorithms (including query algorithms, Shor's algorithm for…
Quantum computing is a winsome field that concerns with the behaviour and nature of energy at the quantum level to improve the efficiency of computations. In recent years, quantum computation is receiving much attention for its capability…
The initial state creation is a starting point of many quantum algorithms and usually is considered as a separate subroutine not included into the algorithm itself. There are many algorithms aimed on creation of special class of states. Our…
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…
We try to minimize the number of qubits needed to factor an integer of n bits using Shor's algorithm on a quantum computer. We introduce a circuit which uses 2n+3 qubits and O(n^3 lg(n)) elementary quantum gates in a depth of O(n^3) to…
We present a novel benchmark application of a quantum algorithm to Feynman loop integrals. The two on-shell states of a Feynman propagator are identified with the two states of a qubit and a quantum algorithm is used to unfold the causal…
The quantum guesswork quantifies the minimum number of queries needed to guess the state of a quantum ensemble if one is allowed to query only one state at a time. Previous approaches to the computation of the guesswork were based on…
One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve the problem…
Several prominent quantum computing algorithms--including Grover's search algorithm and Shor's algorithm for finding the prime factorization of an integer--employ subcircuits termed 'oracles' that embed a specific instance of a mathematical…