Results 1  10
of
21
PolynomialTime Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
 SIAM J. on Computing
, 1997
"... A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. ..."
Abstract

Cited by 1278 (4 self)
 Add to MetaCart
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and which have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum computer. These algorithms take a number of steps polynomial in the input size, e.g., the number of digits of the integer to be factored.
Reliable quantum computers
 Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
, 1998
"... The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment. Recovery from errors can work effectively even if occasional mist ..."
Abstract

Cited by 165 (3 self)
 Add to MetaCart
The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. Furthermore, encoded quantum information can be processed without serious propagation of errors. Hence, an arbitrarily long quantum computation can be performed reliably, provided that the average probability of error per quantum gate is less than a certain critical value, the accuracy threshold. A quantum computer storing about 106 qubits, with a probability of error per quantum gate of order 106, would be a formidable factoring engine. Even a smaller lessaccurate quantum computer would be able to perform many useful tasks. This paper is based on a talk presented at the ITP Conference on Quantum Coherence
Quantum information with rydberg atoms
 Rev. Mod. Phys
, 2010
"... Rydberg atoms with principal quantum number n1 have exaggerated atomic properties including dipoledipole interactions that scale as n4 and radiative lifetimes that scale as n3. It was proposed a decade ago to take advantage of these properties to implement quantum gates between neutral atom qubits. ..."
Abstract

Cited by 45 (2 self)
 Add to MetaCart
(Show Context)
Rydberg atoms with principal quantum number n1 have exaggerated atomic properties including dipoledipole interactions that scale as n4 and radiative lifetimes that scale as n3. It was proposed a decade ago to take advantage of these properties to implement quantum gates between neutral atom qubits. The availability of a strong longrange interaction that can be coherently turned on and off is an enabling resource for a wide range of quantum information tasks stretching far beyond the original gate proposal. Rydberg enabled capabilities include longrange twoqubit gates, collective encoding of multiqubit registers, implementation of robust lightatom quantum interfaces, and the potential for simulating quantum manybody physics. The advances of the last decade are reviewed, covering both theoretical and experimental aspects of Rydbergmediated quantum information processing.
Addition on a quantum computer
"... A new method for computing sums on a quantum computer is introduced. This technique uses the quantum Fourier transform and reduces the number of qubits necessary for addition by removing the need for temporary carry bits. This approach also allows the addition of a classical number to a quantum supe ..."
Abstract

Cited by 28 (0 self)
 Add to MetaCart
(Show Context)
A new method for computing sums on a quantum computer is introduced. This technique uses the quantum Fourier transform and reduces the number of qubits necessary for addition by removing the need for temporary carry bits. This approach also allows the addition of a classical number to a quantum superposition without encoding the classical number in the quantum register. This method also allows for massive
Circuit for Shor’s algorithm using 2n+3 qubits
 54
, 2002
"... 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 implement the factorization algorithm. The circuit is computable ..."
Abstract

Cited by 22 (0 self)
 Add to MetaCart
(Show Context)
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 implement the factorization algorithm. The circuit is computable in polynomial time on a classical computer and is completely general as it does not rely on any property of the number to be factored. 1
Distributed quantum computing: A distributed Shor algorithm
, 2004
"... We present a distributed implementation of Shor’s quantum factoring algorithm on a distributed quantum network model. This model provides a means for small capacity quantum computers to work together in such a way as to simulate a large capacity quantum computer. In this paper, entanglement is used ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
(Show Context)
We present a distributed implementation of Shor’s quantum factoring algorithm on a distributed quantum network model. This model provides a means for small capacity quantum computers to work together in such a way as to simulate a large capacity quantum computer. In this paper, entanglement is used as a resource for implementing nonlocal operations between two or more quantum computers. These nonlocal operations are used to implement a distributed factoring circuit with polynomially many gates. This distributed version of Shor’s algorithm requires an additional overhead of O((log N) 2) communication complexity, where N denotes the integer to be factored. Keywords: Shor’s algorithm, factoring algorithm, distributed quantum algorithms, quantum circuit. 1.
Quantum Computing with Superconductors
, 2004
"... Superconductive technology is one of the most promising approaches to quantum computing because it offers devices with little dissipation, ultrasensitive magnetometers, and electrometers for state readout, largescaleintegration, and a family of classical electronics that could be used for quantum ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
Superconductive technology is one of the most promising approaches to quantum computing because it offers devices with little dissipation, ultrasensitive magnetometers, and electrometers for state readout, largescaleintegration, and a family of classical electronics that could be used for quantum bit (qubit) control. The challenges this technology faces, however, are substantial: for example, control of the qubit to a part in $10 R must be accomplished with analog control pulses. But even after this is done, the accuracy is limited by the unavoidable decay of quantum information in the system. Recent experiments suggest the time over which this decay occurs is < 1 µs, though it is expected to lengthen as experimental methods improve. A 1µs decay time would mandate a very difficult to achieve maximum time of $100 ps per analog operation. Thus, quantum computing is, simultaneously a promising technology for solving certain very hard problems in computer science and a
Reversible Arithmetic Coding for Quantum Data Compression
 IEEE Transactions on Information Theory
"... We study the problem of compressing a block of symbols (a block quantum state) emitted by a memoryless quantum Bernoulli source. We present a simpletoimplement quantum algorithm for projecting, with high probability, the block quantum state onto the typical subspace spanned by the leading eigensta ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
We study the problem of compressing a block of symbols (a block quantum state) emitted by a memoryless quantum Bernoulli source. We present a simpletoimplement quantum algorithm for projecting, with high probability, the block quantum state onto the typical subspace spanned by the leading eigenstates of its density matrix. We propose a fixedrate quantum ShannonFano code to compress the projected block quantum state using a per symbol code rate that is slightly higher than the von Neumann entropy limit. Finally, we propose quantum arithmetic codes to efficiently implement quantum ShannonFano codes. Our arithmetic encoder/decoder have a cubic circuit and a cubic computational complexity in the block size. The encoder and decoder are quantummechanical inverses of each other, and constitute an elegant example of reversible quantum computation. Keywords: quantum computation, quantum information theory, quantum measurement, noiseless coding, reversible computation, Schumacher coding, a...