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Epilogue: Quantum Computing
Published in Vivek Kale, Parallel Computing Architectures and APIs, 2019
As stated in the Preface, the requirements of massive parallelism envisaged in the future is achievable more effectively through quantum computing. This epilogue explores the very idea of quantum computing. In 1994, Peter Shor (a research scientist at AT&T Bell Laboratories) wrote a paper in which he described the first algorithm specifically intended for quantum computation. Shor’s algorithm takes advantage of the power of quantum superposition to implement a set of mathematical operations that enable a machine to rapidly factor very large integers. Given a quantum computer of sufficient power, the factorization could be accomplished orders of magnitude faster than is possible with even the most advanced silicon-based computers. Although these computations seem trivial, they represent proofs of the concept of factorization, with staggering implications if the same algorithms can be run on quantum computers with many more qubits.
Basics, Applications, and Design of Reversible Circuits
Published in Tomasz Wojcicki, Krzysztof Iniewski, VLSI: Circuits for Emerging Applications, 2017
Nevertheless, using these quantum mechanical phenomena, quantum computation allows for breaching complexity bounds which are valid for computing devices based on conventional mechanics. The Grover search [3] and the factorization algorithm by Shor [4] rank among the most famous examples for quantum algorithms that solve problems in time complexities, which cannot be achieved using conventional computing. The first algorithm addresses thereby the search of an item in an unsorted database with k items in time O(k), whereas conventional methods cannot be performed using less than linear time. Shor’s algorithm performs prime factorization in polynomial time, that is, the algorithm is exponentially faster than its best known conventional counterpart. First physical realizations of quantum circuits have been presented in the work of Vandersypen et al. [5].
Special-purpose and future architectures
Published in Joseph D. Dumas, Computer Architecture, 2016
Then, in 1994, Peter Shor (a research scientist at AT&T Bell Laboratories) wrote a paper in which he described the first algorithm specifically intended for quantum computation. Shor’s algorithm takes advantage of the power of quantum superposition to implement a set of mathematical operations that enable a machine to rapidly factor very large integers. Given a quantum computer of sufficient power, the factorization could be accomplished orders of magnitude faster than is possible with even the most advanced silicon-based computers. Shor’s algorithm has already been run on the 7-qubit computer developed by IBM, factoring the number 15 into the numbers 3 and 5. (Later, other researchers factored 143 into 11 and 13 using an “adiabatic factoring” algorithm and four qubits.) Although these computations seem trivial, they represent proofs of the concept of factorization, with staggering implications if the same algorithms can be run on quantum computers with many more qubits.
Quantum computing to solve scenario-based stochastic time-dependent shortest path routing
Published in Transportation Letters, 2023
Vinayak V. Dixit, Chence Niu, David Rey, S. Travis Waller, Michael W. Levin
There has been ground breaking theoretical work that demonstrated quantum algorithms relying on quantum logic gates can provide significant speedups, one of the most celebrated being the Shor’s algorithm (Shor 1994.), that demonstrated that quantum computers can solve the prime factorization problem exponentially faster than classical computers, having significant implications on cryptography. Recently ‘Quantum Supremacy’ was demonstrated on a problem that would take a classical supercomputer 10,000 years to be completed by 53 qubit Sycamore processor in 200 s (Arute et al. 2019). Applications of quantum algorithms in the field of transportation and traffic have been limited. Dixit and Jian (Dixit and Jian 2022a) used quantum gates for drive cycle analysis, that has applications to safety and emissions. Some other transportation problems such as traveling salesman problem, vehicle routing problem, traffic signals control problem, and traffic flow optimization problem have been investigated (Papalitsas et al. 2019; Warren 2020)– (Neukart et al. 2017).
Systematic Survey: Secure and Privacy-Preserving Big Data Analytics in Cloud
Published in Journal of Computer Information Systems, 2023
Arun Amaithi Rajan, Vetriselvi V
The majority of authentication mechanisms in classical cryptosystems are based on cryptographic primitives. For instance, RSA and ElGamal are cryptosystems built on factorization or discrete logarithm hard problems. It is widely assumed that such primitives are vulnerable to quantum algorithms. Shor’s algorithm32 is a quantum algorithm that solves discrete logarithm and factorization problems in sub-exponential time complexity. So, if we continue to have the same cryptosystem, there is a chance that quantum computers will attack secure applications within polynomial time in the future. So, with a longer vision, more works are being done in quantum cryptography.33 As we have hard problems in traditional systems, such as discrete logarithm, there are some hard problems in the quantum environment also such as lattice problems which prompted scientists to develop quantum cryptography algorithms. A survey on lattice-based cryptography implementations in software and hardware by Nejatollahi et al.34 gives an overview of existing algorithms in post-quantum cryptography based on lattice problems. The authors worked on implementations which tackles different issues such as memory footprint, energy, security and, given some proposals for lattices in information security
Leveraging the power of quantum computing for breaking RSA encryption
Published in Cyber-Physical Systems, 2021
Moolchand Sharma, Vikas Choudhary, R. S. Bhatia, Sahil Malik, Anshuman Raina, Harshit Khandelwal
Modular arithmetic is a part of mathematics that revolves around the remainders of integers. Shor’s algorithm for factorisation uses this as a basis for finding prime factors more efficiently. Shor introduced an algorithm for integer factorisation that is used for finding the prime factors of a number. When running on a quantum computer, the algorithm takes very little time to find the prime factors of the number – running in polynomial time. The efficiency of Shor’s algorithm is due to the efficiency of the quantum Fourier transform, and modular exponentiation by repeated squaring. The RSA and the algorithm are based on the same finite group theory. Shor’s algorithm gives us the best efficiency, but it relies on Size of Quantum Computers, which are not possible right now [20,21].