Realization of Quantum Oracles using Symmetries of Boolean Functions

2020 ◽  
Vol 20 (5&6) ◽  
pp. 418-448
Author(s):  
Peng Gao ◽  
Yiwei Li ◽  
Marek Perkowski ◽  
Xiaoyu Song
Keyword(s):  
Boolean Functions ◽  
Design Methodology ◽  
Symmetric Functions ◽  
Quantum Circuit ◽  
Published Data ◽  
Quantum Cost ◽  
Practical Realization ◽  
Grover Algorithm ◽  
Logic Minimization ◽  
Quantum Oracle

Designing a quantum oracle is an important step in practical realization of Grover algorithm, therefore it is useful to create methodologies to design oracles. Lattice diagrams are regular two-dimensional structures that can be directly mapped onto a quantum circuit. We present a quantum oracle design methodology based on lattices. The oracles are designed with a proposed method using generalized Boolean symmetric functions realized with lattice diagrams. We also present a decomposition-based algorithm that transforms non-symmetric functions into symmetric or partially symmetric functions. Our method, which combines logic minimization, logic decomposition, and mapping, has lower quantum cost with fewer ancilla qubits. Overall, we obtain encouraging synthesis results superior to previously published data.

scholarly journals A framework for reducing the overhead of the quantum oracle for use with Grover’s algorithm with applications to cryptanalysis of SIKE

2020 ◽  
Vol 15 (1) ◽  
pp. 143-156
Author(s):  
Jean-François Biasse ◽  
Benjamin Pring
Keyword(s):  
Search Algorithm ◽  
Circuit Complexity ◽  
Quantum Circuit ◽  
Grover’S Algorithm ◽  
Search Problems ◽  
Trade Offs ◽  
Single Target ◽  
Grover's Algorithm ◽  
Quantum Oracle ◽  
The Cost

AbstractIn this paper we provide a framework for applying classical search and preprocessing to quantum oracles for use with Grover’s quantum search algorithm in order to lower the quantum circuit-complexity of Grover’s algorithm for single-target search problems. This has the effect (for certain problems) of reducing a portion of the polynomial overhead contributed by the implementation cost of quantum oracles and can be used to provide either strict improvements or advantageous trade-offs in circuit-complexity. Our results indicate that it is possible for quantum oracles for certain single-target preimage search problems to reduce the quantum circuit-size from $O\left(2^{n/2}\cdot mC\right)$ (where C originates from the cost of implementing the quantum oracle) to $O(2^{n/2} \cdot m\sqrt{C})$ without the use of quantum ram, whilst also slightly reducing the number of required qubits.This framework captures a previous optimisation of Grover’s algorithm using preprocessing [21] applied to cryptanalysis, providing new asymptotic analysis. We additionally provide insights and asymptotic improvements on recent cryptanalysis [16] of SIKE [14] via Grover’s algorithm, demonstrating that the speedup applies to this attack and impacting upon quantum security estimates [16] incorporated into the SIKE specification [14].

scholarly journals Crypto-Archaeology: unearthing design methodology of DES s-boxes

2017 ◽  
Author(s):  
Sankhanil Dey ◽  
Ranjan Ghosh
Keyword(s):  
Boolean Function ◽  
Boolean Functions ◽  
Design Methodology ◽  
Block Cipher ◽  
Block Ciphers ◽  
Public Domain ◽  
Differential Cryptanalysis ◽  
Linear Cryptanalysis ◽  
Strict Avalanche Criterion ◽  
Independence Criterion

US defence sponsored the DES program in 1974 and released it in 1977. It remained as a well-known and well accepted block cipher until 1998. Thirty-two 4-bit DES S-Boxes are grouped in eight each with four and are put in public domain without any mention of their design methodology. S-Boxes, 4-bit, 8-bit or 32-bit, find a permanent seat in all future block ciphers. In this paper, while looking into the design methodology of DES S-Boxes, we find that S-Boxes have 128 balanced and non-linear Boolean Functions, of which 102 used once, while 13 used twice and 92 of 102 satisfy the Boolean Function-level Strict Avalanche Criterion. All the S-Boxes satisfy the Bit Independence Criterion. Their Differential Cryptanalysis exhibits better results than the Linear Cryptanalysis. However, no S-Boxes satisfy the S-Box-level SAC analyses. It seems that the designer emphasized satisfaction of Boolean-Function-level SAC and S-Box-level BIC and DC, not the S-Box-level LC and SAC.

scholarly journals PRESERVATION OF STOVE HEATING IN A WOODEN HOUSE BUILT IN THE 19–20th CENTURIES IN TOMSK

2020 ◽  
Vol 22 (1) ◽  
pp. 63-74
Author(s):  
T. Yu. Reznichenko
Keyword(s):  
Design Methodology ◽  
Historical Review ◽  
Published Data ◽  
Rapid Loss ◽  
Heating Systems ◽  
Engineering Equipment ◽  
Wooden House ◽  
Research Findings ◽  
Practical Implications

Purpose: The aim of this work is to identify and collect the data on the engineering equipment routinely used for stove heating, which possesses a unique architectural potential determining its typology and preservation. Design/methodology/approach: In addition to a fullscale study, the historical review is given. This study determines the principles the stove arrangement in wooden houses. Research findings: A rapid loss of both historical wooden houses and stove heating systems is shown, which are considered to be the key elements for maintaining a valuable historical environment. A need for determining the causes of the destruction and loss of historical houses is shown. Originality/value: The research includes the not yet published data on historical houses, in particular, at the address 33, October street, Tomsk, Russia, built in the 19– 20th centuries, which is of high architectural potential. Practical implications: The results can be used in preservation of engineering equipment of stove heating in historical wooden houses.

REDUCING QUANTUM COST OF REVERSIBLE CIRCUITS FOR HOMOGENEOUS BOOLEAN FUNCTIONS

2010 ◽  
Vol 19 (07) ◽  
pp. 1423-1434 ◽  
Author(s):  
AHMED YOUNES
Keyword(s):  
Low Power ◽  
Boolean Functions ◽  
Quantum Computers ◽  
Quantum Cost ◽  
Power Devices ◽  
Computing Systems ◽  
Factorization Algorithm ◽  
Reversible Circuits

Homogeneous Boolean functions have many applications in computing systems, e.g., cryptography. This paper presents a factorization algorithm for reducing the quantum cost of the reversible circuits for that class of Boolean functions. The algorithm reduces the multi-calculation of any common parts of the circuit. This allows Homogeneous Boolean related applications to be implemented efficiently on novel computing paradigms such as quantum computers and low power devices.

Improving the quantum cost of reversible Boolean functions using reorder algorithm

2018 ◽  
Vol 17 (5) ◽  
Author(s):  
Taghreed Ahmed ◽  
Ahmed Younes ◽  
Ashraf Elsayed
Keyword(s):  
Boolean Functions ◽  
Quantum Cost

scholarly journals Optimal ILP-Based Approach for Gate Location Assignment and Scheduling in Quantum Circuits

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Naser Mohammadzadeh ◽  
Tayebeh Bahreini ◽  
Hossein Badri
Keyword(s):  
Circuit Design ◽  
Design Methodology ◽  
Ion Trap ◽  
Quantum Circuit ◽  
Physical Design ◽  
Quantum Circuits ◽  
Mixed Integer ◽  
Routing And Scheduling ◽  
Design And Synthesis ◽  
Proposed Model

Physical design and synthesis are two key processes of quantum circuit design methodology. The physical design process itself decomposes into scheduling, mapping, routing, and placement. In this paper, a mathematical model is proposed for mapping, routing, and scheduling in ion-trap technology in order to minimize latency of the circuit. The proposed model which is a mixed integer linear programming (MILP) model gives the optimal locations for gates and the best sequence of operations in terms of latency. Experimental results show that our scheme outperforms the other schemes for the attempted benchmarks.

Successful rebounds: how firms overcome their middle age crisis

2018 ◽  
Vol 39 (3) ◽  
pp. 3-8
Author(s):  
Candace Ten Brink ◽  
Betsy D. Gelb ◽  
Robert Keller
Keyword(s):  
Design Methodology ◽  
New Products ◽  
Published Data ◽  
Regression Analyses ◽  
Organizational Changes ◽  
Content Type ◽  
Technology Firms ◽  
Industry Performance ◽  
Performance Decline ◽  
Practical Implications

Purpose This paper aims to examine technology-based firms that successfully turned around a decline in performance, to report what they did and what characterized the firms themselves, relating those actions and characteristics to effective rebounds. Design/methodology/approach The authors use published data, including financial data, to examine 59 successful rebounds, and then apply regression analyses to relate firm actions and characteristics to performance. Findings Strategic moves by these firms included layoffs, new products and new inter-company relationships. However, none of those actions predicted rebound success, either individually or in combination. Successful rebounds were associated only with smaller size and a deeper decline – from exceeding the industry performance median to falling far below it. Research limitations/implications Technology firms may or may not represent all middle-aged companies in terms of authors’ implications, that a one-size-fits-all turnaround formula is unavailable. Practical implications Wise managers will therefore consider various scenarios to prepare for decline and test several if possible. Further, the finding that dramatic drops in performance are associated with successful rebounds should warn managers who think that a competitor’s major problems mean they will disappear; they may be likelier to rebound than a competitor experiencing only a mild performance decline. Originality/value Managers who think they have THE answer to decline can profit from the news that one cannot count on layoffs, on new products or on new relationships to turn around performance decline. And, the small-is-beautiful (for rebounds) result suggests rethinking the assumption that bigger is better and making organizational changes in large organizations to allow them to imitate the flexibility advantages that a smaller firm achieves.

Method for Organizing Grover's Quantum Oracle

2014 ◽  
Vol 21 (04) ◽  
pp. 1450011
Author(s):  
Hideaki Ito ◽  
Saburou Iida
Keyword(s):  
Quantum Computation ◽  
Knapsack Problem ◽  
Time Complexity ◽  
Quantum Circuit ◽  
Space Complexity ◽  
Complete Problems ◽  
Black Boxes ◽  
Np Complete ◽  
Quantum Oracle ◽  
Toffoli Gates

In a quantum computation, some algorithms use oracles (black boxes) for abstract computational objects. This paper presents an example for organizing Grover's quantum oracle by synthesizing several unitary gates such as CNOT gates, Toffoli gates, and Hadamard gates. As an example, we show a concrete quantum circuit for the knapsack problem, which belongs to the class of NP-complete problems. The time complexity of an oracle for the knapsack problem is estimated to be O(n2), where n is the number of variables. And the same order is obtained for space complexity.

QUANTUM CIRCUITS FOR PROBABILISTIC ENTANGLEMENT TELEPORTATION VIA A PARTIALLY ENTANGLED PAIR

2007 ◽  
Vol 05 (05) ◽  
pp. 717-728 ◽  
Author(s):  
XIU-BO CHEN ◽  
QIAO-YAN WEN ◽  
FU-CHEN ZHU
Keyword(s):  
Quantum Circuit ◽  
The Other ◽  
Quantum Circuits ◽  
Entangled State ◽  
Practical Realization ◽  
Entanglement Teleportation ◽  
Probabilistic Teleportation ◽  
Partially Entangled State ◽  
Positive Operator Valued Measure ◽  
Many Particles

It deserves mentioning that the quantum circuit, i.e. quantum logic network, is essential to the practical realization of teleportation in experiment. Using only one partially entangled pair, we first propose two novel strategies for probabilistically teleporting any partially entangled state of a bipartite system. The feature of the present protocol is to weaken the requirement for the quantum channel, and also to cut down the number of entangled particles initially shared by the sender and receiver. On the other hand, we explicitly construct the generalized measurement described by the positive operator-valued measure (POVM). Two kinds of efficient quantum circuits for implementing the teleportation are offered. In addition, we generalize the two-particle probabilistic teleportation to the system of many particles.

scholarly journals Properties of the Reed-Muller spectrum of symmetric functions

2007 ◽  
Vol 20 (3) ◽  
pp. 281-294
Author(s):  
Claudio Moraga ◽  
Radomir Stankovic
Keyword(s):  
Boolean Functions ◽  
Symmetric Functions ◽  
Spectral Domain

Different forms of symmetry based on cofactors of Boolean functions are characterized in the Reed Muller spectral domain. Furthermore it is shown that if the arguments of the function are reordered, the permutation that is needed on the truth vector applies also on the spectrum of the function.

Sign in / Sign up

Export Citation Format

Share Document