scholarly journals Quantum Period Finding against Symmetric Primitives in Practice

2021 ◽  
pp. 1-27
Author(s):  
Xavier Bonnetain ◽  
Samuel Jaques
Keyword(s):  
Linear Algebra ◽  
Block Cipher ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Independent Interest ◽  
Quantum Cryptanalysis ◽  
Reasonable Amount ◽  
The Cost ◽  
State Size

We present the first complete descriptions of quantum circuits for the offline Simon’s algorithm, and estimate their cost to attack the MAC Chaskey, the block cipher PRINCE and the NIST lightweight finalist AEAD scheme Elephant. These attacks require a reasonable amount of qubits, comparable to the number of qubits required to break RSA-2048. They are faster than other collision algorithms, and the attacks against PRINCE and Chaskey are the most efficient known to date. As Elephant has a key smaller than its state size, the algorithm is less efficient and its cost ends up very close to or above the cost of exhaustive search.We also propose an optimized quantum circuit for boolean linear algebra as well as complete reversible implementations of PRINCE, Chaskey, spongent and Keccak which are of independent interest for quantum cryptanalysis. We stress that our attacks could be applied in the future against today’s communications, and recommend caution when choosing symmetric constructions for cases where long-term security is expected.

scholarly journals Qulacs: a fast and versatile quantum circuit simulator for research purpose

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 559
Author(s):  
Yasunari Suzuki ◽  
Yoshiaki Kawase ◽  
Yuya Masumura ◽  
Yuria Hiraga ◽  
Masahiro Nakadai ◽  
...  
Keyword(s):  
Fault Tolerant ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Research Purpose ◽  
Numerical Techniques ◽  
Circuit Simulator ◽  
Speed Up ◽  
Near Term

To explore the possibilities of a near-term intermediate-scale quantum algorithm and long-term fault-tolerant quantum computing, a fast and versatile quantum circuit simulator is needed. Here, we introduce Qulacs, a fast simulator for quantum circuits intended for research purpose. We show the main concepts of Qulacs, explain how to use its features via examples, describe numerical techniques to speed-up simulation, and demonstrate its performance with numerical benchmarks.

scholarly journals A co-design framework of neural networks and quantum circuits towards quantum advantage

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Weiwen Jiang ◽  
Jinjun Xiong ◽  
Yiyu Shi
Keyword(s):  
Neural Network ◽  
Cost Reduction ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Design Framework ◽  
Unitary Matrices ◽  
Classical Computing ◽  
Classical Computer ◽  
The Cost

AbstractDespite the pursuit of quantum advantages in various applications, the power of quantum computers in executing neural network has mostly remained unknown, primarily due to a missing tool that effectively designs a neural network suitable for quantum circuit. Here, we present a neural network and quantum circuit co-design framework, namely QuantumFlow, to address the issue. In QuantumFlow, we represent data as unitary matrices to exploit quantum power by encoding n = 2k inputs into k qubits and representing data as random variables to seamlessly connect layers without measurement. Coupled with a novel algorithm, the cost complexity of the unitary matrices-based neural computation can be reduced from O(n) in classical computing to O(polylog(n)) in quantum computing. Results show that on MNIST dataset, QuantumFlow can achieve an accuracy of 94.09% with a cost reduction of 10.85 × against the classical computer. All these results demonstrate the potential for QuantumFlow to achieve the quantum advantage.

scholarly journals ON THE GAP OF HAMILTONIANS FOR THE ADIABATIC SIMULATION OF QUANTUM CIRCUITS

2013 ◽  
Vol 11 (07) ◽  
pp. 1350063 ◽  
Author(s):  
ANAND GANTI ◽  
ROLANDO SOMMA
Keyword(s):  
Upper Bound ◽  
Spectral Gap ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Search Problem ◽  
Adiabatic Evolution ◽  
Unstructured Search ◽  
Time Quantum ◽  
The Cost ◽  
The Impact

The time or cost of simulating a quantum circuit by adiabatic evolution is determined by the spectral gap of the Hamiltonians involved in the simulation. In "standard" constructions based on Feynman's Hamiltonian, such a gap decreases polynomially with the number of gates in the circuit, L. Because a larger gap implies a smaller cost, we study the limits of spectral gap amplification in this context. We show that, under some assumptions on the ground states and the cost of evolving with the Hamiltonians (which apply to the standard constructions), an upper bound on the gap of the order 1/L follows. In addition, if the Hamiltonians satisfy a frustration-free property, the upper bound is of the order 1/L2. Our proofs use recent results on adiabatic state transformations, spectral gap amplification, and the simulation of continuous-time quantum query algorithms. They also consider a reduction from the unstructured search problem, whose lower bound in the oracle cost translates into the upper bounds in the gaps. The impact of our results is that improving the gap beyond that of standard constructions (i.e. 1/L2), if possible, is challenging.

scholarly journals F-Divergences and Cost Function Locality in Generative Modelling with Quantum Circuits

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1281
Author(s):  
Chiara Leadbeater ◽  
Louis Sharrock ◽  
Brian Coyle ◽  
Marcello Benedetti
Keyword(s):  
Fault Tolerant ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Quantum Devices ◽  
Leibler Divergence ◽  
Variation Distance ◽  
Near Term ◽  
Generative Modelling

Generative modelling is an important unsupervised task in machine learning. In this work, we study a hybrid quantum-classical approach to this task, based on the use of a quantum circuit born machine. In particular, we consider training a quantum circuit born machine using f-divergences. We first discuss the adversarial framework for generative modelling, which enables the estimation of any f-divergence in the near term. Based on this capability, we introduce two heuristics which demonstrably improve the training of the born machine. The first is based on f-divergence switching during training. The second introduces locality to the divergence, a strategy which has proved important in similar applications in terms of mitigating barren plateaus. Finally, we discuss the long-term implications of quantum devices for computing f-divergences, including algorithms which provide quadratic speedups to their estimation. In particular, we generalise existing algorithms for estimating the Kullback–Leibler divergence and the total variation distance to obtain a fault-tolerant quantum algorithm for estimating another f-divergence, namely, the Pearson divergence.

scholarly journals FPGA Based Hardware Abstraction of Quantum Computing System

2021 ◽  
Author(s):  
Madiha Khalid ◽  
Najam ul Islam MUHAMMAD ◽  
Umar Mujahid Khokhar ◽  
Atif Jafri ◽  
Hongsik Choi
Keyword(s):  
Quantum Computing ◽  
Embedded System ◽  
Computing System ◽  
Quantum Circuit ◽  
Atomic Scale ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Chip Design ◽  
Computational Resources ◽  
The Cost

Abstract The number of transistors per unit area are increasing every year by virtue of Moore’s law. It is estimated that the current rate of evolution in the field of chip design will reduce the transistor to atomic scale by 2024. At atomic level the quantum mechanical characteristics dominate, affecting the ability of transistors to store information in the form of bits. The quantum computers have been proposed as one way to effectively deal with this predicament. The quantum computing circuits utilize the spinning characteristics of electron to store information. This paper describes a proposition of resource efficient FPGA based quantum circuit abstraction. A non-programmable embedded system capable of storing, introducing a phase shift in the qubit and its measurement is implemented. The main objective of the proposed abstraction is to provide a FPGA based platform comprising of fundamental sub blocks for designing quantum circuits. A primary quantum key distribution algorithm i.e BB84 is implemented on the proposed platform as a proof of concept. The distinguishing feature of the proposed design is the flexibility to enhance the quantum circuit emulation accuracy at the cost of computational resources. The proposed emulation exhibits two principal properties of the quantum computing i.e. parallelism and probabilistic measurement.

Primary varicose veins

Phlebologie ◽  
2010 ◽  
Vol 39 (03) ◽  
pp. 133-137
Author(s):  
H. Partsch
Keyword(s):  
Varicose Veins ◽  
Compression Therapy ◽  
Daily Practice ◽  
Clinical Severity ◽  
Compression Stockings ◽  
Primary Varicose Veins ◽  
The Cost ◽  
Convincing Data ◽  
Long Term Studies

SummaryBackground: Compression stockings are widely used in patients with varicose veins. Methods: Based on published literature three main points are discussed: 1. the rationale of compression therapy in primary varicose veins, 2. the prescription of compression stockings in daily practice, 3. studies required in the future. Results: The main objective of prescribing compression stockings for patients with varicose veins is to improve subjective leg complaints and to prevent swelling after sitting and standing. No convincing data are available concerning prevention of progression or of complications. In daily practice varicose veins are the most common indication to prescribe compression stockings. The compliance depends on the severity of the disorder and is rather poor in less severe stages. Long-term studies are needed to proof the cost-effectiveness of compression stockings concerning subjective symptoms and objective signs of varicose veins adjusted to their clinical severity. Conclusion: Compression stockings in primary varicose veins are able to improve leg complaints and to prevent swelling.

An Evaluation of Provincial Macroeconomic Performance in Vietnam

2017 ◽  
pp. 34-47
Author(s):  
Hoi Le Quoc ◽  
Nam Pham Xuan ◽  
Tuan Nguyen Anh
Keyword(s):  
Development Strategy ◽  
Institutional Transformation ◽  
Economic Indicators ◽  
Macroeconomic Performance ◽  
Economic Development Strategy ◽  
Socio Economic Development ◽  
The Cost ◽  
Development Objectives ◽  
First Time

The study was targeted at developing a methodology for constructing a macroeconomic performance index at a provincial level for the first time in Vietnam based on 4 groups of measurements: (i) Economic indicators; (ii) oriented economic indicators; (iii) socio-economic indicators; and (iv) economic - social – institutional indicators. Applying the methodology to the 2011 - 2015 empirical data of all provinces in Vietnam, the research shows that the socio-economic development strategy implemented by those provinces did not provide balanced outcomes between growth and social objectives, sustainability and inclusiveness. Many provinces focused on economic growth at the cost of structural change, equality and institutional transformation. In contrast, many provinces were successful in improving equality but not growth. Those facts threaten the long-term development objectives of the provinces.

scholarly journals Connectivity matrix model of quantum circuits and its application to distributed quantum circuit optimization

2021 ◽  
Vol 20 (7) ◽  
Author(s):  
Ismail Ghodsollahee ◽  
Zohreh Davarzani ◽  
Mariam Zomorodi ◽  
Paweł Pławiak ◽  
Monireh Houshmand ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Quantum Computer ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Connectivity Matrix ◽  
Circuit Optimization ◽  
Novel Approach ◽  
The Matrix ◽  
Minimum Number ◽  
Two Phases

AbstractAs quantum computation grows, the number of qubits involved in a given quantum computer increases. But due to the physical limitations in the number of qubits of a single quantum device, the computation should be performed in a distributed system. In this paper, a new model of quantum computation based on the matrix representation of quantum circuits is proposed. Then, using this model, we propose a novel approach for reducing the number of teleportations in a distributed quantum circuit. The proposed method consists of two phases: the pre-processing phase and the optimization phase. In the pre-processing phase, it considers the bi-partitioning of quantum circuits by Non-Dominated Sorting Genetic Algorithm (NSGA-III) to minimize the number of global gates and to distribute the quantum circuit into two balanced parts with equal number of qubits and minimum number of global gates. In the optimization phase, two heuristics named Heuristic I and Heuristic II are proposed to optimize the number of teleportations according to the partitioning obtained from the pre-processing phase. Finally, the proposed approach is evaluated on many benchmark quantum circuits. The results of these evaluations show an average of 22.16% improvement in the teleportation cost of the proposed approach compared to the existing works in the literature.

scholarly journals Efficient Implementation of PRESENT and GIFT on Quantum Computers

2021 ◽  
Vol 11 (11) ◽  
pp. 4776
Author(s):  
Kyungbae Jang ◽  
Gyeongju Song ◽  
Hyunjun Kim ◽  
Hyeokdong Kwon ◽  
Hyunji Kim ◽  
...  
Keyword(s):  
Block Cipher ◽  
Search Algorithm ◽  
Block Ciphers ◽  
Quantum Circuits ◽  
Security Level ◽  
Symmetric Key ◽  
Grover Search ◽  
Target Block ◽  
Symmetric Key Cryptography ◽  
Grover Search Algorithm

Grover search algorithm is the most representative quantum attack method that threatens the security of symmetric key cryptography. If the Grover search algorithm is applied to symmetric key cryptography, the security level of target symmetric key cryptography can be lowered from n-bit to n2-bit. When applying Grover’s search algorithm to the block cipher that is the target of potential quantum attacks, the target block cipher must be implemented as quantum circuits. Starting with the AES block cipher, a number of works have been conducted to optimize and implement target block ciphers into quantum circuits. Recently, many studies have been published to implement lightweight block ciphers as quantum circuits. In this paper, we present optimal quantum circuit designs of symmetric key cryptography, including PRESENT and GIFT block ciphers. The proposed method optimized PRESENT and GIFT block ciphers by minimizing qubits, quantum gates, and circuit depth. We compare proposed PRESENT and GIFT quantum circuits with other results of lightweight block cipher implementations in quantum circuits. Finally, quantum resources of PRESENT and GIFT block ciphers required for the oracle of the Grover search algorithm were estimated.

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