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 Analysis and limitations of modified circuit-to-Hamiltonian constructions

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 94 ◽  
Author(s):  
Johannes Bausch ◽  
Elizabeth Crosson
Keyword(s):  
Upper Bound ◽  
Ground State ◽  
Spectral Gap ◽  
General Setting ◽  
Quantum Circuit ◽  
Many Body ◽  
Graph Diameter ◽  
Uniform Distributions ◽  
Labeled Graphs ◽  
Constant Output

Feynman's circuit-to-Hamiltonian construction connects quantum computation and ground states of many-body quantum systems. Kitaev applied this construction to demonstrate QMA-completeness of the local Hamiltonian problem, and Aharanov et al. used it to show the equivalence of adiabatic computation and the quantum circuit model. In this work, we analyze the low energy properties of a class of modified circuit Hamiltonians, which include features like complex weights and branching transitions. For history states with linear clocks and complex weights, we develop a method for modifying the circuit propagation Hamiltonian to implement any desired distribution over the time steps of the circuit in a frustration-free ground state, and show that this can be used to obtain a constant output probability for universal adiabatic computation while retaining theΩ(T−2)scaling of the spectral gap, and without any additional overhead in terms of numbers of qubits.Furthermore, we establish limits on the increase in the ground energy due to input and output penalty terms for modified tridiagonal clocks with non-uniform distributions on the time steps by proving a tightO(T−2)upper bound on the product of the spectral gap and ground state overlap with the endpoints of the computation. Using variational techniques which go beyond theΩ(T−3)scaling that follows from the usual geometrical lemma, we prove that the standard Feynman-Kitaev Hamiltonian already saturates this bound. We review the formalism of unitary labeled graphs which replace the usual linear clock by graphs that allow branching and loops, and we extend theO(T−2)bound from linear clocks to this more general setting. In order to achieve this, we apply Chebyshev polynomials to generalize an upper bound on the spectral gap in terms of the graph diameter to the context of arbitrary Hermitian matrices.

Linear Nearest Neighbor Realization of Quantum Circuits Using Clustering and Look-ahead Policy

2020 ◽  
Vol 29 (16) ◽  
pp. 2050263
Author(s):  
Anirban Bhattacharjee ◽  
Chandan Bandyopadhyay ◽  
Bappaditya Mondal ◽  
Hafizur Rahaman
Keyword(s):  
Nearest Neighbor ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Physical Realization ◽  
Emerging Trends ◽  
Look Ahead ◽  
Wide Range ◽  
Clustering Approach ◽  
On Chip ◽  
The Impact

In the last couple of years, quantum computing has come out as emerging trends of computation not only due to its immense popularity but also for its commitment towards physical realization of quantum circuit in on-chip units. At the same time, the process of physical realization has faced several design constraints and one such problem is nearest neighbor (NN) enforcement which demands all the operating qubits to be placed adjacent in the implementable circuit. Though SWAP gate embedment can transform a design into NN architecture, it still creates overhead in the design. So, designing algorithms to restrict the use of SWAPs bears high importance. Considering this fact, in this work, we are proposing a heuristic-based improved qubit placement strategy for efficient implementation of NN circuit. Two different design policies are being developed here. In the first scheme, a global reordering technique based on clustering approach is shown. In the second scheme, a local reordering technique based on look-ahead policy is developed. This look-ahead strategy considers the impact over the gates in the circuit and thereby estimates the effect using a cost metric to decide the suitable option for SWAP implementation. Furthermore, the joint use of both the ordering schemes also has been explored here. To ascertain the correctness of our design algorithms, we have tested them over a wide range of benchmarks and the obtained results are compared with some state-of-the-art design approaches. From this comparison, we have witnessed a considerable reduction on SWAP cost in our design scheme against the reported works’ results.

scholarly journals QUANTUM AUCTIONS USING ADIABATIC EVOLUTION: THE CORRUPT AUCTIONEER AND CIRCUIT IMPLEMENTATIONS

2008 ◽  
Vol 06 (04) ◽  
pp. 815-839 ◽  
Author(s):  
SAIKAT GUHA ◽  
TAD HOGG ◽  
DAVID FATTAL ◽  
TIMOTHY SPILLER ◽  
RAYMOND G. BEAUSOLEIL
Keyword(s):  
Quantum Circuit ◽  
Quantum States ◽  
Quantum Circuits ◽  
Adiabatic Evolution ◽  
Auction Algorithm ◽  
Final Measurement

We examine a proposed auction algorithm using quantum states to represent bids and distributed adiabatic search to find the winner.1 When the auctioneer follows the protocol, the final measurement giving the outcome of the auction also destroys the bid states, thereby preserving the privacy of losing bidders. We describe how a dishonest auctioneer could alter the protocol to violate this privacy guarantee, and present methods by which bidders can counter such attacks. We also suggest possible quantum circuit implementations of the auction protocol, and quantum circuits to perpetrate and to counter attacks by a dishonest auctioneer.

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 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 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.

scholarly journals Estimating Gibbs partition function with quantum Clifford sampling

2022 ◽  
Author(s):  
Yusen Wu ◽  
Jingbo B Wang
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Sampling Technique ◽  
Quantum Circuit ◽  
Quantum Systems ◽  
Quantum Circuits ◽  
Partition Functions ◽  
Stochastic Matrices ◽  
Many Body ◽  
Quantum Devices

Abstract The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum system and phenomenon. However, for interacting many-body quantum systems, its calculation generally involves summing over an exponential number of terms and can thus quickly grow to be intractable. Accurately and efficiently estimating the partition function of its corresponding system Hamiltonian then becomes the key in solving quantum many-body problems. In this paper we develop a hybrid quantumclassical algorithm to estimate the partition function, utilising a novel Clifford sampling technique. Note that previous works on quantum estimation of partition functions require O(1/ε√∆)-depth quantum circuits [17, 23], where ∆ is the minimum spectral gap of stochastic matrices and ε is the multiplicative error. Our algorithm requires only a shallow O(1)-depth quantum circuit, repeated O(n/ε2) times, to provide a comparable ε approximation. Shallow-depth quantum circuits are considered vitally important for currently available NISQ (Noisy Intermediate-Scale Quantum) devices.

Discrete-time quantum walk on circular graph: Simulations and effect of gate depth and errors

2021 ◽  
pp. 2150008
Author(s):  
Iyed Ben Slimen ◽  
Amor Gueddana ◽  
Vasudevan Lakshminarayanan
Keyword(s):  
Discrete Time ◽  
Quantum Computer ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Quantum Circuits ◽  
Time Quantum ◽  
Universal Quantum ◽  
Circuit Decomposition ◽  
Circular Graph ◽  
The Impact

We investigate the counterparts of random walks in universal quantum computing and their implementation using standard quantum circuits. Quantum walks have been recently well investigated for traversing graphs with certain oracles. We focus our study on traversing a 1D graph, namely a circle, and show how to implement a discrete-time quantum walk in quantum circuits built with universal CNOT and single qubit gates. We review elementary quantum gates and circuit decomposition techniques and propose a generalized version of all CNOT-based circuits of the quantum walk. We simulated these circuits on five different qubits IBM-Q quantum devices. This quantum computer has nonperfect gates based on superconducting qubits, and, therefore, we analyzed the impact of the CNOT errors and CNOT-depth on the fidelity of the circuit.

Demonstrating Nutrient Cost Gradients: A Brooklyn Case Study

2014 ◽  
Vol 84 (5-6) ◽  
pp. 244-251 ◽  
Author(s):  
Robert J. Karp ◽  
Gary Wong ◽  
Marguerite Orsi
Keyword(s):  
Low Income ◽  
Energy Content ◽  
Food Selection ◽  
The United States ◽  
United States Department ◽  
Micronutrient Deficiencies ◽  
Caloric Density ◽  
Low Income Families ◽  
The Cost ◽  
The Impact

Abstract. Introduction: Foods dense in micronutrients are generally more expensive than those with higher energy content. These cost-differentials may put low-income families at risk of diminished micronutrient intake. Objectives: We sought to determine differences in the cost for iron, folate, and choline in foods available for purchase in a low-income community when assessed for energy content and serving size. Methods: Sixty-nine foods listed in the menu plans provided by the United States Department of Agriculture (USDA) for low-income families were considered, in 10 domains. The cost and micronutrient content for-energy and per-serving of these foods were determined for the three micronutrients. Exact Kruskal-Wallis tests were used for comparisons of energy costs; Spearman rho tests for comparisons of micronutrient content. Ninety families were interviewed in a pediatric clinic to assess the impact of food cost on food selection. Results: Significant differences between domains were shown for energy density with both cost-for-energy (p < 0.001) and cost-per-serving (p < 0.05) comparisons. All three micronutrient contents were significantly correlated with cost-for-energy (p < 0.01). Both iron and choline contents were significantly correlated with cost-per-serving (p < 0.05). Of the 90 families, 38 (42 %) worried about food costs; 40 (44 %) had chosen foods of high caloric density in response to that fear, and 29 of 40 families experiencing both worry and making such food selection. Conclusion: Adjustments to USDA meal plans using cost-for-energy analysis showed differentials for both energy and micronutrients. These differentials were reduced using cost-per-serving analysis, but were not eliminated. A substantial proportion of low-income families are vulnerable to micronutrient deficiencies.

TRANSFER FİYATLAMA UYGULAMASININ İŞLETME PERFORMANSINA ETKİSİ VE VERGİSEL AÇIDAN DEĞERLENDİRİLMESİ

2014 ◽  
Vol 1 (2) ◽  
pp. 187
Author(s):  
Serdar KUZU
Keyword(s):  
Business Performance ◽  
Transfer Pricing ◽  
Tax Law ◽  
Economic Activities ◽  
Tax System ◽  
Goods And Services ◽  
Tax Legislation ◽  
International Transactions ◽  
The Cost ◽  
The Impact

The size of international trade continues to extend rapidly from day to day as a result of the globalization process. This situation causes an increase in the economic activities of businesses in the trading area. One of the main objectives of the cost system applied in businesses is to be able to monitor the competitors and the changes that can be occured as a result of the developments in the sector. Thus, making cost accounting that is proper according to IAS / IFRS and tax legislation has become one of the strategic targets of the companies in most countries. In this respect, businesses should form their cost and pricing systems according to new regulations. Transfer pricing practice is usefull in setting the most proper price for goods that are subject to the transaction, in evaluating the performance of the responsibility centers of business, and in determining if the inter-departmental pricing system is consistent with targets of the business. The taxing powers of different countries and also the taxing powers of different institutions in a country did not overlap. Because of this reason, bringing new regulations to the tax system has become essential. The transfer pricing practice that has been incorporated into the Turkish Tax System is one of the these regulations. The transfer pricing practice which includes national and international transactions has been included in the Corporate Tax Law and Income Tax Law. The aim of this study is to analyse the impact of goods and services transfer that will occur between departments of businesses on the responsibility center and business performance, and also the impact of transfer pricing practice on the business performance on the basis of tax-related matters. As a result of the study, it can be said that transfer pricing practice has an impact on business performance in terms of both price and tax-related matters.

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