scholarly journals Quantum arithmetic operations based on quantum fourier transform on signed integers

2020 ◽  
Vol 18 (06) ◽  
pp. 2050035
Author(s):  
Engin Şahin
Keyword(s):  
Fourier Transform ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Quantum Fourier Transform ◽  
Arithmetic Operations ◽  
Absolute Value ◽  
Addition And Subtraction ◽  
Quantum Arithmetic

The quantum Fourier transform (QFT) brings efficiency in many respects, especially usage of resource, for most operations on quantum computers. In this study, the existing QFT-based and non-QFT-based quantum arithmetic operations are examined. The capabilities of QFT-based addition and multiplication are improved with some modifications. The proposed operations are compared with the nearest quantum arithmetic operations. Furthermore, novel QFT-based subtraction, division and exponentiation operations are presented. The proposed arithmetic operations can perform nonmodular operations on all signed numbers without any limitation by using less resources. In addition, novel quantum circuits of two’s complement, absolute value and comparison operations are also presented by using the proposed QFT-based addition and subtraction operations.

scholarly journals Implementation of the quantum Fourier transform on a hybrid qubit–qutrit NMR quantum emulator

2015 ◽  
Vol 13 (07) ◽  
pp. 1550059 ◽  
Author(s):  
Shruti Dogra ◽  
Arvind Dorai ◽  
Kavita Dorai
Keyword(s):  
Fourier Transform ◽  
Quantum Algorithms ◽  
Quantum Computers ◽  
Quantum Fourier Transform ◽  
Specific Implementation ◽  
Circuit Decomposition

The quantum Fourier transform (QFT) is a key ingredient of several quantum algorithms and a qudit-specific implementation of the QFT is hence an important step toward the realization of qudit-based quantum computers. This work develops a circuit decomposition of the QFT for hybrid qudits based on generalized Hadamard and generalized controlled-phase gates, which can be implemented using selective rotations in NMR. We experimentally implement the hybrid qudit QFT on an NMR quantum emulator, which uses four qubits to emulate a single qutrit coupled to two qubits.

scholarly journals Human-Competitive Evolution of Quantum Computing Artefacts by Genetic Programming

2006 ◽  
Vol 14 (1) ◽  
pp. 21-40 ◽  
Author(s):  
Paul Massey ◽  
John A. Clark ◽  
Susan Stepney
Keyword(s):  
Fourier Transform ◽  
Quantum Computing ◽  
Genetic Programming ◽  
Quantum Algorithms ◽  
Quantum Circuits ◽  
Quantum Fourier Transform ◽  
Competitive Evolution ◽  
Specific Quantum

We show how Genetic Programming (GP) can be used to evolve useful quantum computing artefacts of increasing sophistication and usefulness: firstly specific quantum circuits, then quantum programs, and finally system-independent quantum algorithms. We conclude the paper by presenting a human-competitive Quantum Fourier Transform (QFT) algorithm evolved by GP.

scholarly journals QUANTUM PHASE ESTIMATION WITH AN ARBITRARY NUMBER OF QUBITS

2013 ◽  
Vol 11 (01) ◽  
pp. 1350008
Author(s):  
CHEN-FU CHIANG
Keyword(s):  
Fourier Transform ◽  
Quantum Computing ◽  
Diophantine Approximation ◽  
Great Difficulty ◽  
Quantum Computers ◽  
Phase Estimation ◽  
Quantum Fourier Transform ◽  
Factorization Algorithm ◽  
Simultaneous Diophantine Approximation ◽  
Parallel Circuits

Due to the great difficulty in scalability, quantum computers are limited in the number of qubits during the early stages of the quantum computing regime. In addition to the required qubits for storing the corresponding eigenvector, suppose we have additional k qubits available. Given such a constraint k, we propose an approach for the phase estimation for an eigenphase of exactly n-bit precision. This approach adopts the standard recursive circuit for quantum Fourier transform (QFT) in [R. Cleve and J. Watrous, Fast parallel circuits for quantum fourier transform, Proc. 41st Annual Symp. on Foundations of Computer Science (2000), pp. 526–536.] and adopts classical bits to implement such a task. Our algorithm has the complexity of O(n log k), instead of O(n2) in the conventional QFT, in terms of the total invocation of rotation gates. We also design a scheme to implement the factorization algorithm by using k available qubits via either the continued fractions approach or the simultaneous Diophantine approximation.

Synthesis of quantum circuits for $d$-level systems by using cosine-sine

2009 ◽  
Vol 9 (5&6) ◽  
pp. 423-443
Author(s):  
Y. Nakajima ◽  
Y. Kawano ◽  
H. Sekigawa ◽  
M. Nakanishi ◽  
S. Yamashita ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Quantum Circuit ◽  
Previous Method ◽  
Quantum Circuits ◽  
Divide And Conquer ◽  
Synthesis Methods ◽  
Quantum Fourier Transform ◽  
Asymptotically Optimal ◽  
Polynomial Size

We study the problem of designing minimal quantum circuits for any operations on $n$ qudits by means of the cosine-sine decomposition. Our method is based on a divide-and-conquer strategy. In that strategy, the size of the produced quantum circuit depends on whether the partitioning is balanced. We provide a new cosine-sine decomposition based on a balanced partitioning for $d$-level systems. The produced circuit is not asymptotically optimal except when $d$ is a power of two, but, when the number of qudits $n$ is small, our method can produce the smallest quantum circuit compared to the circuits produced by other synthesis methods. For example, when $d=3$ (three-level systems) and $n=2$ (two qudits), then the number of two-qudit operations called CINC, which is a generalized versions of CNOT, is 36 whereas the previous method needs 156 CINC gates. Moreover, we show that our method is useful for designing a polynomial-size quantum circuit for the radix-$d$ quantum Fourier transform.

scholarly journals MEASURED QUANTUM FOURIER TRANSFORM OF 1024 QUBITS ON FIBER OPTICS

2004 ◽  
Vol 02 (01) ◽  
pp. 119-131 ◽  
Author(s):  
AKIHISA TOMITA ◽  
KAZUO NAKAMURA
Keyword(s):  
Fourier Transform ◽  
Fiber Optics ◽  
Error Probability ◽  
Quantum Computers ◽  
Quantum Fourier Transform ◽  
Simple Circuit

Quantum Fourier transform (QFT) is a key function to realize quantum computers. A QFT followed by measurement was demonstrated on a simple circuit based on fiber-optics. The QFT was shown to be robust against imperfections in the rotation gate. Error probability was estimated to be 0.01 per qubit, which corresponded to error-free operation on 100 qubits. The error probability can be further reduced by taking the majority of the accumulated results. The reduction of error probability resulted in a successful QFT demonstration on 1024 qubits.

Design of New Quantum/Reversible Ternary Subtractor Circuits

2015 ◽  
Vol 25 (02) ◽  
pp. 1650014 ◽  
Author(s):  
Asma Taheri Monfared ◽  
Majid Haghparast
Keyword(s):  
Quantum Computing ◽  
Significant Role ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Computing Technology ◽  
Arithmetic Operations ◽  
Toffoli Gate ◽  
Computational Systems

Ternary quantum circuits play a significant role in future quantum computing technology because they have many advantages over binary quantum circuits. Subtraction is considered as being one of the key arithmetic operations; hence, subtractors are very essential for the construction of various computational units of quantum computers and other complex computational systems. In this paper, we have proposed the realization of a quantum reversible ternary half-subtractor circuit using a generalized ternary gate, a ternary Toffoli gate, and a ternary C2NOT gate. Based on the realization of the ternary half-subtractor, we proposed the realization of a ternary full-subtractor.

The addition and subtraction of quantum matrix based on GNEQR

2019 ◽  
Vol 17 (07) ◽  
pp. 1950056
Author(s):  
Hai-Sheng Li ◽  
Yusi Xu ◽  
Yunbai Qin ◽  
Deli Fu ◽  
Hai-Ying Xia
Keyword(s):  
Simulation Experiment ◽  
Quantum Algorithms ◽  
Simulation Method ◽  
Quantum Circuits ◽  
The Novel ◽  
Arithmetic Operations ◽  
Matrix Operations ◽  
Addition And Subtraction ◽  
Quantum Matrix ◽  
First Time

The efficient quantum circuits of arithmetic operations are important to perform quantum algorithms. To implement efficient matrix operations, we first modify the generalized model of the novel enhanced quantum representation of digital images (GNEQR) to store unsigned and signed integer matrices. Next, we design the circuits of the circuits of quantum addition, quantum modulo addition, quantum subtraction, and quantum modulo subtraction, these operations all keeping two operands unchanged. Then, we propose the circuits of quantum matrix addition, quantum matrix modulo addition, quantum matrix subtraction, and quantum matrix modulo subtraction for the first time. Furthermore, we present a simulation method to verify the correctness of the proposed arithmetic operations of matrix. The results of simulation experiment show that the propose arithmetic operations of matrix are efficient and correct.

scholarly journals Quantum Computing Concepts with Deutsch Jozsa Algorithm

2019 ◽  
Vol 3 (1) ◽  
Author(s):  
Poornima Aradyamath ◽  
Naghabhushana N M ◽  
Rohitha Ujjinimatad
Keyword(s):  
Fourier Transform ◽  
Quantum Computing ◽  
Quantum Computation ◽  
Mathematical Description ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Quantum Computers ◽  
Quantum Fourier Transform ◽  
Basic Concepts ◽  
Classical Computer

In this paper, we briefly review the basic concepts of quantum computation,  entanglement,  quantum cryptography and quantum fourier  transform.   Quantum algorithms like Deutsch Jozsa, Shor’s   factorization and Grover’s data search are developed using fourier  transform  and quantum computation concepts to build quantum computers.  Researchers are finding a way to build quantum computer that works more efficiently than classical computer.  Among the  standard well known  algorithms  in the field of quantum computation  and communication we  describe  mathematically Deutsch Jozsa algorithm  in detail for  2  and 3 qubits.  Calculation of balanced and unbalanced states is shown in the mathematical description of the algorithm.

scholarly journals Classical simulations of Abelian-group normalizer circuits with intermediate measurements

2014 ◽  
Vol 14 (3&4) ◽  
pp. 181-216
Author(s):  
Juan Bermejo-Vega ◽  
Maarten Van den Nest
Keyword(s):  
Fourier Transform ◽  
Abelian Group ◽  
Probability Distribution ◽  
Normal Form ◽  
Abelian Groups ◽  
Finite Abelian Group ◽  
Quadratic Functions ◽  
Quantum Circuits ◽  
Quantum Fourier Transform ◽  
Finite Abelian Groups

Quantum normalizer circuits were recently introduced as generalizations of Clifford circuits: a normalizer circuit over a finite Abelian group G is composed of the quantum Fourier transform (QFT) over G, together with gates which compute quadratic functions and automorphisms. In \cite{VDNest_12_QFTs} it was shown that every normalizer circuit can be simulated efficiently classically. This result provides a nontrivial example of a family of quantum circuits that cannot yield exponential speed-ups in spite of usage of the QFT, the latter being a central quantum algorithmic primitive. Here we extend the aforementioned result in several ways. Most importantly, we show that normalizer circuits supplemented with intermediate measurements can also be simulated efficiently classically, even when the computation proceeds adaptively. This yields a generalization of the Gottesman-Knill theorem (valid for n-qubit Clifford operations) to quantum circuits described by arbitrary finite Abelian groups. Moreover, our simulations are twofold: we present efficient classical algorithms to sample the measurement probability distribution of any adaptive-normalizer computation, as well as to compute the amplitudes of the state vector in every step of it. Finally we develop a generalization of the stabilizer formalism relative to arbitrary finite Abelian groups: for example we characterize how to update stabilizers under generalized Pauli measurements and provide a normal form of the amplitudes of generalized stabilizer states using quadratic functions and subgroup cosets.

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