Block-based quantum-logic synthesis (original) (raw)
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An Extended Approach for Generating Unitary Matrices for Quantum Circuits
Computers, Materials & Continua, 2019
In this paper, we do research on generating unitary matrices for quantum circuits automatically. We consider that quantum circuits are divided into six types, and the unitary operator expressions for each type are offered. Based on this, we propose an algorithm for computing the circuit unitary matrices in detail. Then, for quantum logic circuits composed of quantum logic gates, a faster method to compute unitary matrices of quantum circuits with truth table is introduced as a supplement. Finally, we apply the proposed algorithm to different reversible benchmark circuits based on NCT library (including NOT gate, Controlled-NOT gate, Toffoli gate) and generalized Toffoli (GT) library and provide our experimental results.
Quantum Circuit Synthesis using a New Quantum Logic Gate Library of NCV Quantum Gates
International Journal of Theoretical Physics, 2016
Since Controlled-Square-Root-of-NOT (CV, CV †) gates are not permutative quantum gates, many existing methods cannot effectively synthesize optimal 3-qubit circuits directly using the NOT, CNOT, Controlled-Square-Root-of-NOT quantum gate library (NCV), and the key of effective methods is the mapping of NCV gates to four-valued quantum gates. Firstly, we use NCV gates to create the new quantum logic gate library, which can be directly used to get the solutions with smaller quantum costs efficiently. Further, we present a novel generic method which quickly and directly constructs this new optimal quantum logic gate library using CNOT and Controlled-Square-Root-of-NOT gates. Finally, we present several encouraging experiments using these new permutative gates, and give a careful analysis of the method, which introduces a new idea to quantum circuit synthesis.
The pressure of fundamental limits on classical computation and the promise of exponential speedups from quantum effects have recently brought quantum circuits [10] to the attention of the Electronic Design Automation community . We discuss efficient quantum logic circuits which perform two tasks: (i) implementing generic quantum computations and (ii) initializing quantum registers. In contrast to conventional computing, the latter task is nontrivial because the state-space of an n-qubit register is not finite and contains exponential superpositions of classical bit strings. Our proposed circuits are asymptotically optimal for respective tasks and improve earlier published results by at least a factor of two.
Synthesis of quantum-logic circuits
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2006
The pressure of fundamental limits on classical computation and the promise of exponential speedups from quantum effects have recently brought quantum circuits [10] to the attention of the Electronic Design Automation community . We discuss efficient quantum logic circuits which perform two tasks: (i) implementing generic quantum computations and (ii) initializing quantum registers. In contrast to conventional computing, the latter task is nontrivial because the state-space of an n-qubit register is not finite and contains exponential superpositions of classical bit strings. Our proposed circuits are asymptotically optimal for respective tasks and improve earlier published results by at least a factor of two.
Algebraic Characterization of CNOT-Based Quantum Circuits with its Applications on Logic Synthesis
2007
The exponential speed up of quantum algorithms and the fundamental limits of current CMOS process for future design technology have directed attentions toward quantum circuits. In this paper, the matrix specification of a broad category of quantum circuits, i.e. CNOT-based circuits, are investigated. We prove that the matrix elements of CNOT-based circuits can only be zeros or ones. In addition, the columns or rows of such a matrix have exactly one element with the value of 1.
Synthesis of multi-qudit hybrid and d-valued quantum logic circuits by decomposition
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Recent research in generalizing quantum computation from 2-valued qudits to d-valued qudits has shown practical advantages for scaling up a quantum computer. A further generalization leads to quantum computing with hybrid qudits where two or more qudits have different finite dimensions. Advantages of hybrid and d-valued gates (circuits) and their physical realizations have been studied in detail by Muthukrishnan and Stroud (Physical Review A, 052309, 2000), Daboul et al. (J. Phys. A: Math. Gen. 36 2525-2536, 2003), and Bartlett et al (Physical Review A, Vol.65, 052316, 2002). In both cases, a quantum computation is performed when a unitary evolution operator, acting as a quantum logic gate, transforms the state of qudits in a quantum system. Unitary operators can be represented by square unitary matrices. If the system consists of a single qudit, then Tilma et al (J.Phys. A: Math. Gen. 35 (2002) 10467-10501) have shown that the unitary evolution matrix (gate) can be synthesized in terms of its Euler angle parameterization. However, if the quantum system consists of multiple qudits, then a gate may be synthesized by matrix decomposition techniques such as QR factorization and the Cosine-sine Decomposition (CSD). In this article, we present a CSD based synthesis method for n qudit hybrid quantum gates, and as a consequence, derive a CSD based synthesis method for n qudit gates where all the qudits have the same dimension.
Efficient decomposition of single-qubit gates into V basis circuits
Physical Review A, 2013
We develop the first constructive algorithms for compiling single-qubit unitary gates into circuits over the universal V basis. The V basis is an alternative universal basis to the more commonly studied {H, T } basis. We propose two classical algorithms for quantum circuit compilation: the first algorithm has expected polynomial time (in precision log(1/ )) and offers a depth/precision guarantee that improves upon state-of-the-art methods for compiling into the {H, T } basis by factors ranging from 1.86 to log 2 (5). The second algorithm is analogous to direct search and yields circuits a factor of 3 to 4 times shorter than our first algorithm, and requires time exponential in log(1/ ); however, we show that in practice the runtime is reasonable for an important range of target precisions.
Cost Reduction in Nearest Neighbour Based Synthesis of Quantum Boolean Circuits
Engineering Letters, 2008
Quantum computer algorithms require an 'oracle' as an integral part. An oracle is a reversible quantum Boolean circuit, where the inputs are kept unchanged at the outputs and the functional outputs are realized along ancillary input constants (0 or 1). Recently, a nearest neighbour template based synthesis method of quantum Boolean circuits has been proposed to overcome the adjacency requirement of the input qubits of physical quantum gates. The method used SWAP gates to bring the input qubits of quantum CNOT or C 2 NOT gates adjacent. In this paper, we propose cost reduction techniques such as ancillary constant determination to reduce the number of NOT gates and variable ordering and product grouping to reduce the number of SWAP gates required in nearest neighbour template based synthesis. The proposed approach significantly reduces the quantum realization cost of the synthesized quantum Boolean circuit than that of the original nearest neighbour template based synthesis.
Synthesis of ternary quantum logic circuits by decomposition
Arxiv preprint quant-ph/0511041, 2005
Recent research in multi-valued logic for quantum computing has shown practical advantages for scaling up a quantum computer. Multivalued quantum systems have also been used in the framework of quantum cryptography, and the concept of a qudit cluster state has been proposed by generalizing the qubit cluster state. An evolutionary algorithm based synthesizer for ternary quantum circuits has recently been presented, as well as a synthesis method based on matrix factorization.In this paper, a recursive synthesis method for ternary quantum circuits based on the Cosine-Sine unitary matrix decomposition is presented
Journal of Physics: Conference Series
One of the most important aspects of quantum computation is quantum entanglement, it is an interesting feature of quantum physics, and has many important applications such as quantum teleportation, cryptography, quantum computation, and dense coding. It is an essential task in quantum computing to design circuits that create an entangled system, and many circuits were implied in the quantum computers that generate the desired entangled state of a system. In this paper, we suggest a general method to design different quantum circuits that produce an entangled system for any number of qubits in different manners. Also, we apply the suggested method in order to design different 4-qubits entanglement creating circuits. The results show that it is possible to design different entanglement creating circuits for any number of qubits by following certain method that will be discussed in the paper, and in the case of 4-qubits system we are going to look only at two circuits, the first create...