Abstract
Every quantum algorithm is represented by set of quantum circuits. Any optimization scheme for a quantum algorithm and quantum computation is very important especially in the arena of quantum computation with limited number of qubit resources. Major obstacle to this goal is the large number of elemental quantum gates to build even small quantum circuits. Here, we propose and demonstrate a general technique that significantly reduces the number of elemental gates to build quantum circuits. This is impactful for the design of quantum circuits, and we show below this could reduce the number of gates by 60% and 46% for the four- and five-qubit Toffoli gates, two key quantum circuits, respectively, as compared with simplest known decomposition. Reduced circuit complexity often goes hand-in-hand with higher efficiency and bandwidth. The quantum circuit optimization technique proposed in this work would provide a significant step forward in the optimization of quantum circuits and quantum algorithms, and has the potential for wider application in quantum computation.
Highlights
Every quantum algorithm is represented by set of quantum circuits
The efficient design of quantum circuits for processing quantum information is a fundamental problem in quantum algorithm design and quantum computation because qubits are very expensive resources[12,13,14,15,16,17,18,19,20,21,22]
The present results offer an efficient methodology for the design of complex quantum circuits which are the building blocks of quantum computers and quantum information processors
Summary
Every quantum algorithm is represented by set of quantum circuits. Any optimization scheme for a quantum algorithm and quantum computation is very important especially in the arena of quantum computation with limited number of qubit resources. The efficient design of quantum circuits for processing quantum information is a fundamental problem in quantum algorithm design and quantum computation because qubits are very expensive resources[12,13,14,15,16,17,18,19,20,21,22] This is especially important in the regime of quantum computation with limited number of q ubits[13,14,15,16,17,18,19,20,21,22]. In the case of the conventional logic design there is an efficient method called the Karnaugh map[32] Applying this method to simplify quantum circuits is nontrivial because the representation of the quantum state evolution in Hilbert space by classical Boolean algebra through Karnaugh map is not quite s traightforward[33,34]. For simplicity, we denote I and O for the identity and null 2 × 2 matrices in 2-dimensional Hilbert space, rssettaasttpeeessc||t10i00v elaaynn. ddIn||10t11h i ; ,srrceeosspmpeepccattiicvvtee2llyy-..qOLuibnkieetwcnaoisnteae,txtiohpnea,nftidrhsCet f1ai(nrUsdt)atihnnedtshteheceocsnoemdcocpnoadlcutcmqounlubomitfnb1 ̃aosf2isc0 ̃aosr2rfceoosllprorowenssdp.sontodsthtoe two two qubit qubit
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