Tight Bounds on the Synthesis of 3-bit Reversible Circuits: NFT Library

The reversible circuit synthesis problem can be reduced to permutation group. This allows Schreier-Sims Algorithm for the strong generating set-finding problem to be used to find tight bounds on the synthesis of 3-bit reversible circuits using the NFT library. The tight bounds include the maximum and minimum length of 3-bit reversible circuits, the maximum and minimum cost of 3-bit reversible circuits. The analysis shows better results than that found in the literature for the lower bound of the cost. The analysis also shows that there are 1960 universal reversible sub-libraries from the main NFT library.Comment: 18 pages. arXiv admin note: text overlap with arXiv:1101.438

The block-ZXZ synthesis of an arbitrary quantum circuit

Given an arbitrary $2^w \times 2^w$ unitary matrix $U$, a powerful matrix decomposition can be applied, leading to four different syntheses of a $w$-qubit quantum circuit performing the unitary transformation. The demonstration is based on a recent theorem by F\"uhr and Rzeszotnik, generalizing the scaling of single-bit unitary gates ($w=1$) to gates with arbitrary value of~$w$. The synthesized circuit consists of controlled 1-qubit gates, such as NEGATOR gates and PHASOR gates. Interestingly, the approach reduces to a known synthesis method for classical logic circuits consisting of controlled NOT gates, in the case that $U$ is a permutation matrix.Comment: Improved (non-sinkhorn) algorithm to obtain the proposed circui

Almost-classical quantum computers

By means of a subgroup of the 2 X 2 unitary matrices, i.e. a subgroup Q of U(2), acting on a single qubit, we create a group X, acting on w qubits. If Q equals the group of order 2 consisting of the follower and the inverter, we recover S_{2^w}, i.e. the permutation matrices describing a classical reversible computer acting on w bits. If Q is another group of two 2 X 2 matrices, then a new kind of computing appears

Programming Quantum Computers Using Design Automation

Recent developments in quantum hardware indicate that systems featuring more than 50 physical qubits are within reach. At this scale, classical simulation will no longer be feasible and there is a possibility that such quantum devices may outperform even classical supercomputers at certain tasks. With the rapid growth of qubit numbers and coherence times comes the increasingly difficult challenge of quantum program compilation. This entails the translation of a high-level description of a quantum algorithm to hardware-specific low-level operations which can be carried out by the quantum device. Some parts of the calculation may still be performed manually due to the lack of efficient methods. This, in turn, may lead to a design gap, which will prevent the programming of a quantum computer. In this paper, we discuss the challenges in fully-automatic quantum compilation. We motivate directions for future research to tackle these challenges. Yet, with the algorithms and approaches that exist today, we demonstrate how to automatically perform the quantum programming flow from algorithm to a physical quantum computer for a simple algorithmic benchmark, namely the hidden shift problem. We present and use two tool flows which invoke RevKit. One which is based on ProjectQ and which targets the IBM Quantum Experience or a local simulator, and one which is based on Microsoft's quantum programming language Q$\#$.Comment: 10 pages, 10 figures. To appear in: Proceedings of Design, Automation and Test in Europe (DATE 2018

A unified approach to quantum computation and classical reversible computation

The design of a quantum computer and the design of a classical computer can be based on quite similar circuit designs. The former is based on the subgroup structure of the infinite group of unitary matrices, whereas the latter is based on the subgroup structure of the finite group of permutation matrices. Because these two groups display similarities as well as differences, the corresponding circuit designs are comparable but not identical