Compare Papers
Paper 1
Minimization of AND-XOR Expressions with Decoders for Quantum Circuits
Sonia Yang, Ali Al-Bayaty, Marek Perkowski
- Year
- 2026
- Journal
- arXiv preprint
- DOI
- arXiv:2601.02515
- arXiv
- 2601.02515
This paper introduces a new logic structure for reversible quantum circuit synthesis. Our synthesis method aims to minimize the quantum cost of reversible quantum circuits with decoders. In this method, multi-valued input, binary output (MVI) functions are utilized as a mathematical concept only, but the circuits are binary. We introduce the new concept of ``Multi-Valued Input Fixed Polarity Reed-Muller (MVI-RM)" forms. Our decoder-based circuit uses three logical levels in contrast to commonly-used methods based on Exclusive-or Sum of Products (ESOP) with two levels (AND-XOR expressions), realized by Toffoli gates. In general, the high number of input qubits in the resulting Toffoli gates is a problem that greatly impacts the quantum cost. Using decoders decreases the number of input qubits in these Toffoli gates. We present two practical algorithms for three-level circuit synthesis by finding the MVI-FPRM: products-matching and the newly developed butterfly diagrams. The best MVI-FPRM forms are factorized and reduced to approximate Multi-Valued Input Generalized Reed-Muller (MVI-GRM) forms.
Open paperPaper 2
Synthesis of Arbitrary Quantum Circuits to Topological Assembly: Systematic, Online and Compact
Alexandru Paler, Austin G. Fowler, Robert Wille
- Year
- 2017
- Journal
- arXiv preprint
- DOI
- arXiv:1711.01387
- arXiv
- 1711.01387
It is challenging to transform an arbitrary quantum circuit into a form protected by surface code quantum error correcting codes (a variant of topological quantum error correction), especially if the goal is to minimise overhead. One of the issues is the efficient placement of magic state distillation sub circuits, so-called distillation boxes, in the space-time volume that abstracts the computation's required resources. This work presents a general, systematic, online method for the synthesis of such circuits. Distillation box placement is controlled by so-called schedulers. The work introduces a greedy scheduler generating compact box placements. The implemented software, whose source code is available online, is used to illustrate and discuss synthesis examples. Synthesis and optimisation improvements are proposed.
Open paper