Related papers: Minimum Synthesis Cost of CNOT Circuits
We investigate quantum circuits built from arbitrary single-qubit operations combined with programmable all-to-all multiqubit entangling gates that are native to, among other systems, trapped-ion quantum computing platforms. We report a…
In this paper, we study the close relationship between Reed-Muller codes and single-qubit phase gates from the perspective of $T$-count optimization. We prove that minimizing the number of $T$ gates in an $n$-qubit quantum circuit over CNOT…
Existing quantum compilers optimize quantum circuits by applying circuit transformations designed by experts. This approach requires significant manual effort to design and implement circuit transformations for different quantum devices,…
We give an overview of the circuit optimisation methods used by tket, a compiler system for quantum software developed by Cambridge Quantum Computing Ltd. We focus on a novel technique based around phase gadgets, a family of multi-qubit…
The synthesis approaches for quantum circuits typically aim at minimizing the number of lines or gates. Given the tight restrictions on those logical resources in physical implementations, we propose to view the problem fundamentally…
A common approach to quantum circuit transformation is to use the properties of a specific gate set to create an efficient representation of a given circuit's unitary, such as a parity matrix or stabiliser tableau, and then resynthesise an…
A large-scale quantum circuit can be partitioned into multiple subcircuits through circuit cutting, where each subcircuit is executed multiple times and the expectation value of the original circuit is reconstructed by classical…
We present a quantum synthesis algorithm designed to produce short circuits and to scale well in practice. The main contribution is a novel representation of circuits able to encode placement and topology using generic "gates", which allows…
Quantum circuits of a general quantum gate acting on multiple $d$-level quantum systems play a prominent role in multi-valued quantum computation. We first propose a new recursive Cartan decomposition of semi-simple unitary Lie group…
Although many of works have been done in multivalued quantum logic synthesis, the question whether multivalued quantum circuits are more efficient than the conventional binary quantum circuits is still open. In this article we devote to the…
Quantum circuit synthesis is the process in which an arbitrary unitary operation is decomposed into a sequence of gates from a universal set, typically one which a quantum computer can implement both efficiently and fault-tolerantly. As…
In this paper we study the Clifford+Toffoli universal fault-tolerant gate set. We introduce a generating set in order to represent any unitary implementable by this gate set and with this we derive a bound on the Toffoli-count of arbitrary…
As quantum computing resources remain scarce and error rates high, minimizing the resource consumption of quantum circuits is essential for achieving practical quantum advantage. Here we consider the natural problem of, given a circuit $C$,…
In the noisy intermediate-scale quantum era, mid-circuit measurement and reset operations facilitate novel circuit optimization strategies by reducing a circuit's qubit count in a method called resizing. This paper introduces two such…
Optimizing quantum circuits by reducing circuit depth is essential for improving the efficiency and scalability of quantum algorithms, particularly as quantum hardware continues to evolve. This can be achieved by restructuring quantum…
Let $n\geq 8$ be divisible by 4. The Clifford-cyclotomic gate set $\mathcal{G}_n$ is the universal gate set obtained by extending the Clifford gates with the $z$-rotation $T_n = \mathrm{diag}(1,\zeta_n)$, where $\zeta_n$ is a primitive…
Reversible computation is one of the most promising emerging technologies of the future. The usage of reversible circuits in computing devices can lead to a significantly lower power consumption. In this paper we study reversible logic…
We study in detail the algebraic structures underlying quantum circuits generated by CNOT gates. Our results allow us to propose polynomial-time heuristics to reduce the number of gates used in a given CNOT circuit and we also give…
We present an algorithm for computing depth-optimal decompositions of logical operations, leveraging a meet-in-the-middle technique to provide a significant speed-up over simple brute force algorithms. As an illustration of our method we…
Since an n-qubit circuit consisting of CNOT gates can have up to $\Omega(n^2/\log{n})$ CNOT gates, it is natural to expect that $\Omega(n^2/\log{n})$ Toffoli gates are needed to apply a controlled version of such a circuit. We show that the…