Related papers: Minimum Synthesis Cost of CNOT Circuits
Most work in quantum circuit optimization has been performed in isolation from the results of quantum fault-tolerance. Here we present a polynomial-time algorithm for optimizing quantum circuits that takes the actual implementation of…
While a couple of impressive quantum technologies have been proposed, they have several intrinsic limitations which must be considered by circuit designers to produce realizable circuits. Limited interaction distance between gate qubits is…
We focus on the depth optimization of CNOT circuits on hardwares with limited connectivity. We adapt the algorithm from Kutin et al. that implements any $n$-qubit CNOT circuit in depth at most $5n$ on a Linear Nearest Neighbour (LNN)…
We present new optimal and heuristic algorithms for exact synthesis of multi-qubit unitaries and isometries. For example, our algorithms find Clifford and T circuits for unitaries with entries in $\mathbb{Z}[i,1/\sqrt{2}]$. The optimal…
We present an algorithm that decomposes any $n$-qubit Clifford operator into a circuit consisting of three subcircuits containing only CNOT or CPHASE gates with layers of one-qubit gates before and after each of these subcircuits. As with…
We report optimal and asymptotically optimal reversible circuits composed of NOT, CNOT, and Toffoli (NCT) gates, keeping the count by the subsets of the gate types used. This study fine tunes the circuit complexity figures for the…
Although quantum computers have the potential to efficiently solve certain problems considered difficult by known classical approaches, the design of a quantum circuit remains computationally difficult. It is known that the optimal gate…
We propose a method of compiling that permits to identify quantum circuits able to simulate arbitrary $n$-qubit unitary operations via the adjustment of angles in single-qubit gates therein. The method of compiling itself extends older…
Optimal synthesis of reversible functions is a non-trivial problem. One of the major limiting factors in computing such circuits is the sheer number of reversible functions. Even restricting synthesis to 4-bit reversible functions results…
This paper examines QAOA in the context of parity network synthesis. We propose a pair of algorithms for parity network synthesis and linear circuit inversion. Together, these algorithms can build the diagonal component of the QAOA circuit,…
The paper discusses various applications of permutation group theory in the synthesis of reversible logic circuits consisting of Toffoli gates with negative control lines. An asymptotically optimal synthesis algorithm for circuits…
Optimal synthesis of reversible functions is a non-trivial problem. One of the major limiting factors in computing such circuits is the sheer number of reversible functions. Even restricting synthesis to 4-bit reversible functions results…
Unitary decomposition is a widely used method to map quantum algorithms to an arbitrary set of quantum gates. Efficient implementation of this decomposition allows for translation of bigger unitary gates into elementary quantum operations,…
What is the time-optimal way of realizing quantum operations? Here, we show how important instances of this problem can be related to the study of shortest paths on the surface of a sphere under a special metric. Specifically, we provide an…
This paper considers the problem of quantum compilation from an optimization perspective by fixing a circuit structure of CNOTs and rotation gates then optimizing over the rotation angles. We solve the optimization problem classically and…
We present quantum circuits for comparison and increment operations that achieve an asymptotically optimal gate count of $\Theta(n)$ and depth of $\Theta(\log n)$ over the Clifford+Toffoli gate set, while using a provably minimal number of…
We investigate the problem of synthesizing T-depth optimal quantum circuits over the Clifford+T gate set. First we construct a special subset of T-depth 1 unitaries, such that it is possible to express the T-depth-optimal decomposition of…
Before executing a quantum algorithm, one must first decompose the algorithm into machine-level instructions compatible with the architecture of the quantum computer, a process known as quantum compiling. There are many different quantum…
IBM has made several quantum computers available to researchers around the world via cloud services. Two architectures with five qubits, one with 16, and one with 20 qubits are available to run experiments. The IBM architectures implement…
With the successful demonstration of transversal CNOTs in many recent experiments, it is the right moment to examine its implications on one of the most critical parts of fault-tolerant computation -- magic state preparation. Using an…