Efficient Decomposition of Unitary Matrices in Quantum Circuit Compilers

Abstract

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 the translation of bigger unitary gates into elementary quantum operations, which is key to executing these algorithms on existing quantum computers. The decomposition can be used as an aggressive optimization method for the whole circuit, as well as to test part of an algorithm on a quantum accelerator. For the selection and implementation of the decomposition algorithm, perfect qubits are assumed. We base our decomposition technique on Quantum Shannon Decomposition, which generates O(344n) controlled-not gates for an n-qubit input gate. In addition, we implement optimizations to take advantage of the potential underlying structure in the input or intermediate matrices, as well as to minimize the execution time of the decomposition. Comparing our implementation to Qubiter and the UniversalQCompiler (UQC), we show that our implementation generates circuits that are much shorter than those of Qubiter and not much longer than the UQC. At the same time, it is also up to 10 times as fast as Qubiter and about 500 times as fast as the UQC.

Approaching the theoretical limit in quantum gate decomposition

“…(The execution time was measured on an Intel Core i7 CPU having 8 threads.) However, these execution times are still not competitive with current implementations of the CSD or QSD implementations [27], for larger problems than 4 qubits, the decomposition time exceeds the limit of an acceptable time scale. Still, the low CN OT gate count close to the theoretical lower limit might justify the increased execution time in many use-cases.…”

“…4 and 4.2, the SO algorithm is also applicable to optimize a gate structure on architectures with specific properties or limitations. In addition, the developed SO algorithm can be mixed with QSD to optimize the number of gates by letting the SO algorithm to decompose small unitaries generated during the QSD procedure [27].…”

“…For this reason, our implementation is not expected to be competitive in speed with other well known decomposition implementations, such as was reported in Ref. [27]. Still, in order to increase the computational performance of our implementation of the sequential optimization algorithm the solver engine was implemented in native C++/C programming language.…”

“…Recently an efficient implementation of the QSD method developed in the OpenQL [26] package was published in Ref. [27].…”

Optimisation-free Classification and Density Estimation with Quantum Circuits

“…Therefore, even though the general unitary U X is known, we need to decompose it into the primitive quantum gates of a quantum computer. Several algorithms for arbitrary unitary decomposition have been suggested [27][28][29][30]. In this work, we use the algorithm proposed in Ref.…”