Universal Quantum Circuit of Near-Trivial Transformations

TL;DR

This paper develops universal quantum circuits capable of approximating any single-qubit or near-trivial transformation with arbitrary precision, advancing the design of universal quantum computers.

Contribution

It constructs universal quantum circuits for single-qubit rotations and extends to n-qubit near-trivial transformations, using encoded ancillary inputs.

Findings

Universal circuits for $R_y( heta)$ and $R_z( heta)$ with arbitrary precision.

Construction of a universal quantum circuit for any n-qubit near-trivial transformation.

Circuit outputs include a bit string encoding the transformation and the transformation result.

Abstract

Any unitary transformation can be decomposed into a product of a group of near-trivial transformations. We investigate in details the construction of universal quantum circuit of near trivial transformations. We first construct two universal quantum circuits which can implement any single-qubit rotation $R_y(\theta)$ and $R_z(\theta)$ within any given precision, and then we construct universal quantum circuit implementing any single-qubit transformation within any given precision. Finally, a universal quantum circuit implementing any $n$-qubit near-trivial transformation is constructed using the universal quantum circuits of $R_y(\theta)$ and $R_z(\theta)$. In the universal quantum circuit presented, each quantum transformation is encoded to a bit string which is used as ancillary inputs. The output of the circuit consists of the related bit string and the result of near-trivial transformation. Our result may be useful for the design of universal quantum computer in the future.