Universal quantum computation via quantum controlled classical operations

TL;DR

This paper demonstrates that classical computation augmented with quantum control can achieve universal quantum computation, showing that even simple primitive computers can become universal with quantum control of logarithmic size.

Contribution

It introduces a computational model combining classical gates with quantum control, proving its equivalence to universal quantum computation and highlighting the power of quantum control systems.

Findings

Classical gates with quantum control can perform universal quantum computation.

A primitive computer with SWAP gates can become universal with quantum control.

Quantum control of logarithmic size enhances computational power.

Abstract

A universal set of gates for (classical or quantum) computation is a set of gates that can be used to approximate any other operation. It is well known that a universal set for classical computation augmented with the Hadamard gate results in universal quantum computing. Motivated by the latter, we pose the following question: can one perform universal quantum computation by supplementing a set of classical gates with a quantum control, and a set of quantum gates operating solely on the latter? In this work we provide an affirmative answer to this question by considering a computational model that consists of $2n$ target bits together with a set of classical gates controlled by log$(2n+1)$ ancillary qubits. We show that this model is equivalent to a quantum computer operating on $n$ qubits. Furthermore, we show that even a primitive computer that is capable of implementing only SWAP gates, can be lifted to universal quantum computing, if aided with an appropriate quantum control of logarithmic size. Our results thus exemplify the information processing power brought forth by the quantum control system.