Quantum computers are able to perform certain calculations exponentially faster than classical computers, a property referred to as quantum advantage. However, understanding the origin of quantum advantage remains challenging. One method to tackle this challenge is to partition the components of a quantum computer (e.g., states, operations, measurements) into two subsets: those that implement computations that are efficiently simulatable by a classical computer, i.e., that do not provide quantum advantage, and those that are, in principle, capable of promoting such simulatable architectures to a universal quantum computer, also called resources.
Using this approach it is natural to ask whether there exists a sufficient condition for an arbitrary quantum state to promote an otherwise simulatable subset of quantum circuits to universality, hence enabling exponentially faster computations. Although this question has been answered for quantum architectures based on two-level systems (or “qubits”), until now no sufficient condition has existed for quantum computers based on systems with infinite levels, also called continuous-variable systems, such as the quantized electromagnetic field. In this work, we provide a sufficient condition for universality, and hence for quantum advantage, for continuous-variable quantum computers.
To achieve this goal, we establish a connection between these two types of architectures. Using ideas from quantum error correction, we formulate a general framework for mapping continuous-variable states onto qubit states, proving two main results. First, we provide a resource-theory grounded interpretation of these mappings, thereby showing that they yield a rigorous way to extract qubit quantum information from a continuous-variable state. Second, we use known results in the resource theory of quantum computation for qubits to establish our sufficient criterion for continuous-variable states. Beyond these findings we expect that the connection between continuous-variable and qubit settings unveiled here may prove fruitful in addressing other quantum-advantage-related questions.
https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.5.020337
