Quantum Analogue Computing

TL;DR

This paper reviews quantum computing, emphasizing quantum simulation as a promising application, and discusses how quantum analogue computers could serve as efficient architectures, highlighting challenges and lessons from classical analogue computing.

Contribution

It introduces the concept of quantum analogue computers and explores their potential advantages and challenges in quantum simulation.

Findings

Quantum simulation encodes data directly in Hilbert space.

Quantum analogue computers offer an efficient architecture for simulation.

Precision and error correction are significant challenges.

Abstract

We briefly review what a quantum computer is, what it promises to do for us, and why it is so hard to build one. Among the first applications anticipated to bear fruit is quantum simulation of quantum systems. While most quantum computation is an extension of classical digital computation, quantum simulation differs fundamentally in how the data is encoded in the quantum computer. To perform a quantum simulation, the Hilbert space of the system to be simulated is mapped directly onto the Hilbert space of the (logical) qubits in the quantum computer. This type of direct correspondence is how data is encoded in a classical analogue computer. There is no binary encoding, and increasing precision becomes exponentially costly: an extra bit of precision doubles the size of the computer. This has important consequences for both the precision and error correction requirements of quantum simulation, and significant open questions remain about its practicality. It also means that the quantum version of analogue computers, continuous variable quantum computers (CVQC) becomes an equally efficient architecture for quantum simulation. Lessons from past use of classical analogue computers can help us to build better quantum simulators in future.