Riverlane researchers have transformed a previously error-prone quantum application into a fault-tolerant (aka error-resilient) set of instructions.

While quantum computers promise to solve many applications significantly faster than modern computers, current quantum devices are significantly hindered by noise.

Quantum error correction can help reduce this noise, but there is a significant gap between what is achievable on current quantum hardware and what many applications require.

This new work bridges this gap by constructing an error-correcting experiment for simulating the hydrogen molecule. It also provides key insights on how to make early fault-tolerant quantum computing useful.

The paper *Compilation of a simple chemistry application to quantum error correction primitives* was published last week in Physical Review Research. It is another step on Riverlane’s road to solve quantum error correction across multiple qubit types.

**The problem with errors**

Today’s quantum computers make approximately one error every few hundred quantum operations. But to unlock world-changing use cases will require billions of reliable quantum operations, or quantum gates (Figure 1).

As a result, we can’t do anything useful with quantum computers unless we address errors. A set of techniques called quantum error correction can solve this problem.

If cracked, quantum error correction will unlock fault-tolerant quantum computers, which help prevent errors from spreading during the error correction process or during a computation - it’s a massive, multi-faceted problem.

Error-correcting codes are a vital piece of the puzzle. These codes work by encoding many noisy physical qubits to represent a smaller number of much less noisy logical qubits.

Tools (like the Lattice Surgery Compiler) currently exist to translate logical quantum circuits to run on an error-correcting code, but they tend to be written with large-scale applications in mind. These large-scale applications will unlock world-changing applications but also require equally large-scale quantum computers to run.

This paper focuses on what can be done in the near-term to help researchers understand how to run the first applications on early error-corrected quantum computers.

It explains how we have transformed a previously error-prone quantum circuit (aka a set of quantum gates) into a fault-tolerant (aka error-resilient) set of instructions.

**Beyond quantum memory**

This work bridges the gap between today’s quantum memory experiments and future fault-tolerant quantum computers, providing scientists with the key to understand and unlock near-term applications.

A quantum memory experiment is where you try to preserve the quantum state without making any changes to that state. It's like if you were tasked with memorising a number for a long amount of time – a difficult task but one that holds little commercial value.

We’ve already cracked quantum memory: Riverlane’s current decoder (DD1) enables quantum memory demonstrations. This is an important step for demonstrating quantum error correction, but it’s application to real-world use cases is extremely limited.

This latest work pushes us forward to useful quantum computing – allowing quantum scientists to devise error correction experiments beyond quantum memory. It provides a quantum error correction benchmark which is more complex than quantum memory but less complex than other large-scale applications.

The project took a quantum circuit developed for estimating the ground state of the hydrogen molecule (H2) and translated it into a fault-tolerant instruction set.

**Why H****2****? **

H2 is one of the simplest molecules to simulate, but implementing this simulation on a quantum error-correcting code requires all the building blocks that we need to implement larger applications. It is a useful benchmark to ensure future error-corrected quantum computers are functioning properly and will help scientists to unlock large-scale applications, faster.

This is because developing a tool which can translate from logical circuits to a fault-tolerant instruction set, and ideally doing so in a way which can be checked against the original logical circuit, will help automate what would otherwise be a significant manual effort.

In other words, it allows researchers to profile the error-corrected version of a quantum circuit, helping us understand what steps need to be optimised and identify potential unit tests for hardware companies.

What’s more, this work gives us an idea of which operations are particularly important when implementing a quantum circuit in a fault-tolerant way. Quantum scientists can then use these results to decide what operations and benchmarks they are going to focus on when assessing and improving the performance of their qubits.

You can read the full paper here.