Quantum Error Correction Software
Fault tolerant quantum computing relies upon accurate, scalable and fast quantum error correction techniques.
Designing a quantum computer requires in-depth knowledge of quantum error correction, which is necessary to achieve fault tolerance. While quantum hardware engineering is crucial for increasing qubit quality, the inherent fragility of quantum systems and complexity of the surrounding environment means all errors can never be eliminated. Quantum error correction (QEC) requires mid-circuit measurement, feedback control and a robust software architecture to track and correct errors as they occur. Riverlane is building the pre-eminent software tool for QEC. With world-leading experts on our team we are designing a robust, scalable and multi-function architecture solution to make quantum error correction accessible.
Quantum error correction poses many challenges, but it is an active area of research with new ideas and advances in the state of the art appearing regularly. By encoding a single-qubit quantum state into an entangled state of many physical qubits, we are able to reliably detect and correct errors as they happen. Classical systems exhibit many features useful for error correction that quantum systems do not.
Non-destructive access to data
Classical bits are either 0 or 1, and measuring a classical bit does not change the value. This is not true for qubits, as direct measurement collapses quantum superposition and destroys important information
Copying data
Bits are easily copied across data registers creating an accessible pathway to redundancy. The No-Cloning theorem prevents this in quantum mechanics.
​
Error classifications
Classical systems only exhibit bit flip errors (bits flipping from 0 to 1 or vice versa). Quantum systems experience bit flips and phase flips — errors with no classical analogue.
At the heart of quantum error correction is the concept of encoding multiple noisy physical qubits (left) into one virtual, or “logical” qubit (right). With appropriate noise profiles, the relative quality of this logical qubit will be higher than the component physical qubits.
We do not have non-destructive access to the encoded quantum data. Therefore, we require more qubits to act as auxiliaries. By temporarily entangling the auxiliary qubits with the data qubits, and measuring the state of the auxiliaries, we are able to extract partial data about the quality of the encoded state. This process is known as syndrome extraction and the partial information we receive is known as the syndrome.
When we receive the syndrome, we must process it in order to gain confidence in the error that could have occurred. This is known as decoding, and is in general an NP-Hard problem. Therefore, even if we have access to a high performing quantum encoding scheme, it must come paired with a decoder in order to be useful. Riverlane has demonstrated some of the fastest decoders in the community [1] as well as pioneering new ideas on addressing decoding bottlenecks [2].
Rotated Surface Code is one of the most successful quantum codes to date. Green circles represent data qubits, and orange qubits are the auxiliaries. Each face (or plaquette) has an auxiliary qubit assigned and it detects either bit flip (grey) or phase flip (blue) errors on the neighbouring data qubits. Implementing this, or any other, code on quantum hardware requires in-depth knowledge of not only QEC theory, but also the native gate set, noise profiles, connectivity, qubit quality...
While Riverlane has extensive expertise on the surface code, we are conducting research into codes with alternative connectivity. Given the unique characteristics of Universal Quantum’s hardware, specifically shuttling techniques, codes that require long-range connectivity can be implemented more easily than on competing superconducting devices.
