Launching SHYPS
QLDPC is the New Error Correction

Executive Summary

Quantum computing is set to drive a technological revolution, solving complex challenges beyond the reach of classical methods. From materials design and drug discovery to alternative energy, its impact will reshape industries and unlock unprecedented possibilities. Qubits — as quantum bits, the foundational building blocks for quantum computers are known — are notoriously susceptible to “noise” from their environment. Left alone, this noise makes the entire system unreliable. To reach the point where quantum systems can run commercial-scale applications, quantum “error correction” is required to address the high sensitivity to that noise.

The traditional method for quantum error correction has been surface codes, due to their impressive time efficiency and low connectivity requirements. However, the downside to surface codes is the huge overhead: thousands of physical qubits are needed for each applicationgrade logical qubit. This large ratio of physical to logical qubits has contributed to projections that put commercial-scale quantum computing decades in the future due to the sheer number and size of systems that would be required to run useful applications.

Another class of codes, Quantum Low-Density Parity Check (QLDPC) codes, emerged about 20 years ago as a promising means to lower overheads. However, researchers had been unable to discover an implementation of efficient quantum computing in these codes, leaving them useful for memory (i.e., storage for quantum states) but lacking the ability to perform the applications that will make quantum computing so impactful.

Being able to create more logical qubits for the same number of physical qubits redefines the path to commercially valuable quantum computing from primarily focusing on large-scale physical qubit manufacturing to one considering efficient overall quantum system production. Unlocking efficient logic in a QLDPC code moves the goalposts for commercial-scale quantum computing 5x, 10x, even 20x closer as more efficient quantum error correction enables quantum computers to reach the computing capability that unlocks algorithms with exponential quantum advantage using vastly fewer physical resources.

In a breakthrough new result, Photonic has constructed a family of QLDPC codes, Subsystem Hypergraph Product Simplex codes (SHYPS), with an efficient logic implementation. These codes are only available to high connectivity architectures, such as Photonic’s Entanglement First™ architecture.

A New Family of QLDPC Codes for Efficient Fault-Tolerant Quantum Computing

Photonic has developed a new family of QLDPC codes, called Subsystem Hypergraph Product Simplex (SHYPS) codes. This new family of QLDPC codes was designed to perform quantum logic and error correction efficiently, greatly reducing the overhead requirements for quantum systems. The fast and lean SHYPS codes are competitive with surface codes when it comes to logical clock time and performance, with the significant benefit of requiring 5x to 20x fewer physical qubits per logical qubit.

This breakthrough could accelerate the timeline for commercial quantum computing by years, if not decades, by addressing key requirements for efficient, fault-tolerant quantum computing. Each of these requirements are outlined in this paper, with a focus on the impact of the SHYPS code family. Overarchingly, SHYPS relies on short logical operations and non-local connectivity. Importantly, the overhead efficiencies increase as it scales.

Details on code construction and performance metrics can be found in the paper “Computing Efficiently in QLDPC Codes.” The paper features the [49,9,4] code, which has a physical to logical qubit ratio of 49:9 for SHYPS compared to 225:9 for the surface code. The SHYPS family of codes is scalable, meaning that it starts small (e.g., 49 physical qubits) but can encompass increasing numbers of physical qubits, creating larger counts of logical qubits as it grows.

Realizing Large Scale Quantum Computing

Realizing the promise of QLDPC codes and accelerating the path to efficient large-scale quantum computing requires both a high connectivity architecture and a QLDPC code set that supports efficient quantum computation while having “good” error correction properties. In other words, an integrated, comprehensive approach is required for computing operations as well as detecting and correcting errors. Each of the fundamental requirements are outlined below, with a corresponding description of how SHYPS either vastly improves or holds the leading edge on performance.

Efficient quantum computation is the ability of a quantum system to do more with less, be it physical resources, time, or the number of operations to complete a program. Two main factors that influence efficiency are the physical to logical qubit ratio, and the ability to run efficient logical operations.

Physical to Logical Qubit Ratio: A good ratio — or rate — makes commerciallyrelevant quantum more practically feasible by lowering the number of physical qubits needed, reducing the size and cost of systems needed to run large application.

With surface codes, each code block – made of hundreds or thousands of physical qubits – can only hold one single logical qubit. In contrast, QLDPC codes can encode multiple logical qubits in a single code block. As a result, they can be structured to have much lower overheads. To achieve nine logical qubits with surface code requires nine blocks of surface code. With a small SHYPS code, it is possible to get nine logical qubits using only a single block of code. Simply put, QLDPC codes generate more logical qubits per physical qubit. Increasing the size of a SHYPS code (i.e., including more physical qubits) enables more logical qubits to be encoded per block whereas increasing the size of the block of surface code will still result in only a single logical qubit. SHYPS increases efficiency of quantum computation by decreasing the total physical qubit resource requirements needed.