Alice & Bob, a quantum computing company, has developed a new error-correction code that could revolutionize quantum computing. The code, known as quantum error correction (QEC), operates multiple noisy qubits to encode the information of an error-free logical qubit. The company has also developed “cat qubits” which are inherently protected against one type of noise, reducing the need for error correction. This could make quantum computing more economically viable by reducing the number of qubits needed. The company also explores the use of low-density parity check (LDPC) codes to further reduce the QEC overhead.
Quantum Computing and the Challenge of Error Correction
Quantum computers have the potential to revolutionize many fields of research by solving problems that are currently beyond the reach of classical supercomputers. However, for quantum algorithms to work effectively, qubits must operate with extremely low error rates. Today’s best-quality qubits have error rates of 0.1 to 1%, which is far from the required accuracy. The lack of significant improvement in physical error rates in recent years has been a concern.
Quantum error correction (QEC) is a method that can address a large part of this problem. The most widely studied QEC code, the surface code, uses about a thousand noisy qubits arranged on a square array to encode a single logical qubit. However, the cost of implementing QEC is high. For instance, a single logical qubit with a thousand physical qubits requires an extra-large dilution refrigerator and three racks packed with microwave cables, components, and instruments, costing about 10 million USD and a 50 kW power supply.
The Potential of Cat Qubits
One possible solution to the error correction problem is to use a type of qubit that is inherently protected against one type of noise. Cat qubits, used by Alice & Bob, are such qubits. They reduce error correction to a 1D problem, requiring only 30 cat qubits compared to nearly 1000 qubits in the standard approach. This could potentially reduce the number of qubits required by 60 times for large practical problems like Shor’s factorization algorithm.
The Promise of LDPC Codes
Another option is to use low-density parity check (LDPC) codes, which outperform the surface code. LDPC codes can be implemented by adding extra connections between distant qubits on a surface code tile. This allows encoding of 14 to 30 logical qubits from a single surface code tile, which would otherwise encode only one logical qubit. However, this approach poses significant engineering challenges and limits operational speed.
Combining Cat Qubits and LDPC Codes
Alice & Bob, in collaboration with Inria, have explored the possibility of combining cat qubits and LDPC codes. They found a 2D pattern of cat qubits with low-degree local connectivity that encodes up to five times more logical qubits than if arranged in a row. This approach also allows for the parallelization of logical gates.
A processor based on LDPC cat qubits would consist of an LDPC array on one chip, acting as an efficient quantum memory, and a 2D auxiliary array of cat qubits on a flip chip, acting as the computing part of the processor. This approach overcomes the experimental hurdles of using LDPC codes while pushing the quantum error correction overhead to its theoretical limit.
The Future of Quantum Computing
The combination of LDPC codes and cat qubits could dramatically reduce the number of qubits needed to build a useful quantum computer. For instance, only 100,000 qubits would be needed to run Shor’s algorithm, 200 times less than with standard qubits. This approach could make the first applications of quantum computing in areas like fundamental physics and chemistry feasible with a 1500 cat-qubit processor.
The race to provide useful quantum computing is a dual challenge: building increasingly large quantum processors and reducing the size at which such a processor is useful. The use of LDPC codes on cat qubits could significantly accelerate progress on the second track, bringing us closer to the era of useful quantum computing.
