Hardware & Errors
Logical Qubit
An error-protected qubit built by combining many physical qubits using quantum error correction.
Definition
A logical qubit is a unit of fault-tolerant quantum information, built by encoding the state of one 'ideal' qubit across many real, error-prone physical qubits using a quantum error-correcting code. The redundancy allows errors to be detected and corrected without directly measuring (and destroying) the protected information.
In depth
A logical qubit is a qubit encoded across many physical qubits so that errors can be detected and corrected. Instead of trusting one fragile device, the information is spread over a group of entangled qubits, and the group is monitored continuously. Done well, the logical qubit is far more reliable than any of its parts, and its reliability improves as the group gets larger, so long as the physical qubits are good enough. This is what turns noisy hardware into a computer that can run long calculations.
The overhead is large. The surface code with distance d needs about 2 d squared physical qubits per logical qubit, so a logical error rate of 10 to the minus 9 may need about 1,000 physical qubits each, and an algorithm with thousands of logical qubits needs millions of physical ones. Higher-rate codes, such as quantum LDPC codes, aim to cut this by about ten times. Neutral atoms, trapped ions, and superconducting devices have all shown logical qubits in recent years: Harvard and QuEra demonstrated 48 logical qubits in 2023, Microsoft with Quantinuum reported 12 logical qubits in 2024 and with Atom Computing 24 entangled logical qubits, and Google's Willow showed a logical memory outlasting its best physical qubit in 2024.
Counting logical qubits needs care. Some reported numbers use error-detecting codes with small distance, and the logical error rates differ widely, so two machines with the same count are not equivalent. The metrics to ask for are the code distance, the logical error rate per cycle or per gate, and whether logical gates and not just memory were demonstrated. IBM's roadmap aims for a 200-logical-qubit machine, called Starling, in 2029, and other vendors have comparable targets.
Technical Definition
The number of physical qubits required per logical qubit depends on the error-correcting code used and the target logical error rate; surface code implementations often cited in research require on the order of hundreds to over a thousand physical qubits per logical qubit at useful error rates.
Visual Explanation: An Analogy
Think of a logical qubit like a single important message sent multiple times through a noisy phone line using different phrasings — if most copies arrive correctly, the receiver can confidently reconstruct the original message even if a few copies got garbled.
Key facts
| Item | Detail |
|---|---|
| Surface code overhead | About 2 d squared physical qubits per logical qubit at distance d |
| Harvard and QuEra (2023) | 48 logical qubits on neutral atoms |
| Microsoft and partners (2024) | 12 logical qubits with Quantinuum and 24 entangled logical qubits with Atom Computing |
| Google Willow (2024) | A distance-7 logical memory with lifetime longer than its best physical qubit |
| Roadmap target | IBM aims for 200 logical qubits in Starling by 2029 |
Where the idea comes from
The idea of encoding a qubit in many qubits dates to Shor's 1995 code. The first experiments encoded single logical qubits around 2014 to 2016, and since 2021 multiple groups have demonstrated logical qubits that improve with code size.
Real-World Use Cases
- Required for running large, complex algorithms like Shor's Algorithm reliably
- The central goal of quantum error correction research
- Google's Willow processor notably demonstrated logical error rates decreasing as more physical qubits were added
How it differs from related ideas
- A physical qubit is a real device with errors, and a logical qubit is an encoded qubit built from many of them.
- Error detection only flags errors, while error correction fixes them.
- A logical qubit's quality is given by its logical error rate, which varies between demonstrations.
Common Misconceptions
- A logical qubit is not just a 'better' physical qubit — it's an entirely different kind of unit built from many physical qubits working together.
Frequently asked questions
What is a logical qubit?
A qubit whose information is encoded in many physical qubits using an error-correcting code, making it much more reliable than a single physical qubit.
How many physical qubits make one logical qubit?
Anywhere from a handful in small demonstrations to roughly a thousand for high reliability in the surface code, with newer codes aiming for fewer.
Have logical qubits been demonstrated?
Yes. Several groups have shown logical qubits on ions, atoms, and superconducting devices, including a 48-logical-qubit result on neutral atoms in 2023.
Related Terms
Keep exploring
- Algorithm: Quantum Error-Correcting Codes (Shor Code, Surface Code)
- Algorithm: Shor's Algorithm
- Hardware: Google Willow
- Hardware: QuEra Aquila
- Hardware: Quantinuum H2