How many physical qubits are needed to encode a logical qubit on an
-- ion trap,
-- superconducting,
-- neutral atom,
-- photonic,
-- spin
quantum computer based on today's technologies?
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1$\begingroup$ This is pretty broad right now. Maybe consider asking “what factors determine the number of physical qubits needed to encode a logical qubit, as applied to current (2021) devices?” $\endgroup$– Mark SpinelliCommented Nov 19, 2021 at 3:54
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$\begingroup$ What do you mean by "encode a logical bit"? Qubits are a superset of regular 0/1 bits. I can just use the collapsed state of a Qubit as a classical bit...but that wouldn't be very wise since I could just use a regular bit for that. $\endgroup$– Bertrand Einstein IVCommented Nov 19, 2021 at 20:00
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$\begingroup$ The answer depends on quantum error correction codes, which you use. Any ECC performs exactly the same regardless of the physical medium. The only difference is: "is this QC scheme has enough gate fidelity for this ECC to be effective?" $\endgroup$– totikomCommented Nov 22, 2021 at 18:11
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$\begingroup$ @totikom, thank you for the comments. So the original question is, given the fidelity of different QC hardware, how many physical qubits will be required to encode a logical qubit ? $\endgroup$– davidCommented Nov 24, 2021 at 17:57
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1 Answer
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The answer depends on several factors:
- The desired error rate of the logical qubit.
- The physical qubit fidelities in the given platform (e.g. two-qubit gate fidelity, idling errors, measurement errors etc.)
- The quantum error correction code being used. In particular, there are some error correcting codes which can be more efficient than others.
- Properties of noise in the system can also be exploited to reduce overheads.
Just to expand on point (1), getting to increasingly small error rates of the logical qubit requires increasingly more physical qubits. One can create a logical qubit with less than 10 physical qubits, but to get to very low error rates allowing for very deep circuits then you will likely want something like thousands of physical qubits per logical qubit.
