What Is a Near-perfect Qubit?

  1. In a nutshell — noisy qubits, perfect logical qubits, and near-perfect qubits
  2. Noisy qubits — in the short term
  3. Perfect logical qubits — for the long run
  4. Near-perfect qubits — for the medium term
  5. Near-perfect qubits — to accelerate the path to perfect logical qubits
  6. Logical qubits require near-perfect qubits
  7. Achieving near-perfect qubits would obviate some not insignificant fraction of the need for full quantum error correction
  8. Near-perfect qubits will be good enough — true fault tolerance will not be needed, generally
  9. Perfect logical qubits are the preferred solution, but they simply aren’t available now or any time soon
  10. Near-perfect qubits are more practical — quantum error correction is too hard
  11. There are two distinct purposes for near-perfect qubits
  12. Near-perfect qubits are of value in their own right, even without quantum error correction
  13. So, it’s a win-win to keep pushing towards more-perfect (near-perfect) qubits
  14. Very limited initial capacities of logical qubits will greatly limit their use
  15. Even with logical qubits, some applications may benefit from the higher performance of near-perfect physical qubits
  16. Even with logical qubits, larger applications may need to operate directly on near-perfect physical qubits
  17. Even with near-perfect qubits, the nuances of subtle remaining errors may make it a game of Russian Roulette
  18. Some algorithms and applications will simply need the clarity and certainty of perfect logical qubits
  19. My own preference is for near-perfect qubits over overly-complex quantum error correction
  20. It’s a real race — quantum error correction vs. near-perfect qubits — the outcome is unclear
  21. Are all logical qubits perfect logical qubits? Yes!
  22. Error rates and qubit fidelity
  23. Nines of qubit fidelity
  24. Probabilities and cumulative effects, shot counts and circuit repetitions
  25. Terms and definitions
  26. Informal levels of qubit fidelity
  27. How close to perfect is a near-perfect qubit?
  28. Near-perfect logical qubits and near-perfect physical qubits
  29. Error-free qubits — either perfect logical qubits or near-perfect qubits
  30. Effectively error-free qubits — near-perfect qubits with a very high qubit fidelity (very low error rate)
  31. Fault-free qubits — synonym for error-free qubits — either perfect logical qubits or near-perfect qubits
  32. Stable qubits — synonym for error-free qubits — either perfect logical qubits or near-perfect qubits
  33. NISQ devices (NISQ quantum computers, NISQ quantum processors)
  34. Actually, most quantum computers have been NSSQ devices — small-scale, not NISQ intermediate-scale
  35. NISQ has always been just a stepping stone, not a platform for real applications
  36. Beyond NISQ — NPISQ and FTISQ
  37. NPSSQ and NPLSQ for near-perfect small-scale and large-scale quantum devices
  38. Post-NISQ quantum computers — near-perfect qubits or perfect logical qubits
  39. Post-noisy quantum computers
  40. Near-perfect qubits are an essential requirement for achieving practical quantum computing
  41. Background for how I arrived at near-perfect qubits
  42. Prior art?
  43. How noisy is noisy for a noisy qubit?
  44. How close to perfect is a near-perfect qubit?
  45. Are three nines good enough for a near-perfect qubit?
  46. Are 3.5 nines good enough for a near-perfect qubit?
  47. Are six nines good enough for a perfect logical qubit?
  48. Doesn’t the tiny residual error of even the best error-corrected qubits make them near-perfect qubits?
  49. Even near-perfect qubits crumble near the limits of coherence times
  50. Caveat: Near-perfect qubits are still limited by coherence time
  51. Even with perfect logical qubits, some applications may benefit from the higher performance of near-perfect physical qubits
  52. Near-perfect qubits are likely needed to achieve quantum advantage
  53. Whether quantum advantage can be achieved with only near-perfect qubits remains an open question
  54. Near-perfect physical qubits may be sufficient to achieve The ENIAC Moment for niche applications
  55. Likely need logical qubits to achieve The FORTRAN Moment for widespread adoption of quantum computing
  56. Irony: By the time qubits get good enough for efficient error correction, they may be good enough for many applications without the need for error correction
  57. Do we really need quantum error correction if we can achieve near-perfect qubits? Probably, eventually
  58. Maybe we don’t really need quantum error correction if we can engineer and mass produce near-perfect qubits
  59. Unclear if non-elite staff can solve production-scale problems with near-perfect qubits
  60. Prospects for near-perfect qubits
  61. When can we expect near-perfect qubits?
  62. Vendors need to publish roadmaps for near-perfect qubits
  63. Nobody expects near-perfect qubits imminently, so we should maintain a focus on pursuing quantum error correction
  64. Which is likely to come first, full quantum error correction or near-perfect qubits?
  65. Are trapped-ion qubits closer to near-perfect? Not quite
  66. Are neutral-atom qubits in the same ballpark as trapped-ion qubits for qubit fidelity? Unclear
  67. Real applications should remain based on simulation until near-perfect qubits are available
  68. How close to perfect must near-perfect qubits be to enable perfect logical qubits?
  69. How many nines will become the gold standard for near-perfect qubits to enable logical qubits? It remains to be seen
  70. Let application developers decide between near-perfect qubits and perfect logical qubits
  71. Near-perfect qubits are a poor man’s perfect logical qubits, but for many applications that will be good enough
  72. Possibility of a Quantum Winter if we don’t get near-perfect qubits within two years
  73. More on perfect logical qubits
  74. Summary and conclusions

In a nutshell — noisy qubits, perfect logical qubits, and near-perfect qubits

Grossly over-simplifying, but capturing the essence of the distinctions, qubit fidelity is a spectrum from terrible to great, with three interesting broad general buckets for the spectrum:

  1. Noisy qubits. Generally no more than a few dozen quantum operations can be performed before an error occurs. At best, somewhere between a hundred and a thousand operations before an error.
  2. Near-perfect qubits. Thousands of operations can be performed before an error occurs. At best, up to ten thousand operations before an error occurs.
  3. Perfect logical qubits. No limit to the number of operations which can be performed — without any errors. At least a million operations without error. Possibly many millions, a billion, even a trillion, or more.

Noisy qubits — in the short term

Noisy qubits suck. We only use them because we have no other choice. Actually, we do have a choice — classical quantum simulation — but when it comes to real quantum hardware, we have no choice, at present.

Perfect logical qubits — for the long run

Physicists and computer scientists have a proposed solution called quantum error correction (QEC) which completely eliminates the errors, but… implementation of that proposal is going to take a number of years — three to five years or even longer.

Near-perfect qubits — for the medium term

Near-perfect qubits are an admittedly stopgap measure to achieve a large fraction of the benefit of full quantum error correction at a small fraction of the cost.

Near-perfect qubits — to accelerate the path to perfect logical qubits

As an added benefit, as the qubit fidelity of near-perfect qubits continues to rise, that will reduce the number of physical qubits required to implement each logical qubit under quantum error correction. So, efforts to pursue near-perfect qubits will not only not detract from pursuit of quantum error correction, but will enhance and accelerate progress towards full, automatic, and transparent quantum error correction and the resultant perfect logical qubits.

Logical qubits require near-perfect qubits

Just to reemphasize the point from the previous section, logical qubits do effectively require near-perfect qubits.

  1. More physical qubits would be needed for each logical qubit. Too many.
  2. Given that physical qubits will continue to be relatively scarce, this means that for a given number of physical qubits you would get fewer logical qubits. Too few.
  3. The residual error even after full quantum error correction (QEC) would be greater. Too great.

Achieving near-perfect qubits would obviate some not insignificant fraction of the need for full quantum error correction

Some algorithms and applications will inherently require full quantum error correction (QEC), but achieving near-perfect qubits would obviate some not insignificant fraction of the need for full quantum error correction. More-perfect qubits are a win-win — better for near-term quantum computers and result in more efficient quantum error correction.

Near-perfect qubits will be good enough — true fault tolerance will not be needed, generally

As a gross generality, it will likely be true that near-perfect qubits will be good enough, and that true fault tolerance will not be needed. But, as with all generalities, there will likely be exceptions.

Perfect logical qubits are the preferred solution, but they simply aren’t available now or any time soon

The life of a quantum algorithm designer or quantum application developers will be much easier using perfect logical qubits, but they simply aren’t available now or any time soon. It may be three to five or even seven years before perfect logical qubits are readily available in any reasonable quantity.

Near-perfect qubits are more practical — quantum error correction is too hard

Achieving perfect logical qubits using quantum error correction (QEC) will be a real watershed moment for quantum computing, opening up the floodgates for development of quantum algorithms and quantum applications by non-elite technical staff, but that’s still an event way off in the distant future, far over the near-term horizon. Quantum error correction is simply way too hard. But in the meantime, incrementally advancing towards greater degrees of near-perfect qubits will soon be within reach.

There are two distinct purposes for near-perfect qubits

Just to summarize the previous sections, there are two distinct purposes for near-perfect qubits:

  1. To enable quantum error correction (QEC) for logical qubits. In the long run.
  2. To enable complex applications using raw physical qubits until quantum error correction becomes available. In the near to medium term.

Near-perfect qubits are of value in their own right, even without quantum error correction

Since not all algorithms and applications will require the full perfection of perfect logical qubits, near-perfect qubits are of value in their own right, even without quantum error correction.

So, it’s a win-win to keep pushing towards more-perfect (near-perfect) qubits

Since near-perfect qubits are usable as-is for some applications and also enable more-efficient quantum error correction, it’s a win-win to keep pushing towards more-perfect (near-perfect) qubits — even after quantum error correction is actually achieved.

Very limited initial capacities of logical qubits will greatly limit their use

Logical qubits will greatly facilitate many applications, but very limited initial capacities of logical qubits will mean that any application needing a significant number of qubits will have to make do with physical qubits.

Even with logical qubits, some applications may benefit from the higher performance of near-perfect physical qubits

Even once logical qubits do become available and in sufficient quantities, some applications may benefit from the higher performance of near-perfect physical qubits.

Even with logical qubits, larger applications may need to operate directly on near-perfect physical qubits

Even once logical qubits become commonplace, there may still be a need or desire for higher performance and larger applications which operate directly on near-perfect physical qubits, without the performance overhead or more limited capacity of logical qubits.

Even with near-perfect qubits, the nuances of subtle remaining errors may make it a game of Russian Roulette

There may well be projects which can achieve success with raw physical near-perfect qubits, but the nuances of subtle remaining errors may make it a game of Russian Roulette, with some teams succeeding spectacularly even while some teams fail spectacularly, and no way to know in advance which is more likely.

Some algorithms and applications will simply need the clarity and certainty of perfect logical qubits

As close to perfect as near-perfect physical qubits might be, some quantum algorithms, quantum applications, quantum algorithm designers, quantum application developers, or even organizations will simply need the absolute clarity and absolute certainty of perfect logical qubits. Where good enough simply isn’t good enough.

My own preference is for near-perfect qubits over overly-complex quantum error correction

Personally, I prefer more simple system designs. Full quantum error correction is in fact more general and less problematic, but at a cost of being very complex. My own preference is for the simplicity and lower cost of near-perfect qubits over overly-complex quantum error correction.

It’s a real race — quantum error correction vs. near-perfect qubits — the outcome is unclear

There’s absolutely no clarity which will happen first, near-perfect qubits sufficient for most quantum algorithms and quantum applications, or physical qubits with a low-enough error rate — and in sufficient quantity — to enable full quantum error correction sufficient for most quantum algorithms and quantum applications.

Are all logical qubits perfect logical qubits? Yes!

There’s no real need to redundantly refer to perfect logical qubits. They really are simply logical qubits. I personally use the redundant term perfect logical qubit to emphasize the point that with logical qubits algorithm designers and application developers no longer have to worry about qubit errors.

Error rates and qubit fidelity

An error rate is the number of operations you can perform before an error is likely. Or, for a given number of operations, the fraction of those operations which are likely to be in error.

Nines of qubit fidelity

Nines of qubit fidelity are a convenient form for expressing qubit reliability and error rates. Basically, count the nines in the reliability, with fractional nines as well:

  1. 90% = one nine. One error in ten operations.
  2. 95% = 1.5 nines. One error in twenty operations.
  3. 96% = 1.6 nines. One error in twenty five operations.
  4. 98% = 1.8 nines. One error in fifty operations.
  5. 99% = two nines. One error in a hundred operations.
  6. 99.5% = 2.5 nines. One error in five hundred operations.
  7. 99.9% = three nines. One error in a thousand operations.
  8. 99.95% = 3.5 nines. One error in five thousand operations.
  9. 99.99% = four nines. One error in ten thousand operations.
  10. 99.999% = five nines. One error in a hundred thousand operations.
  11. 99.9999% = six nines. One error in a million operations.
  12. 99.9999999% = nine nines. One error in a billion operations.
  13. 99.9999999999% = twelve nines. One error in a trillion operations.

Probabilities and cumulative effects, shot counts and circuit repetitions

No single quantum algorithm (circuit) is going to have millions or billions of gates, but these are probabilities of errors, so they also take into account how many times an application might repeat a given circuit before an error might occur. Many thousands or even millions of circuit repetitions are possible for a given circuit or collection of circuits used by an application.

Terms and definitions

We’ve already discussed these terms informally in this paper, but here are their more formal definitions:

  1. Noisy qubits. Qubits which have relatively low fidelity. Errors are relatively common. Significant effort is needed to cope with or to mitigate the errors. Only the most elite quantum algorithm designers and quantum application developers can work well with noisy qubits. Essentially all current and near-term quantum computers. The qubits used in a NISQ device — noisy intermediate-scale quantum device. For more detail, see the NISQ devices section later in this paper.
  2. Near-perfect qubits. Qubits which are close enough to perfect for some or even most quantum algorithms and quantum applications. Little effort is needed to cope with or to mitigate the errors. Less elite quantum algorithm designers and quantum application developers can work well with near-perfect qubits. Some or even most quantum algorithms and quantum applications can accept quantum results as if there were no errors. Not currently available, but expected within the next two to three years, sooner for some applications. Technically, this would no longer be a NISQ device but a NPISQ device — NP = near-perfect. For more detail see the Beyond NISQ — NPISQ and FTISQ section later in this paper.
  3. Perfect logical qubits. Qubits which utilize quantum error correction (QEC) to achieve virtually perfect reliability. May not be absolutely perfect, but few if any quantum applications would be able to detect any errors. No longer requires elite skills for quantum algorithm design and quantum application development. Suitable for widespread adoption of quantum computing. This would no longer be a NISQ device, but a FTISQ device — FT = fault-tolerant.
  1. Corrected qubits. A synonym for perfect logical qubits, to indicate that quantum error correction is in effect.
  2. Stabilized qubits. A synonym for perfect logical qubits, to indicate that quantum error correction is in effect.
  3. Error-free qubits. Either perfect logical qubits or near-perfect qubits, either suitable for execution of a reasonably deep and complex quantum circuit without any significant chance of encountering errors.
  4. Fault-free qubits. Synonym for error-free qubits.
  5. Stable qubits. Synonym for error-free qubits. They could be explicitly stabilized — under quantum error correction (stabilized qubits), or actually be inherently stable due to being near-perfect.
  6. Algorithmic qubits. Term introduced by IonQ — “we introduce Algorithmic Qubits (AQ), which is defined as the largest number of effectively perfect qubits you can deploy for a typical quantum program.” Seems reasonably close to my notion of a near-perfect qubit.
  1. Noisy qubits. Reliability from 65% to 99%. Up to two nines.
  2. Near-perfect qubits. Reliability from 99.99% to 99.999%. Four to five nines.
  3. Perfect logical qubits. Reliability of 99.99999% or better. Minimum of seven nines.
  1. Noisy qubits. Could go as high as 99.9% or even 99.95%. Up to three or even 3.5 nines.
  2. Near-perfect qubits. Could go as low as 99.9% or 99.95% for some applications — three to 3.5 nines. Could go as high as 99.9999 — six nines. In the extreme, it could go as high as nine or even twelve nines.
  3. Perfect logical qubits. Could go as low as 99.9999 — six nines. Could stay above 99.9999999% or even 99.9999999999 — nine nines or even twelve nines.
  1. Noisy qubits. Significant effort is needed to cope with or to mitigate the errors — or a very high tolerance for errors. Only the most elite quantum algorithm designers and quantum application developers can work well with noisy qubits. Or individuals merely wishing to experiment with the technology, doing no more than toy algorithms.
  2. Near-perfect qubits. Little effort is needed to cope with or to mitigate the errors. Less-elite quantum algorithm designers and quantum application developers can work reasonably well with near-perfect qubits, at least sometimes, at least for simpler quantum algorithms and quantum applications.
  3. Perfect logical qubits. No longer requires elite skills for quantum algorithm design and quantum application development. Suitable for widespread adoption of quantum computing.

Informal levels of qubit fidelity

These are simply some informal categories so that we have some common terminology or language to talk about rough scenarios for qubit error rates (adapted from my paper Preliminary Thoughts on Fault-Tolerant Quantum Computing, Quantum Error Correction, and Logical Qubits):

  1. Extremely noisy. Not really usable. But possible during the earliest stages of developing a new qubit technology. May be partially usable for testing and development, but not generally usable. Less than 60% reliable.
  2. Very noisy. Not very reliable. Need significant shot count to develop a statistical average for results. Barely usable. Less than 70% reliable.
  3. Moderately noisy. Okay for experimentation and okay if rerunning multiple times is needed. Not preferred, but workable. 75% to 80% reliable.
  4. Modestly noisy. Frequently computes correctly. Occasionally needs to be rerun. Reasonably usable for NISQ prototyping, but not for production-scale real-world applications. 85% to 96% reliable.
  5. Slightly noisy. Usually gives correct results. Very occasionally needs to be rerun. 97.5% to 99.5% reliable. Generally, two nines of qubit fidelity, but could be up to 2.5 nines, three nines, or even 3.5 nines.
  6. Near-perfect qubit. Just short of perfect qubit. Rare failures, but enough to spoil perfection. Generally, four to five nines of fidelity — 99.99% to 99.999% reliability. Maybe three to 3.5 nines for some applications. Could be either a near-perfect physical qubit or a near-perfect logical qubit, but generally it will be the former unless it is clear from the context.
  7. Near-perfect logical qubit. An error-corrected qubit which has some non-trivial residual error rate.
  8. Near-perfect physical qubit. Generally redundant, but may also be trying to distinguish from a near-perfect logical qubit which has some non-trivial residual error rate.
  9. Virtually-perfect qubit. No detectable errors, or so infrequent to be unnoticeable by the vast majority of applications. Comparable to current classical computing, including ECC memory. Possibly as low as six nines, but generally nine to twelve nines or more, even fifteen nines.
  10. Logical qubit. An ensemble of noisy or near-perfect qubits which utilize quantum error correction (QEC) to achieve an extremely low or even nonexistent error rate. I sometimes use the term perfect logical qubit, which is redundant.
  11. Perfect physical qubit. The mythical ideal. No errors. Ever. No error correction required. Not likely to be practical or even theoretically achievable — under quantum mechanics there is always some non-zero uncertainty.

How close to perfect is a near-perfect qubit?

As the discussion so far should have made clear, there is no definitive answer to this question.

Near-perfect logical qubits and near-perfect physical qubits

Generally, the term near-perfect qubit refers to a single physical qubit without any error correction (QEC). To be more explicit, this is a near-perfect physical qubit.

Error-free qubits — either perfect logical qubits or near-perfect qubits

In truth, all that most quantum algorithm designers and quantum application developers really care about is that their quantum circuits execute without any significant chance of encountering errors. If that can occur with near-perfect qubits most of the time, that’s fine. If it requires full quantum error correction and perfect logical qubits, so be it. Whichever approach works can be referred to as error-free qubits (or fault-free qubits or stable qubits) — quantum circuits of some significant depth and some significant complexity can be reliably executed without encountering errors.

Effectively error-free qubits — near-perfect qubits with a very high qubit fidelity (very low error rate)

At some point, the error rate of near-perfect qubits will be so small (e.g., five nines — one error in 100,000 operations) that most quantum algorithm designers and quantum application developers won’t even notice. At that stage, you could say that near-perfect qubits are effectively error-free qubits.

Fault-free qubits — synonym for error-free qubits — either perfect logical qubits or near-perfect qubits

If the error rate for near-perfect qubits is low enough, such as five nines — one error in 100,000 operations, they can be considered error-free qubits, also known as fault-free qubits, an exact synonym.

Stable qubits — synonym for error-free qubits — either perfect logical qubits or near-perfect qubits

If the error rate for near-perfect qubits is low enough, such as five nines — one error in 100,000 operations, they can be considered error-free qubits, also known as stable qubits, an exact synonym.

NISQ devices (NISQ quantum computers, NISQ quantum processors)

NISQ quantum computers or NISQ devices or NISQ quantum processors are quantum computers based on noisy qubits. The term was proposed by CalTech Prof. John Preskill:

Actually, most quantum computers have been NSSQ devices — small-scale, not NISQ intermediate-scale

Technically, as shown by Preskill’s definition above, intermediate-scale starts at 50 qubits, while most existing quantum computers have had substantially fewer than 50 qubits. I personally refer to these as NSSQ devices — noisy small-scale quantum devices.

NISQ has always been just a stepping stone, not a platform for real applications

From the get-go, NISQ (and NSSQ!) should have been couched as an evolutionary hardware development path towards the near-perfect qubits needed to support perfect logical qubits using quantum error correction, rather than a platform for directly implementing quantum applications with noisy qubits. And, of course, now it looks as if near-perfect qubits themselves should be sufficient to support many or even most quantum applications, without the need to wait for the perfect logical qubits at all.

Beyond NISQ — NPISQ and FTISQ

What terms should we use for quantum computers based on near-perfect qubits if NISQ refers to noisy qubits? My proposal is NPISQ for near-perfect intermediate-scale device. I have a comparable term for full fault-tolerant quantum computers: FTISQ.

NPSSQ and NPLSQ for near-perfect small-scale and large-scale quantum devices

My proposal from the preceding section also proposes new terms for other ranges of qubit capacity beyond intermediate-scale, which is supposed to be reserved for 50 to hundreds of qubits:

  1. NPSSQ. Near-perfect small-scale quantum device. Under 50 qubits.
  2. NPISQ. Near-perfect intermediate-scale quantum device. 50 to a few hundred qubits.
  3. NPLSQ. Near-perfect large-scale quantum device. More than a few hundred to thousands of qubits.

Post-NISQ quantum computers — near-perfect qubits or perfect logical qubits

We’re in the so-called NISQ era of quantum computing since all qubits are currently noisy qubits. The preferred and presumed proper path out of NISQ devices is via perfect logical qubits enabled by quantum error correction (QEC).

Post-noisy quantum computers

As we have seen, post-NISQ is still a somewhat vague and ambiguous term. For most uses, the term post-noisy would probably be more accurate than post-NISQ since it explicitly refers to simply getting past noisy qubits, to fault-tolerant and near-perfect qubits rather than focus on how many qubits.

Near-perfect qubits are an essential requirement for achieving practical quantum computing

There is growing chatter about the coming of practical quantum computing. Granted, it’s a vague marketing and hype buzz term, but does have some value, indicating a more advanced level of sophistication where quantum computers can actually solve production-scale practical real-world problems.

  • A practical quantum computer is capable of solving a wide range of production-scale practical real-world problems through the use of near-perfect qubits.

Background for how I arrived at near-perfect qubits

So, how did I arrive at my current conception of near-perfect qubits?

  1. Quantum error correction was an open research endeavor, not having a clear path or even a clear endpoint, and apparently doomed to taking some indeterminate number of years before it would come to fruition.
  2. Although quantum error correction could be accomplished with even relatively noisy qubits, the less noisy, the better.
  3. With very noisy qubits a very large number of noisy physical qubits would be needed to construct even a single perfect logical qubit.
  4. With much less noisy qubits far fewer noisy physical qubits would be needed to construct each logical qubit.
  5. So, even if perfect logical qubits were the intended and only acceptable goal, much less noisy qubits were the best path to get there.
  6. How much less noisy would be acceptable to pursue perfect logical qubits? No obvious or inherent limit, and the less noisy the fewer physical qubits required and hence the more logical qubits you could construct from a given number of physical qubits.
  7. Physical qubits continue to be expensive and a relatively scarce resource, even years into the future.
  8. So, we need to focus on making the best we can of a relatively limited number of physical qubits. Even 10,000 physical qubits would yield only 50 logical qubits if it took 200 physical qubits to construct each logical qubit.
  9. So, clearly there needed to be a high priority on less-noisy qubits even if perfect logical qubits were going to become the norm for fault-tolerant quantum computing.
  10. So, we needed to focus on less-noisy qubits. How much less noisy? A lot less noisy.
  11. Then it finally dawned on me that if our noisy qubits really were a lot less noisy, maybe we actually could do a fair amount of quantum computation before we ran into errors.
  12. And it also dawned on me that clearly less-noisy qubits were not as good as perfect logical qubits, but since we’re not on a path that will get us to perfect logical qubits any time soon — not in the next few years, if not longer, maybe less-noisy qubits could be a plausible stopgap measure for the years while we await the arrival of perfect logical qubits, at least for some applications which have less demanding qubit fidelity requirements (e.g., relatively shallow circuits or more tolerant of occasional errors.)
  13. The term less-noisy qubit seemed too insufficient to express the degree of noise reduction that was required.
  14. I decided that I wanted a term which was a lot closer to the intended target — perfect logical qubits.
  15. The term near-perfect qubit seemed to fit the bill — an attempt to be as far from noisy as possible, but still not quite to the perfection of a logical qubit.
  16. Further, there was a fivefold benefit to such near-perfect qubits: 1) they accelerate the path to quantum error correction and logical qubits, 2) they reduce the number of physical qubits needed to construct each logical qubit, 3) they increase the logical qubit capacity achieved for a given number of physical qubits, 4) they enable an interesting fraction of quantum algorithms and quantum applications to run correctly without the need for full quantum error correction, and, last but not least, 5) pursuing near-perfect qubits in the short and medium term is not a tradeoff at the expense of quantum error correction and logical qubits, which are in fact accelerated with every advance for near-perfect qubits. Such a deal! Who could resist?!
  17. So, as much as I was determined to continue pursuing fault-tolerant quantum computing, quantum error correction, and perfect logical qubits, I was irresistibly driven to conclude that pursuit of near-perfect qubits was a serious win-win situation for both the near term and the long term, and the medium term as well.

Prior art?

It is very possible that the term near-perfect qubit may have been in use before I came along, but I certainly had not seen any references to it, let alone common usage of it before I began using it in my paper.

How noisy is noisy for a noisy qubit?

First, the obvious worst cases:

  1. Under 50% reliability. Too noisy to be useful for anything.
  2. 51–59% reliability. Not quite as bad, but still unlikely to be useful for much of anything.
  3. 60–65% reliability. Very marginal, but still…
  4. 66–69% reliability. One in three error rate is getting closer to minimal utility.
  5. 70–74% reliability. Getting warmer, some minimal utility, but still…
  1. 75–79% reliability. One in four error rate could have some marginal utility, but still…
  2. 80–89% reliability. One in five error rate is definitely getting warmer.
  1. 90–94% reliability. Useful for some minimal applications.
  2. 95–96.9% reliability. Useful for even more applications.
  1. 97–97.5% reliability. Fairly useful for a minority of applications.
  2. 97.6–98.4% reliability. Not so noisy.
  3. 98.5–98.9% reliability. Even better.
  1. 99% reliability. Two nines. Not so noisy.
  2. 99.1–99.4% reliability. Getting better. Useful for more applications. Whether to still consider this noisy is debatable and a fielder’s choice.
  3. 99.5–99.75% reliability. Even more useful.
  4. 99.9% reliability. Three nines of qubit fidelity is a clear fielder’s choice for being a near-perfect qubit.

How close to perfect is a near-perfect qubit?

There’s no absolute definitive answer as to how close to perfect a near-perfect qubit must be.

Are three nines good enough for a near-perfect qubit?

It’s a fielder’s choice and depends on the particular application whether three nines of qubit fidelity (an error rate of 0.1% for a reliability of 99.9% — one error in a thousand operations) should be considered a near-perfect qubit.

Are 3.5 nines good enough for a near-perfect qubit?

It’s a fielder’s choice and depends on the particular application whether 3.5 nines of qubit fidelity (an error rate of 0.05% for a reliability of 99.95% — one error in five thousand operations) should be considered a near-perfect qubit.

Are six nines good enough for a perfect logical qubit?

I suspect that six nines of qubit fidelity — one error in a million operations — should be quite good enough for many if not most applications requiring error-free operation.

Doesn’t the tiny residual error of even the best error-corrected qubits make them near-perfect qubits?

Okay, technically, yes — even the best quantum error correction (QEC) will still leave at least some tiny residual error, so in that sense even the best error-corrected qubits are still not quite perfect, and hence are technically near-perfect qubits. Or, more properly, near-perfect logical qubits.

Even near-perfect qubits crumble near the limits of coherence times

One unresolved difficulty with near-term quantum computers is what happens for deeper quantum circuits that begin to approach the coherence time for qubits.

Caveat: Near-perfect qubits are still limited by coherence time

As wonderful as near-perfect qubits may seem, they have a key limitation that quantum error correction is able to surmount: coherence time.

Even with perfect logical qubits, some applications may benefit from the higher performance of near-perfect physical qubits

Even once perfect logical qubits become commonplace, there may still be a need or desire for higher performance and larger applications which operate directly on near-perfect physical qubits, without the performance overhead or more limited capacity of logical qubits.

Near-perfect qubits are likely needed to achieve quantum advantage

Without near-perfect qubits, algorithms won’t likely be able to exploit a sufficient number of qubits and a sufficient depth of quantum circuits to actually achieve any dramatic quantum advantage or even substantial quantum advantage over classical computing.

Whether quantum advantage can be achieved with only near-perfect qubits remains an open question

The jury is out. Some may presume that only full quantum error correction will be enough to enable most algorithms and applications to achieve dramatic quantum advantage or at least substantial quantum advantage over classical computing solutions, even while others will be content to rely on only near-perfect physical qubits.

Near-perfect physical qubits may be sufficient to achieve The ENIAC Moment for niche applications

Logical qubits will greatly facilitate many applications, but very limited initial capacities of logical qubits will mean that any application needing a significant number of qubits will have to make do with physical qubits. The good news is that the level of quality needed to enable logical qubits will assure that physical qubits will have near-perfect quality. Still, working with physical qubits will be limited to the most sophisticated, most elite quantum algorithm designers and quantum application developers.

Likely need logical qubits to achieve The FORTRAN Moment for widespread adoption of quantum computing

Although a few sophisticated, elite teams may well be able to achieve The ENIAC Moment for quantum computing — quantum advantage for a production-scale practical real-world application — that won’t help the more-average non-elite organization or development team. Most organizations and teams will require the greater convenience and greater reliability of logical qubits, as well as more advanced and approachable programming models, programming languages, and application frameworks. The confluence of all of these capabilities, underpinned by logical qubits, will enable what I call The FORTRAN Moment of quantum computing — where average, non-elite teams and organizations can tap into the power of quantum computing without requiring the higher level of sophistication needed to work with less than perfect physical qubits. This will finally enable the widespread adoption of quantum computing.

Irony: By the time qubits get good enough for efficient error correction, they may be good enough for many applications without the need for error correction

In truth, qubits can have a fairly high error rate and still be suitable for quantum error correction to achieve logical qubits, but that would require a dramatic number of noisy physical qubits to achieve each logical qubit, which limits the number of logical qubits for a machine of a given capacity of physical qubits. The twin goals are:

  1. Achieve logical qubits as quickly as possible.
  2. Maximize logical qubits for a given number of physical qubits. Achieve a low enough error rate for physical qubits so that only a modest number of physical qubits are needed for each logical qubit.

Do we really need quantum error correction if we can achieve near-perfect qubits? Probably, eventually

Many algorithms and quantum applications will probably do fine with only near-perfect qubits, but ultimately some will still need or want perfect logical qubits.

Maybe we don’t really need quantum error correction if we can engineer and mass produce near-perfect qubits

Although I agree with the analysis of the preceding section that there will always be quantum algorithms and quantum applications which really do need the higher and more reliable fidelity of quantum error correction, I also think that it will be debatable whether we need quantum error correction if we can engineer and mass produce near-perfect qubits.

Unclear if non-elite staff can solve production-scale problems with near-perfect qubits

Although it is very likely that The ENIAC Moment can be achieved using near-perfect qubits, that will likely require elite technical staff. Quantum algorithms and quantum applications of any significant complexity — production-scale for practical real-world applications — will likely remain beyond the reach of non-elite technical staff until The FORTRAN Moment is reached.

Prospects for near-perfect qubits

Although the goal of four to five nines of qubit fidelity for near-perfect qubits is clear, the timing is anything but clear.

  1. Short-term. The next 18 months or so. 2.5, 2.75, three, 3.25, 3.5, and 3.75 nines.
  2. Medium term. Two years. Four nines.
  3. Longer term. Three to four or maybe five years. 4.25, 4.5, 4.75, and then five nines, maybe even 5.5 nines.

When can we expect near-perfect qubits?

Read the preceding section for more details, but it’s relatively safe to presume that we will see at least a preliminary form of near-perfect qubits over the next 18 months.

Vendors need to publish roadmaps for near-perfect qubits

Quantum computer hardware vendors haven’t yet even acknowledged this concept of near-perfect qubits. In addition to doing so, they need to transparently disclose a roadmap to achieving various levels of near-perfect qubit fidelity — how many nines at what milestones.

  1. 2.5 nines.
  2. 2.75 nines.
  3. Three nines.
  4. 3.25 nines.
  5. 3.5 nines.
  6. 3.75 nines.
  7. Four nines.
  8. 4.25 nines.
  9. 4.50 nines.
  10. 4.75 nines.
  11. Five nines.
  12. Anything above five nines.
  13. Milestones for perfect logical qubits. Including capacities.

Nobody expects near-perfect qubits imminently, so we should maintain a focus on pursuing quantum error correction

Even if near-perfect qubits do in fact become available in 18 months or so, we’re not there yet, so we have to maintain the focus on pursuing quantum error correction.

Which is likely to come first, full quantum error correction or near-perfect qubits?

We really do need true, perfect logical qubits with full quantum error correction, but since that outcome is still far beyond the distant horizon, it’s reasonable to pin substantial hope on near-perfect qubits which might in fact be good enough to serve most needs of many quantum applications — or at least that’s the conjecture.

Are trapped-ion qubits closer to near-perfect? Not quite

The verbal claim is that trapped-ion qubits are significantly higher fidelity than superconducting transmon qubits, but I haven’t seen definitive data, yet.

Are neutral-atom qubits in the same ballpark as trapped-ion qubits for qubit fidelity? Unclear

Neutral-atom qubits are too new for us to know much about them. I presume that they are roughly in the same ballpark as trapped-ion qubits for qubit fidelity, but that is purely speculation on my part.

Real applications should remain based on simulation until near-perfect qubits are available

So, where do we go from here? Researchers and vendors should continue NISQ hardware development, but make it clear that the real goal is near-perfect qubits to enable automatic quantum error correction to enable perfect logical qubits — and for use on their own even before perfect logical qubits become available in reasonably large quantities. But noisy qubits are mere stepping stones towards near-perfect qubits, and not intended for actual application development, not now, not ever.

How close to perfect must near-perfect qubits be to enable perfect logical qubits?

Uhhh… it gets complicated. And you have to get into the quantum threshold theorem, so if you really do want to get into this level of detail, consult my longer paper on quantum error correction and logical qubits:

How many nines will become the gold standard for near-perfect qubits to enable logical qubits? It remains to be seen

There’s no definitive answer on this yet. Maybe four nines. Maybe five nines. Maybe 3.5 nines is good enough.

Let application developers decide between near-perfect qubits and perfect logical qubits

Hopefully, one day, we will have quantum computers that both support full quantum error correction with perfect logical qubits and provide near-perfect qubits. Then the individual application developer can decide which they need for their particular circumstances.

Near-perfect qubits are a poor man’s perfect logical qubits, but for many applications that will be good enough

That’s about it in a nutshell. Perfect logical qubits are the ultimate goal, the prize, but getting there will be a long and winding road, beyond the patience of many. Near-perfect qubits are a shortcut. An imperfect shortcut to be sure, but a fulfilling consolation prize nonetheless.

Possibility of a Quantum Winter if we don’t get near-perfect qubits within two years

Although I’m generally optimistic that we can achieve near-perfect qubits within two years, or at least 3.5 nines of qubit fidelity, it’s quite possible that we might not, in which case it is very possible that deep disillusionment may set in, causing projects to stall, commitment to waver, investment to dry up, and progress, at least on the practical application front, to grind to a near-halt as people retreat and wait until near-perfect qubits or perfect logical qubits based on quantum error correction finally do arrive. In other words, for a Quantum Winter to set in.

More on perfect logical qubits

Perfect logical qubits are a fascinating topic, but beyond the scope of this paper, which is focused on near-perfect qubits. For much more on perfect logical qubits, see my paper on quantum error correction and logical qubits:

Summary and conclusions

  1. Noisy qubits suck. We only use them because we have no other choice. Actually, we do have a choice — classical quantum simulation — but when it comes to real quantum hardware, we have no choice, at present.
  2. Perfect logical qubits using quantum error correction (QEC) are the Holy Grail of quantum computing, but they simply are not within reach any time soon. Three to five years, maybe. Maybe seven years or even longer.
  3. Near-perfect qubits are a happy medium, much better than noisy qubits and they will be available much sooner and in higher capacity than perfect logical qubits.
  4. Near-perfect qubit is not a standard or widely-used term, but is instead my own proposal. I’m not claiming to have invented the term or the concept, but I am certainly promoting the use of the term.
  5. Near-perfect qubits are coming fairly soon. Over the next two years or so.
  6. Near-perfect qubits would generally have four to five nines of qubit fidelity. Maybe as few as 3.5 nines or even as few as three nines for some applications.
  7. Near-perfect qubits are not as good as perfect logical qubits, but they will be good enough for most quantum applications.
  8. Even when perfect logical qubits do become available, they will be in very limited capacities — many physical qubits for even a single logical qubit. Most complex algorithms will have to rely on near-perfect qubits — for years.
  9. Even when perfect logical qubits are available in larger capacities, there will still be algorithms which require even larger capacities or higher performance which are available only using raw physical near-perfect qubits.
  10. Near-perfect qubits will probably be sufficient to reach The ENIAC Moment of demonstrating a production-scale practical real-world quantum application.
  11. But perfect logical qubits will probably be required to reach The FORTRAN Moment where widespread adoption of quantum computing is possible for non-elite quantum algorithm designers and quantum application developers.
  12. Near-perfect qubits are likely needed to achieve any substantial degree of quantum advantage.
  13. Whether quantum advantage can be achieved with only near-perfect qubits alone remains an open question. For some applications, yes. For other applications, no.
  14. Near-perfect qubits are a poor man’s perfect logical qubits, but for many applications that will be good enough.
  15. Near-perfect qubits are an essential requirement for achieving practical quantum computing, both necessary and sufficient. Full quantum error correction (QEC) is not needed or available in the relatively near and medium-term, and noisy NISQ qubits won’t cut it.
  16. There is in fact a fair possibility of a Quantum Winter if we don’t get near-perfect qubits within two years. Not a certainty, but simply a possibility. If a Quantum Winter does occur, it will likely be the result of excessive premature commercialization, a diversion of resources and attention away from the critical research needed to bring near-perfect qubits to fruition.

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Freelance Consultant

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