Beyond NISQ — Terms for Quantum Computers Based on Noisy, Near-perfect, and Fault-tolerant Qubits

NISQ quantum computers are by definition noisy and intermediate scale. That begs the question of what to call a quantum computer which is not noisy or not intermediate scale. This informal paper proposes a collection of alternative terms which reflect the future arrival of quantum error correction (QEC) for fault-tolerant quantum computing with logical qubits, as well as near-perfect qubits with much higher fidelity than current noisy qubits, as well a range of sizes or qubit counts beyond only intermediate scale.

This informal paper expands on a proposal which was embedded in an earlier paper — in the section NISQ vs. fault-tolerant and near-perfect, small-scale, and large-scale:

• Preliminary Thoughts on Fault-Tolerant Quantum Computing, Quantum Error Correction, and Logical Qubits
• https://jackkrupansky.medium.com/preliminary-thoughts-on-fault-tolerant-quantum-computing-quantum-error-correction-and-logical-1f9e3f122e71

Topics discussed in this informal paper:

1. Technical definition of NISQ
2. Questions to be answered
3. Degree of noisiness
4. Near-perfect qubit fidelity
5. Simulation vs. intermediate scale
6. Most current real quantum computers are technically not NISQ devices
7. Wider range of qubit fidelity — noisy, near-perfect, and fault-tolerant qubits
8. Synonyms for fault-tolerant
9. Specifying fidelity for near-perfect qubits
10. Default fidelity for near-perfect is an open issue
11. Specifying fidelity for noisy qubits
12. Wider range of qubit counts
13. Combining qubit fidelity and qubit count
14. 50 or so qubits — small vs. intermediate?
15. All nine combinations of qubit fidelity and qubit count
16. Examples using the synonyms
17. NSSQ — Noisy Small-Scale Quantum devices
18. NISQ — Noisy Intermediate-Scale Quantum devices
19. NLSQ — Noisy Large-Scale Quantum devices
20. NPSSQ — Near-Perfect Small-Scale Quantum devices
21. NPISQ — Near-Perfect Intermediate-Scale Quantum devices
22. NPLSQ — Near-Perfect Large-Scale Quantum devices
23. FTSSQ — Fault-Tolerant Small-Scale Quantum devices
24. FTISQ — Fault-Tolerant Intermediate-Scale Quantum devices
25. FTLSQ — Fault-Tolerant Large-Scale Quantum devices
26. What is post-NISQ?
27. When will post-NISQ begin?
28. Post-noisy is a more accurate term than post-NISQ
29. But for most uses post-NISQ will refer to post-noisy
30. The missing link: connectivity between qubits
31. Summary and conclusions

Technical definition of NISQ

As proposed by Prof. John Preskill, a NISQ device is a noisy intermediate-scale quantum device (quantum computer.) It has noisy qubits and 50 to a few hundred qubits:

• Here “intermediate scale” refers to the size of quantum computers which will be available in the next few years, with a number of qubits ranging from 50 to a few hundred.
• Quantum Computing in the NISQ era and beyond
• https://arxiv.org/abs/1801.00862

Questions to be answered

Preskill’s official definition of NISQ leaves open the questions of what to call devices with:

1. Fewer than 50 qubits. Smaller.
2. More than a few hundred qubits. Larger.
3. Qubits which are not noisy. More reliable. Either full quantum error correction (QEC) logical qubits or simply much higher qubit fidelity than today.

This informal paper proposes answers to those questions.

Degree of noisiness

It would also be helpful to distinguish degrees of noisiness so that 65%, 75%, 85%, 90%, 95%, 98%, 99%, 99.9%, and 99.99% qubit fidelities do not all get treated as equal since some may be sufficient for some applications even as others are not.

Near-perfect qubit fidelity

It would also be helpful to distinguish very low degrees of noisiness as special — as near-perfect, say qubit fidelity such as 99.9% or 99.99% or higher, since they may be sufficient for quite a few applications even while lower fidelities such as 80% or even 90% might not be sufficient for many applications to function at all.

Near-perfect qubit fidelity will still be well-short of the high fidelity of perfect logical qubits which rely on quantum error correction (QEC), but will likely be cheaper, more plentiful, and widely available long before quantum error correction is widely available in reasonable capacities.

Simulation vs. intermediate scale

The choice of 50 qubits as the lower bound for intermediate scale roughly corresponds to the upper limit of the qubit count which can be fully simulated using a classical quantum simulator.

Actually, current classical quantum simulators support fewer than 50 qubits, but at least conceptually simulation of 50 qubits might be reachable in a few years.

This limitation of simulation was the original motivation for the notion of intermediate-scale, the IS in NISQ.

Most current real quantum computers are technically not NISQ devices

Part of the motivation for this paper was that technically, most current real quantum computers are not true NISQ devices since they have fewer than 50 qubits, which is the official lower bound for qubit count for NISQ.

Only three current real quantum computers are true NISQ — intermediate scale, at least 50 qubits — 53-qubit machines from Google and IBM and a 65-qubit machine from IBM.

In the terminology proposed by this paper, current quantum computers with fewer than 50 qubits are actually NSSQ — noisy small-scale (SS) quantum devices.

Wider range of qubit fidelity — noisy, near-perfect, and fault-tolerant qubits

What are the alternatives to noisy?

1. Noisy — N. All current and near-term quantum computers.
2. Near-perfect — NP. Any current, near-term, and longer-term quantum computers with more than a couple of 9’s in their qubit reliability, like 99.9%, 99.99%, 99.999%, and 99.9999% — using only raw physical qubits, no error correction or logical qubits. Close enough to perfection that quite a few applications can get respectable results without the need for quantum error correction and logical qubits.
3. Fault-tolerant — FT. Quantum error correction and logical qubits with 100% reliability of qubits.

Written as a regular expression, the combinations are:

• {N,NP,FT}ISQ

Synonyms for fault-tolerant

Two synonyms are also proposed for fault-tolerant (FT), but FT is the intended preference, for now:

1. P. Perfect qubit.
2. L. Logical qubit.

L is my own addition, but I encountered P and PISQ in this paper, which I encountered only after writing most of this paper:

• Quantum Computing — from NISQ to PISQ
• https://arxiv.org/abs/2106.11840

Specifying fidelity for near-perfect qubits

Since near-perfect is a rather vague and nonspecific term, it might be helpful to be more specific and specify the number of nines of qubit fidelity, such as:

1. NP2. Two nines of qubit fidelity — 99%. Not really near-perfect, but the upper edge of noisy qubits.
2. NP3. Three nines of qubit fidelity — 99.9%.
3. NP3.5. Three and a half nines of qubit fidelity — 99.95%.
4. NP4. Four nines of qubit fidelity — 99.99%.
5. NP4.75. Four and three quarters nines of qubit fidelity — 99.9975%.
6. NP5. Five nines of qubit fidelity — 99.999%.
7. NP6. Six nines of qubit fidelity — 99.9999%.
8. NP7. Seven nines of qubit fidelity — 99.99999%.

For more on nines of qubit fidelity, read my paper:

• Nines of Qubit Fidelity
• https://jackkrupansky.medium.com/nines-of-qubit-fidelity-e6e8680d2bb4

There is no limit on qubit fidelity per se, but I don’t expect qubit fidelities above 9, 12, or 15 nines. But, in theory, maybe 18, 20, or 24 could be possible.

Generally I don’t think people will need that degree of specificity, but occasionally it might be helpful to specify a lower bound, such as NP5 or NP6, to indicate that an application really needs that minimum qubit fidelity or that an algorithm is designed to deliver at least that qubit fidelity.

With the synonyms, the regex is:

• {N,NP(\d+(\.d+)?)?,FT,P,L}

Where (\d+(\.d+)?)? means that a decimal number may optionally be written after NP, specifying some integer number of nines of qubit fidelity and optionally some fraction of a single nine.

The intent of the fraction is to capture a half a nine or thirds or quarters of nines, such as 3.5, 4.25, 4.75, 4.33, 5.67 — any finer granularity is unlikely to have much utility.

Default fidelity for near-perfect is an open issue

There’s no clear and obvious specification of what fidelity constitutes a near-perfect qubit. How many nines of reliability?

About the only thing that is clear, to me, now, is that it will change over time. Three or four nines of qubit fidelity may seem awesome and impressive right now, but a few years from now even four may seem inadequate.

Generally, for now, I would say that the default should be targeted at expected qubit fidelity in a year or two. In other words, people should be simulating quantum algorithms for real quantum computers which will likely become available in one to two years.

So, maybe three or 3.5 nines would be appropriate right now, in September 2021.

But this is currently driven by the fact that quantum computing is still in a pre-commercial stage of ongoing research. Once the research is complete and commercialization is well underway, the default for qubit fidelity should match the average of qubit fidelity over current and available quantum computers, except for research projects targeting the future.

Simulation can of course target an arbitrary point in time in the future, with significantly greater qubit fidelity than even the best of current, existing real quantum computers.

All of that said, personally, I would say that the long-term default fidelity for near-perfect, even once perfect logical qubits become available should probably be six nines — 99.9999%. But in the near and medium term a more moderate degree of fidelity should be presumed, as indicated above, like 3.5 nines — that should be a reasonably happy medium.

Specifying fidelity for noisy qubits

Noisy describes a fairly wide range of qubit fidelity, or maybe we should say qubit infidelity.

Personally, I don’t see much value to qubit fidelity less than about 90%, which is a single nine of qubit fidelity. 85% or 80% at the maximum (or I should say minimum.) Or maybe 75% as an absolute minimum. Qubits with only 65% fidelity can’t be productively used for… anything — other than maybe generating random numbers.

I would suggest that two nines is the rough upper limit for noisy qubits. Three nines, 99.9%, is at the lower bound for near-perfect. And four nines, 99.99%, is clearly in the range of near-perfect.

The N of NISQ (or NSSQ) could be followed by the nines of qubit fidelity, optionally including a fraction, such as:

1. N1. One nine of qubit fidelity — 90%.
2. N1.25. One and a quarter nines of qubit fidelity — 92.5%.
3. N1.5. One and a half nines of qubit fidelity — 95%.
4. N1.75. One and three quarters nines of qubit fidelity — 97.5%.
5. N1.9. 98.5%, approximately.
6. N2. Two nines of qubit fidelity — 99%.
7. N2.5. Two and a half nines of qubit fidelity — 99.5%.
8. N2.75. Two and three quarters nines of qubit fidelity — 99.75%.
9. N2.9. 99.85%, approximately.
10. N3. Three nines of qubit fidelity — 99.9%.

What about qubit fidelities under 90%? This is a bit contrived, but I would suggest these fractional symbolic values:

1. N0.75. 87.5%.
2. N0.5. 85%.
3. N0.075. 82.5%.
4. N0.05. 80%.
5. N0.0075. 77.5%.
6. N0.005. 75%.
7. N0.00075. 72.5%.
8. N0.0005. 70%.
9. N0.000075. 67.5%.
10. N0.00005. 65%.

With the synonyms, the regex is now:

• {N(\d+(\.d+)?)?,NP(\d+(\.d+)?)?,FT,P,L}

Where (\d+(\.d+)?)? means that a decimal number may optionally be written after N, specifying some integer number of nines of qubit fidelity and optionally some fraction of a single nine.

The intent of the fraction is to capture a half a nine or thirds or quarters of nines, such as 1.5, 2.25, 2.75, 2.33, 2.67 — any finer granularity is unlikely to have much utility.

Wider range of qubit counts

In addition to accommodating variability in qubit fidelity, what are the alternatives to intermediate-scale?

1. Small-scale — SS. Under 50 qubits — 1 to 49.
2. Intermediate-scale — IS. 50 to a few hundred qubits. As defined by Preskill in 2018.
3. Large-scale — LS. More than a few hundred qubits.

Written as a regular expression, the combinations are:

• N[SIL]SQ

Some alternative terms are also proposed for subsets of those tree ranges of qubit count:

1. T. Tiny or toy. Too small for any degree of sophistication. 1–23 qubits.
2. M. Medium. A distinct step up from tiny and toy, capable of significantly greater sophistication and even some degree of quantum advantage. Primarily 32–40 qubits, but the full range of 24–49 qubits.
3. XL. Thousands of qubits.
4. XXL. Tens of thousands of qubits.
5. XXXL. Hundreds of thousands of qubits.
6. XXXXL. Millions of qubits.

Maybe additional levels of qubit counts might be needed much further in the future for hundreds of millions, billions, trillions, and even quadrillions of qubits.

Combining qubit fidelity and qubit count

Written as a regular expression and without the synonyms, the combinations for qubit fidelity and qubit count are written as:

• {N,NP,FT}[SIL]SQ

With the synonyms, the regex is:

• {N(\d+(\.d+)?)?,NP(\d+(\.d+)?)?,FT,P,L}{S,I,L,T,M,XL,XXL,XXXL,XXXXL}SQ

Or, the regex can be written as:

• {N(\d+(\.d+)?)?,NP(\d+(\.d+)?)?,FT,P,L}{S,I,X{0,4}L,T,M}SQ

50 or so qubits — small vs. intermediate?

The official definition of NISQ uses a hard 50 as the lower bound for intermediate-scale, but I’m not completely convinced that current 53 and 54-qubit quantum computers are really necessarily intermediate-scale and maybe should be considered closer to the outer fringes of small-scale than intermediate scale.

Similarly, if someone were to build a 48 or 49-qubit quantum computer it might be closer to intermediate-scale than small-scale.

So, I’m inclined to allow for some leeway on the dividing line between small and intermediate scale — call it 50 or so qubits. Where the dividing line is somewhere between 45 and 55 qubits.

All nine combinations of qubit fidelity and qubit count

Ignoring the synonyms, three (N, NP, FT) times three (SS, IS, LS) is nine, so here are the nine combinations:

1. NSSQ — Noisy Small-Scale Quantum devices. Most of today’s quantum computers. Under 50 or so qubits.
2. NISQ — Noisy Intermediate-Scale Quantum devices. 50 or so to a few hundred noisy qubits.
3. NLSQ — Noisy Large-Scale Quantum devices. More than a few hundred to thousands or even millions of noisy qubits.
4. NPSSQ — Near-Perfect Small-Scale Quantum devices. Less than 50 or so near-perfect qubits — with qubit reliability in the range 99.9% to 99.9999%.
5. NPISQ — Near-Perfect Intermediate-Scale Quantum devices. 50 or so to a few hundred near-perfect qubits — with qubit reliability in the range 99.9% to 99.9999%.
6. NPLSQ — Near-Perfect Large-Scale Quantum devices. More than a few hundred to thousands or even millions of near-perfect qubits — with qubit reliability in the range 99.9% to 99.9999%.
7. FTSSQ — Fault-Tolerant Small-Scale Quantum devices. Under 50 or so logical qubits. Perfect computation, but insufficient for quantum advantage.
8. FTISQ — Fault-Tolerant Intermediate-Scale Quantum devices. Start of quantum advantage. Good place to start post-NISQ devices. 50 or so to a few hundred logical qubits.
9. FTLSQ — Fault-Tolerant Large-Scale Quantum devices. Production-scale quantum advantage. More than a few hundred to thousands or even millions of logical qubits.

Examples using the synonyms

A few examples using the synonyms:

1. NTSQ. Most current quantum computers — 1–23 noisy qubits.
2. LTSQ. A minimal number of fault-tolerant logical qubits, from 1 to 23 qubits.
3. LMSQ. 32–40 (or 24–49) logical qubits.
4. NPMSQ. 32–40 (or 24–49) near-perfect qubits.
5. LISQ. 50 or so to a few hundred logical qubits. Equivalent to FTISQ.
6. LSSQ. Under 50 logical qubits. Equivalent to FTSSQ.
7. PISQ. Equivalent to LISQ and FTISQ.
8. PSSQ. Equivalent to LSSQ and FTSSQ.
9. LXLSQ. Thousands of fault-tolerant logical qubits.
10. LXXXXLSQ. Millions of fault-tolerant logical qubits.
11. NPXXXXLSQ. Millions of near-perfect qubits.
12. NXXXXLSQ. Millions of noisy qubits.
13. NP5LSQ. Thousands of near-perfect qubits with five nines of qubit fidelity (99.999%.)
14. NP6MSQ. 32–40 (or 24–49) near-perfect qubits with six nines of qubit fidelity (99.9999%.)
15. NP4TSQ. 1–23 near-perfect qubits with four nines of qubit fidelity (99.99%.)
16. NP4.5TSQ. 1–23 near-perfect qubits with four and a half nines of qubit fidelity (99.99%.)
17. N1SSQ. Up to 50 noisy qubits with a single nine of fidelity — 90%.
18. N1.5SSQ. Up to 50 noisy qubits with one and a half nines of fidelity — 95%.
19. N2SSQ. Up to 50 noisy qubits with two nines of fidelity — 99%.
20. N2.5SSQ. Up to 50 noisy qubits with two and a half nines of fidelity — 99.5%.
21. N3SSQ. Up to 50 noisy qubits with three nines of fidelity — 99.9%.
22. N0.5SSQ. Up to 50 noisy qubits with 85% fidelity.
23. N0.05SSQ. Up to 50 noisy qubits with 80% fidelity.
24. N0.005SSQ. Up to 50 noisy qubits with 75% fidelity.
25. N0.0005SSQ. Up to 50 noisy qubits with 70% fidelity.
26. N0.00005SSQ. Up to 50 noisy qubits with 65% fidelity.

NSSQ — Noisy Small-Scale Quantum devices

Noisy Small-Scale Quantum device, abbreviated NSSQ, is a term I contrived to represent quantum computers with fewer than 50 or so qubits. That covers most of today’s quantum computers.

NISQ — Noisy Intermediate-Scale Quantum devices

Noisy Intermediate-Scale Quantum device, abbreviated NISQ, is an industry-standard term for a quantum computer with 50 or so to a few hundred or so noisy qubits. Despite its proper definition, it is commonly used to refer to all of today’s quantum computers (all with noisy qubits) regardless of the number of qubits.

NLSQ — Noisy Large-Scale Quantum devices

Noisy Large-Scale Quantum device, abbreviated NLSQ, is a term I contrived to represent quantum computers with more than a few hundred to thousands or even millions of noisy qubits.

NPSSQ — Near-Perfect Small-Scale Quantum devices

Near-Perfect Small-Scale Quantum device, abbreviated NPSSQ, is a term I contrived to represent quantum computers with less than 50 or so near-perfect qubits — with qubit reliability in the range 99.9% to 99.9999%.

NPISQ — Near-Perfect Intermediate-Scale Quantum devices

Near-Perfect Intermediate-Scale Quantum device, abbreviated NPISQ, is a term I contrived to represent quantum computers with 50 or so to a few hundred near-perfect qubits — with qubit reliability in the range 99.9% to 99.9999%.

NPLSQ — Near-Perfect Large-Scale Quantum devices

Near-Perfect Large-Scale Quantum device, abbreviated NPLSQ, is a term I contrived to represent quantum computers with more than a few hundred to thousands or even millions of near-perfect qubits — with qubit reliability in the range 99.9% to 99.9999%.

FTSSQ — Fault-Tolerant Small-Scale Quantum devices

Fault-Tolerant Small-Scale Quantum device, abbreviated FTSSQ, is a term I contrived to represent quantum computers with fewer than 50 or so logical qubits with quantum error correction. Perfect computation, but insufficient capacity for quantum advantage.

FTSSQ quantum computers will be the preliminary size of quantum computer in the early days of fault-tolerance since it will take quite a few physical qubits to construct even a single logical qubit. It could take a couple of years to evolve from very tiny FTSSQ devices (even 8 logical qubits would be a large number of physical qubits) to even 32, let alone 50 logical qubits.

FTISQ — Fault-Tolerant Intermediate-Scale Quantum devices

Fault-Tolerant Intermediate-Scale Quantum device, abbreviated FTISQ, is a term I contrived to represent quantum computers with 50 or so to a few hundred logical qubits with quantum error correction. Start of quantum advantage. Good place to start post-NISQ devices.

FTLSQ — Fault-Tolerant Large-Scale Quantum devices

Fault-Tolerant Large-Scale Quantum device, abbreviated FTLSQ, is a term I contrived to represent quantum computers with more than a few hundred to thousands or even millions of logical qubits with quantum error correction. Production-scale quantum advantage.

What is post-NISQ?

There are two hurdles to clear to get beyond NISQ devices — to post-NISQ:

1. Achieving fault tolerance, or at least near-perfect qubits.
2. Getting beyond a few hundred fault-tolerant or near-perfect qubits.

Technically, that second criteria should be achieved to claim post-NISQ, but I’m willing to relax that arm of the criteria — that intermediate scale is sufficient provided that fault tolerance or near-perfect qubits are achieved.

So, I would say that four categories would qualify as post-NISQ devices:

1. NPISQ — Near-Perfect Intermediate-Scale Quantum devices.
2. NPLSQ — Near-Perfect Large-Scale Quantum devices.
3. FTISQ — Fault-Tolerant Intermediate-Scale Quantum devices.
4. FTLSQ — Fault-Tolerant Large-Scale Quantum devices.

Whether quantum advantage can be achieved with only near-perfect qubits is an interesting and open question.

Quantum advantage can only be achieved as a slam dunk with fault-tolerant logical qubits:

1. FTISQ — Fault-Tolerant Intermediate-Scale Quantum devices — where quantum advantage starts.
2. FTLSQ — Fault-Tolerant Large-Scale Quantum devices — where production-scale quantum advantage flourishes.

It’s an interesting question whether fault-tolerant qubits (logical qubits) or near-perfect qubits alone of any capacity, including FTSSQ — Fault-Tolerant Small-Scale Quantum devices and NPSSQ — Near-Perfect Small-Scale Quantum devices, should mark the beginning of post-NISQ. Ideally, probably not, especially since the capacity would be insufficient to enable quantum advantage. And quantum advantage — dramatic quantum advantage — is the real goal.

When will post-NISQ begin?

When will we get beyond NISQ, to post-NISQ? I have no idea at this juncture. Rapid progress has been made in recent years, but the road ahead is very steep.

Even if smaller configurations of logical qubits (8 to 48) are available within a few to five years, intermediate scale, even at a mere 50 logical qubits could take somewhat longer.

And if you want to use production-scale as the hurdle, five to seven years might be a better bet.

Post-noisy is a more accurate term than post-NISQ

As we have seen in the discussion in the prior two sections, 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.

So post-noisy clearly refers to:

1. NPSSQ — Near-Perfect Small-Scale Quantum devices. Less than 50 or so near-perfect qubits — with qubit reliability in the range 99.9% to 99.9999%.
2. NPISQ — Near-Perfect Intermediate-Scale Quantum devices. 50 to a few hundred near-perfect qubits — with qubit reliability in the range 99.9% to 99.9999%.
3. NPLSQ — Near-Perfect Large-Scale Quantum devices. More than a few hundred to thousands or even millions of near-perfect qubits — with qubit reliability in the range 99.9% to 99.9999%.
4. FTSSQ — Fault-Tolerant Small-Scale Quantum devices. Under 50 or so logical qubits. Perfect computation, but insufficient for quantum advantage.
5. FTISQ — Fault-Tolerant Intermediate-Scale Quantum devices. Start of quantum advantage. Good place to start post-NISQ devices. 50 or so to a few hundred logical qubits.
6. FTLSQ — Fault-Tolerant Large-Scale Quantum devices. Production-scale quantum advantage. More than a few hundred to thousands or even millions of logical qubits.

But for most uses post-NISQ will refer to post-noisy

Generally I prefer to use the most accurate terminology, but sometimes that can get tedious and confusing. So, for now, I’ll personally accept the usage of post-NISQ as being equivalent to post-noisy.

As always, context will be the deciding factor as to interpretation. The three main contextual meanings being:

1. Getting past noisy qubits. To either near-perfect or fault tolerant qubits.
2. True fault tolerance. With quantum error correction and logical qubits.
3. Near-perfect is good enough. True fault tolerance is not needed.

The missing link: connectivity between qubits

One critical aspect of quantum computing which is not addressed here is connectivity between qubits for entanglement. Most current real quantum computers have only limited, nearest-neighbor connectivity. At present, only trapped-ion quantum computers support full, any to any connectivity between all qubits.

In theory, limited vs. full connectivity should be integrated into the nomenclature for quantum computers.

But I’ll leave that for a future revision to this paper.

Summary and conclusions

1. NISQ doesn’t even cover most current real quantum computers — only 50 qubits and larger since intermediate-scale means “50 to a few hundred” qubits.
2. The only aspect that NISQ really covers is that the qubits are noisy.
3. Add SS and LS for small-scale and large-scale to move beyond IS for intermediate-scale.
4. Add NP and FT for near-perfect and fault-tolerant qubits to move beyond noisy qubits.
5. Optionally specify a minimum number of nines of qubit fidelity provided or required for near-perfect qubits — NP2, NP3, … NP6, etc. And NP3.5 and NP4.75 as well — fractional nines of reliability.
6. Optionally specify a minimum number of nines of qubit fidelity provided or required for noisy qubits — N1, N2, or N3, etc. And N1.5 and N2.5 as well — fractional nines of reliability. Also, a contrived notation for fewer than a single nine of qubit fidelity — N0.5 for 85%, N0.05 for 80%, N0.005 for 75%, N0.0005 for 70%, and N0.00005 for 65%.
7. Add T and M to be more specific for the lower and upper portions of small-scale, tiny or medium.
8. Add P and L as synonyms for FT (fault-tolerant) — perfect or logical.
9. Add XLS, XXLS, XXXLS, and XXXXLS for thousands, tens of thousands, hundreds of thousands and millions of qubits.
10. Most current real quantum computers are actually NSSQ — small-scale (SS) since they have fewer than 50 qubits. Only three current real quantum computers are true NISQ — intermediate-scale, at least 50 qubits — 53-qubit machines from Google and IBM and a 65-qubit machine from IBM.
11. Unfortunately, this proposed nomenclature does not cover connectivity — nearest neighbor vs. full, any to any connectivity. Hopefully a future update will address that.
12. For now, we wait patiently for more qubits, especially over 50 and even over 100 qubits (IBM has promised 127 within a few months of this writing), as well as improvements in qubit fidelity, approaching near-perfect qubit fidelity.
13. True, perfect, logical qubits are relegated to fantasy, for the indefinite future.
14. NP4ISQ may be the best we can hope for over the next two years — over 50 qubits, maybe 128, 256, or maybe 440 qubits (as promised by IBM) and four nines of qubit fidelity — 99.99% reliability. But we may only achieve three nines of qubit fidelity.

For more of my writing: List of My Papers on Quantum Computing.