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

  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:

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.

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.

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.

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.

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.
  • {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.

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%.
  • {N,NP(\d+(\.d+)?)?,FT,P,L}

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?

Specifying fidelity for noisy qubits

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

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

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.
  • N[SIL]SQ
  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.

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

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.
  6. PISQ. Equivalent to LISQ.
  7. LXLSQ. Thousands of fault-tolerant logical qubits.
  8. LXXXXLSQ. Millions of fault-tolerant logical qubits.
  9. NPXXXXLSQ. Millions of near-perfect qubits.
  10. NXXXXLSQ. Millions of noisy qubits.
  11. NP5LSQ. Thousands of near-perfect qubits with five nines of qubit fidelity (99.999%.)
  12. NP6MSQ. 32–40 (or 24–49) near-perfect qubits with six nines of qubit fidelity (99.9999%.)
  13. NP4TSQ. 1–23 near-perfect qubits with four nines of qubit fidelity (99.99%.)
  14. NP4.5TSQ. 1–23 near-perfect qubits with four and a half nines of qubit fidelity (99.99%.)
  15. N1SSQ. Up to 50 noisy qubits with a single nine of fidelity — 90%.
  16. N1.5SSQ. Up to 50 noisy qubits with one and a half nines of fidelity — 95%.
  17. N2SSQ. Up to 50 noisy qubits with two nines of fidelity — 99%.
  18. N2.5SSQ. Up to 50 noisy qubits with two and a half nines of fidelity — 99.5%.
  19. N3SSQ. Up to 50 noisy qubits with three nines of fidelity — 99.9%.
  20. N0.5SSQ. Up to 50 noisy qubits with 85% fidelity.
  21. N0.05SSQ. Up to 50 noisy qubits with 80% fidelity.
  22. N0.005SSQ. Up to 50 noisy qubits with 75% fidelity.
  23. N0.0005SSQ. Up to 50 noisy qubits with 70% fidelity.
  24. 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.

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.
  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.
  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.

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.

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.

  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.

  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.

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.

--

--

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store