What Is a Practical Quantum Computer?

Jack Krupansky
34 min readMay 3, 2023

The quantum computers of today are not practical quantum computers since they are still in their infancy and too limited and insufficient to be ready for practical use to solve practical real-world problems. This informal paper will briefly define and explore the numerous factors which are critical to achieving a practical quantum computer, and to distinguish practical quantum computers from general-purpose quantum computers in general.

Caveat: My comments here are all focused only on general-purpose quantum computers. Some may also apply to special-purpose quantum computing devices, but that would be beyond the scope of this informal paper. For more on this caveat, see my informal paper:

Topics discussed in this informal paper:

  1. In a nutshell
  2. My elevator pitch for quantum computing
  3. Practical means support for production-scale practical real-world applications and achieving significant quantum advantage, and delivering significant business value
  4. What is a practical quantum computer?
  5. What is a general-purpose quantum computer?
  6. Excludes special-purpose quantum computing devices
  7. Should special-purpose quantum computers be allowed to be considered practical quantum computers? Maybe, a toss-up, but not for now
  8. For now, special-purpose quantum computers meeting practical needs should be considered practical special-purpose quantum computing devices, NOT practical quantum computers
  9. Go for it if a special-purpose quantum computing device fits your needs, but that will likely be more of a rarity than common
  10. The primary distinction between a general-purpose quantum computer and a practical quantum computer
  11. Able to execute the full range of applications expected for quantum computing
  12. Support production-scale applications
  13. Achieves significant quantum advantage over classical computing
  14. Delivers significant business value
  15. Single sentence definition for quantum computer
  16. The essence of quantum computing: exploiting the inherent parallelism of a quantum computer
  17. Why aren’t current quantum computers considered to be practical quantum computers?
  18. Short summary of the primary needs to achieve practical quantum computing
  19. Working at the raw qubit/gate level is not very productive or practical
  20. Is full quantum error correction (QEC) required? Not for most applications with near-perfect qubits
  21. Need for fine granularity of phase, quantum Fourier transform, and quantum phase estimation
  22. All practical quantum computers are general-purpose quantum computers
  23. Not all general-purpose quantum computers are practical quantum computers
  24. NISQ devices are unlikely to be practical quantum computers
  25. Post-NISQ quantum computing is required for practical quantum computing
  26. What is needed to get to a practical quantum computer?
  27. What is practical quantum computing?
  28. A full quantum ecosystem is needed to enable practical quantum computing
  29. 24 to 40-qubit algorithms as the starting point for practical quantum computing
  30. Quantum algorithms using less than 24 qubits simply don’t represent practical quantum computing
  31. Functional roadmaps for the wide range of resource requirements depending on use case and input data
  32. My own proposal for 48 fully-connected near-perfect qubits
  33. The ENIAC Moment as a milestone for practical quantum computing
  34. Three stages for adoption of practical quantum computing for production-scale practical real-world quantum applications
  35. Need for a quantum Hello World app that demonstrates significant quantum advantage using quantum parallelism
  36. Useful quantum computer seems to be a synonym for practical quantum computer
  37. When might a practical quantum computer become available?
  38. Further information on quantum computers
  39. Conclusions

In a nutshell

  1. Practical means support for production-scale practical real-world applications and achieving significant quantum advantage, and delivering significant business value.
  2. The primary distinction between a general-purpose quantum computer and a practical quantum computer is that while the former has all of the required functional capabilities, only the latter has the capacity and quality to support production-scale practical real-world applications.
  3. All practical quantum computers are general-purpose quantum computers. Not limited to a niche or limited range of applications.
  4. Not all general-purpose quantum computers are practical quantum computers. Lack the qubit fidelity, qubit connectivity, granularity of qubit phase and probability amplitude, and maximum circuit size, to enable practical quantum computing.
  5. Able to execute the full range of applications expected for quantum computing.
  6. Support production-scale applications. Running tiny, toy-scale quantum algorithms and prototype applications is not sufficient for a practical quantum computer.
  7. Achieves significant quantum advantage over classical computing. Well beyond the reach of classical computing.
  8. Delivers significant business value. Well beyond the reach of classical computing.
  9. Excludes special-purpose quantum computing devices. Which apply to a more limited range of applications and have a much more limited ability to support arbitrary quantum algorithms. That includes quantum annealers, adiabatic quantum computers, boson sampling devices, photonic quantum computing, neutral-atom qubits, physics simulators, and software-configurable physics experiments.
  10. Should special-purpose quantum computers be allowed to be considered practical quantum computers? Maybe, a toss-up, but not for now.
  11. For now, special-purpose quantum computers meeting practical needs should be considered practical special-purpose quantum computing devices, NOT practical quantum computers. But, be very careful — assessing application needs and matching to device capabilities can be very tricky. It’s an easier task to choose to go with a general-purpose quantum computer, a practical quantum computer.
  12. Go for it if a special-purpose quantum computing device fits your needs, but that will likely be more of a rarity than common
  13. Current quantum computers are not considered to be practical quantum computers. Not up to the task. Capabilities are too limited.
  14. Short summary of the primary needs to achieve practical quantum computing. Qubit count — we’re essentially there. Qubit fidelity. Qubit connectivity. Fine granularity of phase and probability amplitude. Coherence time and gate execution time sufficient to support larger and deeper circuits. High-level programming model with high level data types and operations. Algorithmic building blocks and algorithm design patterns for exploiting quantum parallelism. And a high-level quantum-native programming language to support all of those high-level capabilities. Better simulators supporting higher qubit and quantum state capacity, with higher performance and debugging capabilities.
  15. Working at the raw qubit/gate level is not very productive or practical. A high-level programming model with high level data types and operations, and high-level algorithmic building blocks would dramatically boost productivity, and eliminate the need for most people to even know about raw qubits and gates.
  16. Is full quantum error correction (QEC) required? No, near-perfect qubits should be sufficient for most applications. Some higher-complexity applications will need it, so they will have to wait for a few more additional years.
  17. Need for fine granularity of phase, quantum Fourier transform, and quantum phase estimation. Current NISQ quantum computers are severely constrained by limited granularity of phase and probability amplitude, which preclude support for quantum Fourier transform (QFT), quantum phase estimation (QPE), amplitude amplification, and quantum amplitude estimation (QAE), which are required for many of the more sophisticated quantum algorithms.
  18. NISQ devices are unlikely to be practical quantum computers. Although NISQ devices can be general-purpose quantum computers, they generally lack the qubit fidelity, qubit connectivity, granularity of qubit phase and probability amplitude, and maximum circuit size needed to be practical quantum computers.
  19. Post-NISQ quantum computing is required for practical quantum computing. Post-NISQ quantum computing offers the qubit fidelity, qubit connectivity, granularity of qubit phase and probability amplitude, and maximum circuit size needed to achieve a practical quantum computer.
  20. A full quantum ecosystem is needed to enable practical quantum computing.
  21. 24 to 40-qubit algorithms as the starting point for practical quantum computing. But a change in mindset will be required.
  22. Quantum algorithms using less than 24 qubits simply don’t represent practical quantum computing. There might be some niche applications that can achieve some sort of quantum advantage and deliver some sort of business value using less than 24 qubits, but they would be the very rare exception rather than the norm.
  23. Functional roadmaps for the wide range of resource requirements depending on use case and input data. No one size fits all. The emphasis is on application-level functions or use cases rather than on raw hardware capabilities or dates — what hardware capabilities must be available to enable particular application functions or use cases. For example, as qubit count, gate fidelity, and maximum circuit size incrementally increase, what application use cases and data sizes become practical. For example, what complexity of molecules can be modeled as resources increase. And skip the whole debate and focus on NISQ vs. FTQC to focus on required gate fidelity, regardless of how it is achieved, whether through raw gate fidelity, error mitigation, error suppression, or error correction.
  24. My own proposal for 48 fully-connected near-perfect qubits. It may not be the most optimal configuration, but it’s a place to start. This is what I believe should be the low-end for a practical quantum computer.
  25. Three stages for adoption of practical quantum computing for production-scale practical real-world quantum applications. The ENIAC Moment, configurable packaged quantum solutions, and The FORTRAN Moment.
  26. Need for a quantum Hello World app that demonstrates significant quantum advantage using quantum parallelism. Enable people to more intuitively grasp what’s needed and what’s going on.
  27. As best as I can tell, useful quantum computer seems to be a synonym for practical quantum computer. And useful quantum computing is a synonym for practical quantum computing. I can’t speak to whether those using the terms useful quantum computer/computing are presuming that it is based on a general-purpose quantum computer, but from my own perspective, I would presume so.
  28. There is no really good answer now for the question of when a practical quantum computer might become available. Estimates will vary greatly, from one to ten years. But two to three or four years seems like a plausible working assumption, for now.

My elevator pitch for quantum computing

If you feel unprepared to dive into some of the nuances of what makes a quantum computer a practical quantum computer, you might want to get a modest refresher on quantum computing by reading my elevator pitch for quantum computing:

Practical means support for production-scale practical real-world applications and achieving significant quantum advantage, and delivering significant business value

The primary, essential focus is on production-scale data.

The overall focus is on addressing the full needs of production-scale practical real-world applications.

And achieving significant quantum advantage, and delivering significant business value.

What is a practical quantum computer?

As already mentioned, quantum computers are still in their infancy and too limited and insufficient to be ready for practical use to solve practical real-world problems. So, what is a practical quantum computer? By definition:

  • A practical quantum computer supports production-scale practical real-world quantum applications and achieves significant quantum advantage over classical computing and delivers significant business value which is well beyond the reach of classical computing.
  • Preferably dramatic quantum advantage and extraordinary business value. But significant quantum advantage and significant business value are a good start.

A slightly more functional definition for a practical quantum computer:

  1. A general-purpose quantum computer.
  2. Able to execute a nontrivial quantum circuit and produce measurable results.
  3. Able to execute production-scale production-quality practical real-world applications.
  4. Able to execute some interesting quantum computation that has some practical application or at least a fraction of some practical application.
  5. Able to achieve substantial quantum advantage.
  6. Delivers significant business value.

What is a general-purpose quantum computer?

A general-purpose quantum computer is:

  • A quantum computing device which can be applied to the widest range of applications and programmed for the most general quantum algorithms.
  • This is in contrast with a special-purpose quantum computer or special-purpose quantum computing device which applies to a more limited range of applications and has a much more limited ability to support arbitrary quantum algorithms.
  • Universal gate-based quantum computer is a synonym for a general-purpose quantum computer.

A general-purpose quantum computer might not be a practical quantum computer if it lacks the sufficient resources to enable production-scale applications.

For more on general-purpose quantum computers, see my informal paper:

  • What Is a General-Purpose Quantum Computer?

Excludes special-purpose quantum computing devices

Again, the focus for practical quantum computers is general-purpose quantum computers, not special-purpose quantum computing devices, which apply to a more limited range of applications and have a much more limited ability to support arbitrary quantum algorithms. That includes quantum annealers, adiabatic quantum computers, boson sampling devices, photonic quantum computing, neutral-atom qubits, physics simulators, and software-configurable physics experiments.

For more on this caveat, see my informal paper:

  • What Is a General-Purpose Quantum Computer?

Should special-purpose quantum computers be allowed to be considered practical quantum computers? Maybe, a toss-up, but not for now

What about special-purpose quantum computers or special-purpose quantum computing devices which actually are able to support some limited, niche, but nonetheless practical and production-scale applications — shouldn’t they be considered practical quantum computers? In short, maybe, at least in some cases, and it could be a toss-up, but overall I would say no, not for now.

Some people may strenuously object — especially vendors of such devices, but the goal here is to focus on general-purpose quantum computers and when they achieve the level of capacity and quality to enable production-scale practical real-world applications.

For now, special-purpose quantum computers meeting practical needs should be considered practical special-purpose quantum computing devices, NOT practical quantum computers

So, for now, in the cases where special-purpose quantum computers or special-purpose quantum computing devices actually are able to support some limited, niche, but nonetheless practical and production-scale applications, we should consider them practical special-purpose quantum computing devices, or maybe practical special-purpose quantum computers, but that could be a stretch too far. But in any case, they should not be treated as practical quantum computers, which should be reserved for general-purpose quantum computers.

This of course begs the question of whether or when special-purpose quantum computers or special-purpose quantum computing devices actually are able to support practical and production-scale applications. For now, the point and distinction is moot.

In any case, let’s endeavor to make a clear distinction between general-purpose quantum computers and special-purpose quantum computing devices, whether practical or not.

Go for it if a special-purpose quantum computing device fits your needs, but that will likely be more of a rarity than common

There are indeed going to be situations where a special-purpose quantum computing device may fit your needs in a practical sense, especially for production-scale data, but that will likely be more of a rarity than a common situation. And that would make it a practical special-purpose quantum computing device, not a practical quantum computer.

Be very careful — assessing your application needs and matching them to the capabilities of a specific special-purpose quantum computing device can be extremely tricky. A task best left to the most elite of experts, not the average quantum algorithm designer or quantum application developer.

It’s a much easier task to choose to go with a general-purpose quantum computer.

If you fail with a general-purpose quantum computer, you can easily be forgiven, but if you fail by rejectinge a general-purpose quantum computer and going with a special-purpose quantum computing device, people will be more likely to ask what were you thinking.

A general-purpose quantum computer is the safer choice.

The primary distinction between a general-purpose quantum computer and a practical quantum computer

The primary distinction between a general-purpose quantum computer and a practical quantum computer is that while the former has all of the required functional capabilities, only the latter has the capacity and quality to support production-scale practical real-world applications.

The details of the technical requirements for a practical quantum computer will be discussed in subsequent sections, but include:

  1. Qubit count. Not a problem in many cases even today, except for trapped-ion qubits.
  2. Qubit fidelity.
  3. Qubit connectivity.
  4. Granularity of qubit phase and probability amplitude.
  5. Maximum circuit size. Includes coherence time.

Able to execute the full range of applications expected for quantum computing

Unlike special-purpose quantum computing devices which can execute only a limited range of applications, a general-purpose quantum computer is able to execute the full range of applications that have been promised for quantum computing.

Although this may be subject to the caveat of not necessarily supporting some applications that may require more qubits, greater qubit fidelity, greater qubit connectivity, or greater maximum circuit size than the device supports.

For a summary of the types of applications that have been promised for quantum computing, see my informal paper:

Support production-scale applications

Running tiny, toy-scale quantum algorithms and prototype applications is not sufficient for a practical quantum computer.

The ability to execute production-scale quantum applications which address practical real-world problems is an essential requirement for being a practical quantum computer.

Achieves significant quantum advantage over classical computing

Quantum advantage expresses how much more powerful a quantum solution is compared to a classical solution. Typically expressed as either how many times faster the quantum computer is, or how many years, decades, centuries, millennia, or even millions or billions or trillions of years a classical computer would have to run to do what a quantum computer can do in mere seconds, minutes, or hours.

The ultimate goal of quantum computing is dramatic quantum advantage, a quantum advantage that is truly mind-boggling. Not just 50% or 2X or 4X or even 100X faster, but upwards of a quadrillion X and more faster than a classical computer.

But short of that ultimate goal of dramatic quantum advantage, we can expect a fraction of that goal, which I call fractional quantum advantage.

But still well beyond the reach of classical computing.

Preferably dramatic quantum advantage. But significant quantum advantage is a good start.

For more detailed discussion of quantum advantage, see the relevant sections of my informal paper on quantum computing:

Particularly these sections:

  1. Quantum advantage
  2. Dramatic quantum advantage is the real goal
  3. Quantum advantage — make the impossible possible, make the impractical practical
  4. Fractional quantum advantage
  5. Three levels of quantum advantage — minimal, substantial or significant, and dramatic quantum advantage
  6. Net quantum advantage — discount by repetition needed to get accuracy
  7. What is the quantum advantage of your quantum algorithm or application?
  8. Be careful not to compare the work of a great quantum team to the work of a mediocre classical team

Delivers significant business value

Well beyond the reach of classical computing.

Preferably extraordinary business value. But significant business value is a good start.

Single sentence definition for quantum computer

A quantum computer is a specialized electronic device which is able to perform a fairly small calculation on a very large number of possible solution values all at once using a process known as quantum parallelism, producing a solution value in a very short amount of time.

The essence of quantum computing: exploiting the inherent parallelism of a quantum computer

At its essence, quantum computing enables a quantum application to exploit the inherent parallelism of a quantum computer to evaluate a very large number of potential solutions to a relatively small computation all at once, delivering a result in a very short amount of time.

Why aren’t current quantum computers considered to be practical quantum computers?

We do have quantum computers today, but they are still in their infancy and too limited and insufficient to be ready for practical use to solve practical real-world problems, so they are not practical quantum computers.

So what makes a quantum computer too limited and insufficient to be a practical quantum computer? A number of factors, all of which are critical:

  1. Insufficient qubit capacity. Generally not the limiting factor today since we do have quantum computers with 32, 40, 53, 65, 80, and even 127 qubits. But some quantum computers are even smaller, such as 27 qubits or even 22 qubits.
  2. Insufficient qubit fidelity. The qubits are too susceptible to noise and the error rate is too high for even basic operations. Many people sincerely feel that full quantum error correction (QEC) is needed, but I disagree and feel that near-perfect qubits with four to five nines of qubit fidelity should be sufficient for most applications.
  3. Too noisy. Same as insufficient qubit fidelity.
  4. Insufficient qubit connectivity. Full any-to-any qubit connectivity is required. Some quantum computers do have sufficient qubit connectivity, namely trapped-ion quantum computers, but they may not have sufficient qubits, coherence time, or other factors.
  5. Limited coherence time. Qubits fail to properly retain their quantum state for a sufficient period of time to complete execution of the quantum algorithm. Some quantum computers do have qubits with extended coherence time, but fall short on other factors.
  6. Limited circuit depth or maximum circuit size. Unable to execute quantum algorithms of the desired size. Generally limited by coherence time, but it’s the coherence time divided by the gate execution time which determines that maximum number of quantum logic gates which can be executed in a given quantum algorithm (quantum circuit.)
  7. Limited granularity of phase and probability amplitude. Many of the more sophisticated quantum algorithms require very fine granularity of phase or probability amplitude, such as for quantum Fourier transform (QFT), quantum phase estimation (QPE), amplitude amplification, and quantum amplitude estimation (QAE).
  8. Lack of sophisticated quantum algorithms. Many of the current quantum algorithms available today are either focused on a relatively small or trivial number of qubits or require a very large number of qubits (hundreds, thousands, or even millions.)
  9. Lack of quantum applications ready to utilize quantum algorithms. It’s a chicken and egg problem, but even if we had hardware and algorithms suitable for a practical quantum computer, we when then be waiting on applications which are able to utilize such quantum algorithms.
  10. Inability to achieve any significant quantum advantage. That’s the true objective of even bothering with the complexity of quantum computing.
  11. Not delivering substantial business value. And the real goal is to achieve extraordinary business value. The consequence of not achieving any significant quantum advantage.
  12. Lack of sufficient support software for widespread high-volume usage of quantum applications. Quantum computing systems are just not set up for widespread and high-volume usage.
  13. Lack of a viable business model. No idea how quantum computing should be priced, or how high-availability and redundancy should be priced for practical quantum computers to be an economically-viable business proposition.
  14. Lack of sufficient hardware system capacity. No idea how many quantum applications and quantum algorithms will be executing at a single moment. It’s a chicken and egg problem, but without enough quantum computer systems to satisfy demand, quantum applications won’t be… practical.
  15. Inability to handle production-scale input data. An absolute requirement.
  16. Lack of a high-level programming model. Stuck with a low-level programming model. Difficult to learn and use. Especially problematic for larger and more complex quantum algorithms. Working with raw qubits and gates is not conducive to productivity. High-level data types and operations would boost productivity.
  17. Lack of high-level algorithmic building blocks. Same issues as with the low-level programming model.
  18. Lack of a high-level quantum-native programming language. Based on a high-level programming model.
  19. Need for simulators supporting higher qubit and quantum state capacity, with higher performance and debugging capabilities.
  20. Difficult to transform application problems into quantum algorithms. A consequence of the low-level programming model and the lack of high-level algorithmic building blocks.

Short summary of the primary needs to achieve practical quantum computing

From a hardware perspective, the primary, critical needs to achieve practical quantum computing:

  1. Qubit count. We’re essentially there. Except for trapped-ion qubits.
  2. Qubit fidelity. Really need four nines. Or at least 3.75 nines. Maybe 3.5 nines. Maybe 3.25 nines for some applications.
  3. Qubit connectivity. Really need full any-to-any connectivity.
  4. Fine granularity of phase and probability amplitude. Sufficient for a fairly large quantum Fourier transform or quantum phase estimation. Maybe a million gradations would be best to get started.
  5. Coherence time and gate execution time sufficient to support larger and deeper circuits. Enough for a few thousand gates. Or at least hundreds of gates to get started.

Beyond the hardware:

  1. High-level programming model. With high-level data types and operations to boost productivity.
  2. High-level algorithmic building blocks.
  3. Algorithm design patterns for exploiting quantum parallelism.
  4. High-level quantum-native programming language to support all of those high-level capabilities.
  5. Better simulators. Higher qubit and quantum state capacity. Higher performance. Debugging capabilities.

Working at the raw qubit/gate level is not very productive or practical

As quantum algorithms get significantly more complex, working at the raw qubit/gate level becomes increasingly unproductive.

A high-level programming model with high-level data types and operations, combined with high-level algorithmic building blocks would be much more productive.

In my view, very few people should even know about qubits — and wouldn’t with those higher-level features.

For more on this view, see my informal paper:

Is full quantum error correction (QEC) required? Not for most applications with near-perfect qubits

No, most applications will not require full quantum error correction (QEC) since near-perfect qubits with four to five nines of qubit fidelity should be sufficient for most applications.

Some higher-complexity applications will need it, so they will have to wait for a few more additional years.

In some cases, manual error mitigation or error suppression techniques will help to bridge the twin gaps while we wait for near-perfect qubits and full quantum error correction (QEC).

Granted, we won’t have true logical qubits until we get full quantum error correction (QEC), but many applications won’t need logical qubits if physical qubits have a low-enough error rate as can be achieved with near-perfect qubits.

For more detail on quantum error correction (QEC), see my informal paper:

For more detail on near-perfect qubits, see my informal paper:

In truth, at this juncture, I personally don’t believe that full quantum error correction (QEC) is ever going to be practical. It’s a great idea and will work in theory, but not in practice. For more detail, see my informal paper:

We will have to make do with near-perfect qubits, manual error mitigation, and error suppression. That will likely make some applications impractical at least in the relatively near term, but that’s life and every technology has its limits. As was done with classical computing, constantly pushing down the error rates of physical qubits will be the primary avenue for increasing the breadth and depth of practical quantum applications. Much research and clever engineering will be required.

Need for fine granularity of phase, quantum Fourier transform, and quantum phase estimation

Current NISQ quantum computers are severely constrained by limited granularity of phase and probability amplitude, which preclude support for quantum Fourier transform (QFT), quantum phase estimation (QPE), amplitude amplification, and quantum amplitude estimation (QAE), which are required for many of the more sophisticated quantum algorithms.

Support for these capabilities is needed to achieve practical quantum computing.

All practical quantum computers are general-purpose quantum computers

By definition, all practical quantum computers are general-purpose quantum computers.

Not all general-purpose quantum computers are practical quantum computers

Although by definition all practical quantum computers are general-purpose quantum computers, not all general-purpose quantum computers are practical quantum computers.

A general-purpose quantum computer might not be a practical quantum computer if either:

  1. It has too few qubits. Insufficient to address production-scale practical real-world problems.
  2. It has too low qubit fidelity. Ditto.
  3. It has too limited qubit connectivity. Ditto.
  4. It has too limited coherence time. Ditto.
  5. It fails to support large quantum algorithms. Ditto.
  6. It fails to support production-scale applications. Ditto.

NISQ devices are unlikely to be practical quantum computers

NISQ devices generally lack the qubit fidelity, qubit connectivity, granularity of qubit phase and probability amplitude, and maximum circuit size needed to be practical quantum computers.

Much more is needed…

Post-NISQ quantum computing is required for practical quantum computing

Only when we get to post-NISQ quantum computing will we have the technical capabilities, such as the qubit fidelity, qubit connectivity, granularity of qubit phase and probability amplitude, and maximum circuit size, to enable practical quantum computing.

For more on post-NISQ quantum computing, see my informal paper:

What is needed to get to a practical quantum computer?

Satisfying all of the factors listed in the previous section is limited to a relatively small number of factors:

  1. Research. Much more research is needed. We just don’t know how to solve a lot of these problems.
  2. Computer engineering. Overall design of a quantum computer. The machine architecture as well as the qubits and how they interact and are operated on.
  3. Algorithm design. We have some approaches, but we need a lot more and a lot more refinement.
  4. Quantum computer science. We need to formalize a lot of the ad hoc approaches used to design quantum algorithms. Including formalization of quantum parallelism and quantum advantage.
  5. Quantum software engineering. We need to formalize better methods for overall approaches to both design of quantum algorithms and development of quantum applications, as well as how quantum applications are packaged, tested, benchmarked, deployed, maintained, and enhanced over time. We need a full lifecycle model

What is practical quantum computing?

Practical quantum computing is the fruition of quantum computing, when practical quantum computers themselves come to fruition, coupled with all of the software, algorithms, applications, and other components of quantum computing.

Practical quantum computers are the hardware.

Practical quantum computing is the hardware plus all of the software. As well as the community and ecosystem to support it.

The software includes quantum algorithms, quantum applications, support software, and tools, especially developer tools.

A full quantum ecosystem is needed to enable practical quantum computing.

A full quantum ecosystem is needed to enable practical quantum computing

Quantum hardware and software are not enough for practical quantum computing. A full ecosystem is needed.

Besides the hardware and software, many items are needed for a full quantum ecosystem:

  1. Education.
  2. Training.
  3. Ongoing research.
  4. Consulting.
  5. Conferences.
  6. Publications.
  7. Community.
  8. Ecosystem.

It may be three to five, seven, or even ten years before practical quantum computers are generally available which support production-scale practical real-world quantum applications and achieve dramatic quantum advantage over classical computing and deliver extraordinary business value which is well beyond the reach of classical computing.

24 to 40-qubit algorithms as the starting point for practical quantum computing

At present, few quantum algorithms focused on practical real-world applications use more than even 16 qubits. In fact, I haven’t seen any use even 24 qubits. Oddball computer science experiments excepted.

I would suggest that quantum algorithms using between 24 and 40 qubits are likely to be the low end and starting point for practical quantum computing.

Despite the fact that we can currently simulate quantum algorithms using 24 to 40 qubits, we still are not seeing any quantum algorithms in that range.

It will likely take a significant change in mindset before we do start seeing quantum algorithms in that range.

Quantum algorithms using 48 to 80 qubits are likely to enable even more practical quantum applications, but unfortunately we won’t be able to fully simulate them, which makes their development, debugging, and testing significantly more challenging.

Once again, it will likely take yet another significant change in mindset before we do start seeing quantum algorithms in that range.

And quantum algorithms using 80 to 100 qubits, or 100 to 120 qubits, or 120 to 160 qubits, or even 160 to 250 qubits are well beyond what we can speculate let alone actually support in the next few years.

For more on the dearth of practical quantum algorithms, see my informal paper:

Quantum algorithms using less than 24 qubits simply don’t represent practical quantum computing

While it’s credible to imagine that quantum algorithms using 24 to 40 qubits can represent practical quantum computing, at least as a low end starting point, it simply isn’t credible to believe that quantum algorithms using less than 24 qubits could be solving practical real-word problems and achieving a significant quantum advantage and delivering significant business value.

Some of the qubit capacities unlikely to represent practical quantum computing:

  1. 5 qubits.
  2. 8 qubits. Or 7 qubits.
  3. 10 qubits. Or 9 qubits.
  4. 12 qubits. Or 11 or 13 qubits.
  5. 16 qubits. Or 15 or 17 qubits.
  6. 20 qubits. Or 21 qubits.
  7. 22 qubits. Or 23 qubits.

There might be some niche applications that can achieve some sort of quantum advantage and deliver some sort of business value using less than 24 qubits, but they would be the very rare exception rather than the norm.

Functional roadmaps for the wide range of resource requirements depending on use case and input data

Not every use case will have the same quantum computer resource requirements. Factors affecting the resource requirements include:

  1. The use case.
  2. The input data.
  3. Requirements for output data.
  4. Parameter values which can affect the processing.
  5. Details of the processing in the quantum algorithm.

Resource requirements include:

  1. Qubit count. Either physical or logical qubits, as the remainder of the requirements require.
  2. Two-qubit gate fidelity or error rate. Either the physical gate fidelity, or the net logical gate fidelity if logical qubits and quantum error correction are used.
  3. Maximum circuit size. Implies a combination of coherence time and gate execution time. May imply logical qubits and quantum memory if the physical coherence time is too short or the two-qubit physical gate fidelity is too small for the quantum circuit(s) to be executed.
  4. Qubit connectivity. Implied by the quantum circuit. But full connectivity is the goal — and assumption here.
  5. Granularity of phase and probability amplitude. Required to achieve required precision of results and intermediate quantum state for the quantum circuit(s) to be executed.
  6. Shot count (circuit repetitions). Based on input data and parameters, how many times must the circuit be executed to reliably develop a valid expectation value (result). Larger input data and circuit size will tend to boost the shot count, while increasing qubit/gate fidelity (reducing error rate) will tend to reduce the shot count.

As far as detailing particular use cases, that’s beyond the scope of this informal paper.

The goal of this section is to lay out a template for the wide ranges of resource requirements for various applications or use cases. This is effectively a roadmap, a functional roadmap without dates— or at least a template for a roadmap, but focused on functional resource requirements for use cases rather than raw hardware capabilities of specific quantum computer hardware systems by date. The ultimate dates, the timeline markers, will indeed matter, eventually, but are unknown and irrelevant at this stage.

There are two main types of ranges, or functional roadmaps (without dates), if you will:

  1. Qubit count.
  2. Maximum circuit size.

Some use cases may be more limited by one or the other, or both.

For qubit count-limited use cases, the range would indicate use cases, and data sizes, which are enabled by particular qubit counts. And then secondarily the data sizes, circuit sizes, gate fidelities, and shot counts for each qubit count along the range.

For maximum circuit size-limited use cases, the range would indicate use cases, and data sizes, which are enabled by particular maximum circuit sizes. And then secondarily the data sizes, qubit counts, gate fidelities, and shot counts for each maximum circuit size along the range.

None of the precise details along the ranges can be specified here or at this time; the point here is to layout the outline or template for future work.

That said, here are the suggested qubit count milestones along the qubit count range:

  1. Small qubit count. 8, 12, 16, 20, 24.
  2. Medium qubit count. 28, 32, 40, 44.
  3. Medium-large qubit count. 48, 50, 56, 64.
  4. Large qubit count. 72, 80, 96, 100.
  5. Larger qubit count. 110, 115, 120, 125, 128.
  6. Even larger qubit count. 136, 148, 150, 160, 175, 192, 200, 228, 256.
  7. Very large qubit count. 384, 512, 768, 1024.
  8. Extremely large qubit count. 2048, 3172, 4096, 8192, 16384.

Sure, people talk about tens of thousands and millions of qubits, but… at this stage I’m more focused on even barely achieving practical quantum computing. My feeling at this stage is that 48 to 72 qubits should be sufficient to kick off an era of practical computing. Sure, there are quite a few existing quantum computing systems that exceed this qubit count, but fall short for other resource requirements.

Suggested maximum circuit size milestones along the maximum circuit size range:

  1. Small circuit size. 25, 50, 75, 100, 150 gates.
  2. Medium circuit size. 200, 250, 350, 500, 750.
  3. Medium-large circuit size. 1,000, 1,250, 1,500, 1,750, 2,000, 2,500.
  4. Large circuit size. 3,500, 5,000, 7,500, 10,000, 12,500.
  5. Larger circuit size. 15,000, 17,500, 20,000, 25,000.
  6. Very large circuit size. 35,000, 50,000, 75,000.
  7. Extremely large circuit size. 100,000, 250,000, 500,000, 1 million.

Sure, people talk about millions or even billions of gates, but… at this stage I’m more focused on even barely achieving practical quantum computing. Support for circuits with even just 2,500 to 5,000 gates would be very impressive.

NISQ vs. FTQC?

I suggest that we skip the whole debate and focus on NISQ vs. FTQC (quantum error correction (QEC) and logical qubits) to focus on required gate fidelity, regardless of how it is achieved, whether through raw gate fidelity, error mitigation, error suppression, or error correction.

Width of quantum Fourier Transform (QFT) and quantum phase estimation (QPE)

Besides detailing the particular use cases, it would also be very desirable to provide milestones for width of quantum Fourier Transform (QFT) and quantum phase estimation (QPE) that are supported at various milestones along the range of qubit counts or maximum circuit sizes since QFT/QPE width may be the key limiting factor for a lot of quantum algorithms.

It might be helpful to have a separate range (functional roadmap) for QFT/QPE, with circuit sizes, qubit counts, two-qubit gate fidelities (error rates), use cases, and data sizes as secondary milestones for each QFT/QPE width.

It is especially important for the range (functional roadmap) to specify circuit size and required two-qubit gate fidelity requirements for each use case and data size since many circuits will be critically limited by coherence time and error rate.

Technically, the input width and output width of the QFT/QPE can be different, but here we focus on just the wider width (input or output) or assume the two are the same.

Suggested quantum Fourier Transform (QFT) and quantum phase estimation (QPE) milestone widths:

  1. Small QFT/QPE width. 4, 6, 8, 10, 12.
  2. Medium QFT/QPE width. 16, 20, 24.
  3. Large QFT/QPE width. 28, 32, 36.
  4. Larger QFT/QPE width. 40, 44, 48.
  5. Very large QFT/QPE width. 50, 56, 64, 72, 80.
  6. Extremely large QFT/QPE width. 96, 100, 110, 115, 125, 128, 140, 160, 192, 200.

Sure, people talk about extremely wide QFT/QPE, particularly thousands of qubits for Shor’s factoring algorithm applied to cracking public key encryption for 2048-bit keys, but…at this stage I’m more focused on even barely achieving practical quantum computing. Even a 20-bit QFT/QPE would be very impressive.

Specialized scale for quantum computational chemistry

A specialized scale for quantum computational chemistry in particular would be helpful, such as a sequence of molecules of increasing complexity, as well as the range of computations that chemists find useful. And for each chemistry milestone, give the resource requirements — qubit count, gate fidelity, circuit size, and QFT/QPE width.

Milestones for Shor’s factoring algorithm

Although I personally don’t have high expectations that Shor’s factoring algorithm will ever practically work for larger key sizes, it should work for smaller semiprimes, and it might be a fun and interesting benchmark for non-toy quantum algorithms.

Some suggested milestones for smaller semiprimes for Shor’s factoring algorithm:

  1. Two digits. 7 bits, 343 gates (n³).
  2. Three digits. 10 bits, 1,000 gates.
  3. Four digits, 13 bits, 2,197 gates.
  4. Five digits. 17 bits, 4,913 gates.
  5. Six digits. 20 bits, 8,000 gates.
  6. Seven digits. 23 bits, 12,167 gates.
  7. Eight digits. 27 bits, 19,683 gates.
  8. Nine digits. 30 bits, 27,000 gates.
  9. Ten digits. 33 bits, 35,937 gates.
  10. Eleven digits. 37 bits, 50,653 gates.
  11. Twelve digits. 40 bits, 64,000 gates.

My own proposal for 48 fully-connected near-perfect qubits

The overall definition for a practical quantum computer covers a wide range and is relatively agnostic as to specific targets for the many essential factors.

I did endeavor to write up a proposal for what I believe should be the low-end for a practical quantum computer:

It may not be the most optimal configuration, but it’s a place to start.

I also speculated about a 36-qubit configuration as a stepping stone.

I also speculated about upgrading existing 27-qubit designs to this proposal as an even smaller initial stepping stone.

And I also speculated about a larger, 72-qubit configuration.

The ENIAC Moment as a milestone for practical quantum computing

There would be no better way to prove that we have achieved a practical quantum computer than by demonstrating a production-scale practical real-word quantum application. This is what I have been calling The ENIAC Moment.

For more detail on my concept of The ENIAC Moment, see my informal paper:

Three stages for adoption of practical quantum computing for production-scale practical real-world quantum applications

More than simply a singular moment, I envision three stages for adoption of practical quantum computing for production-scale practical real-world quantum applications:

  1. The ENIAC Moment. Hand-crafted applications. Very limited deployments. Relying on super-elite technical teams at only the most elite of organizations.
  2. Configurable packaged quantum solutions. Widespread deployments of a relatively few applications. Requires no quantum expertise.
  3. The FORTRAN Moment. Higher-level programming model. Widespread development of custom applications. No longer requires super-elite technical teams and is no longer limited to only the most elite of organizations.

For more detail on that three-stage model, see my informal paper:

Need for a quantum Hello World app that demonstrates significant quantum advantage using quantum parallelism

A relatively concise Hello World quantum application would enable people to more intuitively grasp what’s needed and what’s going on with practical quantum computing. It needs to clearly demonstrate both quantum parallelism and significant quantum advantage.

This would include both the quantum algorithm circuit and the quantum application code that uses the result of the quantum computation.

This should be an absolute requirement for demonstrating a practical quantum computer.

It should be tailored for my 48-qubit machine — call it my Hello World machine.

Maybe also a version trimmed down for 36 qubits that can be simulated easier.

And also a tiny version working on a four-qubit register for 2⁴ = 16 states to help visualize how quantum parallelism works, and to intuitively understand the results.

No real point for demonstrating real quantum computers until they are capable of this basic operation. Stick with simulation until then.

Useful quantum computer seems to be a synonym for practical quantum computer

As best as I can tell, the term useful quantum computer seems to be a synonym for the term practical quantum computer.

And the term useful quantum computing seems to be a synonym for the term practical quantum computing.

There may be nuances of difference that I am unaware of, but the terms are defined too vaguely to be sure. For example, I can’t speak to whether those using the terms useful quantum computer/computing are presuming that it is based on a general-purpose quantum computer, but from my own perspective, I would presume so.

When might a practical quantum computer become available?

There is no really good answer now for the question of when a practical quantum computer might become available. Estimates will vary greatly, from:

  1. Within a year. Unlikely.
  2. One to two years. Still unlikely, but at least remotely possible.
  3. Two to three years. Some non-trivial possibility. I’de like to believe it will happen by then, but color me an optimist.
  4. Four to five years. Seems almost a safe bet. Emphasis on almost.
  5. Five years. Feels like a reasonably solid possibility. Still, some non-trivial possibility that not even by then.
  6. Five to seven years. Reasonable likelihood.
  7. Seven to ten years. If not by then, then when?!
  8. Ten years. Definitely by then… right??

Two to three or four years seems like a plausible working assumption, for now.

Further information on quantum computers

For further details on quantum computers, see my informal paper:

Conclusions

  1. Practical means support for production-scale practical real-world applications and achieving significant quantum advantage, and delivering significant business value.
  2. The primary distinction between a general-purpose quantum computer and a practical quantum computer is that while the former has all of the required functional capabilities, only the latter has the capacity and quality to support production-scale practical real-world applications.
  3. All practical quantum computers are general-purpose quantum computers. Not limited to a niche or limited range of applications.
  4. Not all general-purpose quantum computers are practical quantum computers. Lack the qubit fidelity, qubit connectivity, granularity of qubit phase and probability amplitude, and maximum circuit size, to enable practical quantum computing.
  5. Able to execute the full range of applications expected for quantum computing.
  6. Support production-scale applications. Running tiny, toy-scale quantum algorithms and prototype applications is not sufficient for a practical quantum computer.
  7. Achieves significant quantum advantage over classical computing. Well beyond the reach of classical computing.
  8. Delivers significant business value. Well beyond the reach of classical computing.
  9. Excludes special-purpose quantum computing devices. Which apply to a more limited range of applications and have a much more limited ability to support arbitrary quantum algorithms. That includes quantum annealers, adiabatic quantum computers, boson sampling devices, photonic quantum computing, neutral-atom qubits, physics simulators, and software-configurable physics experiments.
  10. Should special-purpose quantum computers be allowed to be considered practical quantum computers? Maybe, a toss-up, but not for now.
  11. For now, special-purpose quantum computers meeting practical needs should be considered practical special-purpose quantum computing devices, NOT practical quantum computers. But, be very careful — assessing application needs and matching to device capabilities can be very tricky. It’s an easier task to choose to go with a general-purpose quantum computer, a practical quantum computer.
  12. Go for it if a special-purpose quantum computing device fits your needs, but that will likely be more of a rarity than common.
  13. Current quantum computers are not considered to be practical quantum computers. Not up to the task. Capabilities are too limited.
  14. Short summary of the primary needs to achieve practical quantum computing. Qubit count — we’re essentially there. Qubit fidelity. Qubit connectivity. Fine granularity of phase and probability amplitude. Coherence time and gate execution time sufficient to support larger and deeper circuits. High-level programming model with high level data types and operations. Algorithmic building blocks and algorithm design patterns for exploiting quantum parallelism. And a high-level quantum-native programming language to support all of those high-level capabilities. Better simulators supporting higher qubit and quantum state capacity, with higher performance and debugging capabilities.
  15. Working at the raw qubit/gate level is not very productive or practical. A high-level programming model with high level data types and operations, and high-level algorithmic building blocks would dramatically boost productivity, and eliminate the need for most people to even know about raw qubits and gates.
  16. Is full quantum error correction (QEC) required? No, near-perfect qubits should be sufficient for most applications. Some higher-complexity applications will need it, so they will have to wait for a few more additional years.
  17. Need for fine granularity of phase, quantum Fourier transform, and quantum phase estimation. Current NISQ quantum computers are severely constrained by limited granularity of phase and probability amplitude, which preclude support for quantum Fourier transform (QFT), quantum phase estimation (QPE), amplitude amplification, and quantum amplitude estimation (QAE), which are required for many of the more sophisticated quantum algorithms.
  18. NISQ devices are unlikely to be practical quantum computers. Although NISQ devices can be general-purpose quantum computers, they generally lack the qubit fidelity, qubit connectivity, granularity of qubit phase and probability amplitude, and maximum circuit size needed to be practical quantum computers.
  19. Post-NISQ quantum computing is required for practical quantum computing. Post-NISQ quantum computing offers the qubit fidelity, qubit connectivity, granularity of qubit phase and probability amplitude, and maximum circuit size needed to achieve a practical quantum computer.
  20. A full quantum ecosystem is needed to enable practical quantum computing.
  21. 24 to 40-qubit algorithms as the starting point for practical quantum computing. But a change in mindset will be required.
  22. Quantum algorithms using less than 24 qubits simply don’t represent practical quantum computing. There might be some niche applications that can achieve some sort of quantum advantage and deliver some sort of business value using less than 24 qubits, but they would be the very rare exception rather than the norm.
  23. Functional roadmaps for the wide range of resource requirements depending on use case and input data. No one size fits all. The emphasis is on application-level functions or use cases rather than on raw hardware capabilities or dates — what hardware capabilities must be available to enable particular application functions or use cases. For example, as qubit count, gate fidelity, and maximum circuit size incrementally increase, what application use cases and data sizes become practical. For example, what complexity of molecules can be modeled as resources increase. And skip the whole debate and focus on NISQ vs. FTQC to focus on required gate fidelity, regardless of how it is achieved, whether through raw gate fidelity, error mitigation, error suppression, or error correction.
  24. My own proposal for 48 fully-connected near-perfect qubits. It may not be the most optimal configuration, but it’s a place to start. This is what I believe should be the low-end for a practical quantum computer.
  25. The ENIAC Moment as a milestone for practical quantum computing. Demonstrating a production-scale practical real-word quantum application would certainly fit the bill for claiming and even proving that we have achieved a practical quantum computer.
  26. Three stages for adoption of practical quantum computing for production-scale practical real-world quantum applications. The ENIAC Moment, configurable packaged quantum solutions, and The FORTRAN Moment.
  27. Need for a quantum Hello World app that demonstrates significant quantum advantage using quantum parallelism. Enable people to more intuitively grasp what’s needed and what’s going on.
  28. As best as I can tell, useful quantum computer seems to be a synonym for practical quantum computer. And useful quantum computing is a synonym for practical quantum computing. I can’t speak to whether those using the terms useful quantum computer/computing are presuming that it is based on a general-purpose quantum computer, but from my own perspective, I would presume so.
  29. There is no really good answer now for the question of when a practical quantum computer might become available. Estimates will vary greatly, from one to ten years. But two to three or four years seems like a plausible working assumption, for now.

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