What Is Dramatic Quantum Advantage?

  1. Minimal quantum advantage. A 1,000X performance advantage over classical solutions. 2X, 10X, and 100X (among others) are reasonable stepping stones.
  2. Substantial or significant quantum advantage. A 1,000,000X performance advantage over classical solutions. 20,000X, 100,000X, and 500,000X (among others) are reasonable stepping stones.
  3. Dramatic quantum advantage. A one quadrillion X (one million billion times) performance advantage over classical solutions. 100,000,000X, a billion X, and a trillion X (among others) are reasonable stepping stones.
  • A performance advantage of one quadrillion X (one million billion) would be extremely compelling and the kind of dramatic quantum advantage that a quantum solution should be expected to deliver compared to a classical solution given all of the bold promises of quantum computing.
  1. There is no standard definition for what constitutes either quantum advantage or dramatic quantum advantage.
  2. I consider a 1,000,000X performance advantage to be the preferred starting point for a compelling dramatic quantum advantage — this should be the primary focus as a threshold for achieving dramatic quantum advantage. But even this would be a mere stepping stone to a much more dramatic quantum advantage. This is what I refer to as a substantial or significant quantum advantage.
  3. I consider a 1,000X performance advantage to be the minimal starting point, but more of a secondary, backup focus, only worthy of attention if a 1,000,000X performance advantage is out of reach. It should be considered more of a distraction or mere stepping stone rather than the primary objective. This is what I refer to as a minimal quantum advantage.
  4. I imagine that most people would probably agree that a performance advantage of one quadrillion X (one million billion) would be extremely compelling and the kind of advantage that a quantum solution should be expected to deliver given all of the bold promises of quantum computing. This would require the use of 50 or more qubits for the core of the quantum computation (2⁵⁰ = one quadrillion.) This is what I refer to as a dramatic quantum advantage.
  5. But for some time-critical niche applications even a 20X to 500X advantage or even a mere 2X to 10X advantage might offer a dramatic and compelling advantage — if a classical solution simply isn’t possible given the severe time constraints and the modest quantum solution is enough to finally enable a solution.
  6. Quantum advantage is generally nonlinear. As the size of the input grows, the advantage also grows, but not necessarily at the same rate as the input grows. Similarly, for smaller input sizes, the quantum advantage will be smaller. There will be some threshold input size where quantum advantage transitions from less than dramatic to very dramatic. Unfortunately, there can be extreme cases where the growth of the advantage eventually slows or the advantage even declines as input size grows, possibly even hitting a wall and failing. Be very cognizant of your input size to get a better handle on the actual quantum advantage.
  7. Beyond any technical metric, what matters most to many is that it just feels like a compelling advantage. It may be more of an emotional matter rather than a strictly technical matter.
  8. Alas, we’re not even close to achieving any significant quantum advantage, let alone dramatic quantum advantage in the near future. The relevance of this paper is for more than a few years from now. Consider it a preview of the future of quantum computing.
  1. Some questions that will be addressed by this paper
  2. Performance advantage is not a constant — depends on input size
  3. Where do we draw the line between a 25% advantage and a one quadrillion advantage?
  4. No standard or even consensus for quantum advantage, let alone for dramatic quantum advantage
  5. Algorithms and applications versus computer hardware alone
  6. A quantum solution versus a classical solution
  7. To each his own
  8. Different users within the same organization may have different expectations
  9. What is quantum advantage?
  10. Other meanings of quantum advantage in other areas of quantum information science
  11. Quantum computational advantage — synonym emphasizing quantum computing
  12. What is dramatic quantum advantage?
  13. Exponential speedup
  14. The ideal quantum advantage is exponential speedup
  15. It just feels like a truly compelling advantage
  16. Quantum advantage tends to be nonlinear
  17. In some cases, any quantum advantage can begin to slow or even decline
  18. Be very cognizant of your input size to get a better handle on the actual quantum advantage
  19. Fly in the ointment: shot count (circuit repetitions)
  20. What Is the actual quantum advantage of your quantum algorithm?
  21. Net quantum advantage
  22. Three categories of quantum advantage
  23. Wall clock problems
  24. Two-hour business process optimization problems
  25. Larger wall clock problems
  26. Be sure to use the same input data when comparing quantum solutions to classical solutions
  27. Ranges of actual quantum advantage
  28. Minimal, substantial or significant, and dramatic quantum advantage
  29. Minimal quantum advantage — 1,000X
  30. Substantial or significant quantum advantage — 1,000,000X
  31. Dramatic quantum advantage — one quadrillion X
  32. Fractional quantum advantage
  33. One, two, and three star quantum advantage
  34. Gold, silver, and bronze levels of quantum advantage
  35. Platinum, stainless steel, and brushed aluminum levels of quantum advantage
  36. Why aren’t 10X to 500X considered dramatic quantum advantage?
  37. Why aren’t 1,000X to 50,000X considered dramatic quantum advantage?
  38. 1,000,000X seems to be the best threshold for dramatic quantum advantage
  39. One quadrillion X would be a very clear and very compelling dramatic quantum advantage
  40. Flip a coin whether 100,000X to 750,000X should be considered significant quantum advantage?
  41. Be sure to divide net quantum advantage by the number of classical processors used by an application
  42. Special case quantum advantage: Generating random numbers
  43. Never underestimate the cleverness of classical programmers
  44. Don’t expect a dramatic quantum advantage from an algorithm offering only a quadratic speedup
  45. Application categories for practical quantum algorithms
  46. Quantum supremacy
  47. What about Google’s claim of quantum supremacy?
  48. Why is it so hard to explain quantum computing?
  49. Standard maximum classical computer configuration for comparisons
  50. Asking questions about quantum advantage should be a key criteria for reviewing algorithms, applications, papers, projects, and products
  51. We’re not there yet anyway
  52. When will we be there?
  53. Will dramatic quantum advantage require quantum error correction and error-free logical qubits?
  54. Is dramatic quantum advantage possible on NISQ quantum computers?
  55. Is any quantum advantage possible on any NISQ quantum computers?
  56. Best path to dramatic quantum advantage — Little data with a big solution space
  57. Summary and conclusions

Some questions that will be addressed by this paper

  1. What is quantum advantage?
  2. What is dramatic quantum advantage?
  3. What is the minimum quantum advantage?
  4. What is a substantial or significant quantum advantage?
  5. What is a fractional quantum advantage?
  6. Is an exponential speedup mandatory?
  7. What is an actual quantum advantage?
  8. What is a net quantum advantage?
  9. Is a 25% advantage a dramatic quantum advantage? 50%? 75%?
  10. Is a 2X advantage a dramatic quantum advantage? 4X? 8X?
  11. Is a 10X advantage a dramatic quantum advantage? 20X? 50X? 75X?
  12. Is a 100X advantage a dramatic quantum advantage? 250X? 500X? 750X?
  13. Is a 1,000X advantage a dramatic quantum advantage? 2,500X? 5,000X? 7,500X?
  14. Is a 10,000X advantage a dramatic quantum advantage? 25,000X? 50,000X? 75,000X?
  15. Is a 100,000X advantage a dramatic quantum advantage? 250,000X? 500,000X? 750,000X?
  16. Is a 1,000,000X advantage a dramatic quantum advantage? 10,000,000X? 100,000,000X? 500,000,000X?
  17. Is a 1,000,000,000X (billion) advantage a dramatic quantum advantage? 10,000,000,000X? 100,000,000,000X? 500,000,000,000X?
  18. Is a trillion X advantage a dramatic quantum advantage?
  19. Is a quadrillion X advantage a dramatic quantum advantage?

Performance advantage is not a constant — depends on input size

  1. Production-scale input size. Of course that can vary greatly. Just pick one. Although this is not practical at this time. Maybe in 5–7 years.
  2. The size of some presumed standardized test case for input which may be significantly smaller than production-scale so that it can actually be run on a real quantum computer or some hardware anticipated within a couple of years.
  3. The maximum input size which can be correctly processed by current quantum computer hardware which is much too limited to handle production-scale input or to handle even some more-desired input size which may become feasible within a couple of years.
  4. Hypothetical input sizes for proposed future quantum computers. Requires tools for estimating performance of a hypothetical quantum computer, using estimates for qubit count, qubit fidelity, gate error rates, maximum circuit depth, etc.
  5. The maximum input size which can be processed on a classical computer. Otherwise a comparison (quantum advantage) cannot be drawn between the quantum and classical solutions.

Where do we draw the line between a 25% advantage and a one quadrillion advantage?

No standard or even consensus for quantum advantage, let alone for dramatic quantum advantage

Algorithms and applications versus computer hardware alone

A quantum solution versus a classical solution

To each his own

Different users within the same organization may have different expectations

What is quantum advantage?

  • quantum advantage. A quantum computer can perform a particular computation significantly faster than even the best classical computer. And in some cases, a quantum computer can perform computations which no classical computer can perform at all — also referred to as quantum supremacy.

Other meanings of quantum advantage in other areas of quantum information science

  1. Quantum effects.
  2. Quantum information.
  3. Quantum computing.
  4. Quantum communication.
  5. Quantum networking.
  6. Quantum metrology.
  7. Quantum sensing.

Quantum computational advantage — synonym emphasizing quantum computing

What is dramatic quantum advantage?

  • Dramatic quantum advantage. Not simply a notable advantage of a quantum algorithm over a classical algorithm, but such a dramatic advantage that there is no question that the quantum-based solution is the only way to go. A 50% improvement or even a 2–4 times improvement might normally be advantageous when comparing two classical solutions, but a quantum solution might require a 10X, 100X, 1,000X, or even a factor of a million or a billion or more over a comparable classical solution to justify the intellectual difficulty and cost of going quantum.

Exponential speedup

The ideal quantum advantage is exponential speedup

It just feels like a truly compelling advantage

Quantum advantage tends to be nonlinear

  1. For n = 10, classical O(2¹⁰) = 1,024, quantum O(10²) = 100 = quantum advantage of 10X.
  2. For n = 15, classical O(2¹⁵) = 32,768, quantum O(15²) = 225 = quantum advantage of 146X.
  3. For n = 20, classical O(2²⁰) = 1,000,000, quantum O(20²) = 400 = quantum advantage of 2,500X.
  1. Start. The input size at which the quantum advantage starts to look attractive.
  2. Nominal. Or Typical. Or Target. The typical input size for the application. Hopefully it is greater than the start threshold, and above the dramatic threshold as well. There’s no guarantee that the input size is greater than the dramatic threshold.
  3. Dramatic. The input size at which quantum advantage becomes truly dramatic.

In some cases, any quantum advantage can begin to slow or even decline

Be very cognizant of your input size to get a better handle on the actual quantum advantage

  1. For n = 19, classical O(2¹⁹) = 524,288, quantum O(19²) = 361 = quantum advantage of 1,452, roughly 1,000.
  2. For n = 30, classical O(2³⁰) = 1,073,741,824, quantum O(30²) = 900 = quantum advantage of 1,193,046, roughly 1,000,000.

Fly in the ointment: shot count (circuit repetitions)

  1. Low qubit fidelity. High error rate for gates and measurements.
  2. Inherently probabilistic nature of quantum computation.
  1. For n = 19, the quantum advantage of 1,452 becomes 14.52 (divided by 100.) Not dramatic at all.
  2. For n = 30, the quantum advantage of 1,193,046 becomes 1,193 (divided by 1,000.) Still reasonably dramatic, but nowhere near as dramatic as 1,000,000.

What Is the actual quantum advantage of your quantum algorithm?

  1. Theoretical quantum advantage. A mathematical comparison of the algorithmic complexity of a quantum algorithm compared to the algorithmic complexity of a comparable classical algorithm. Typically, this will be a quantum algorithm with polynomial complexity or less compared to a classical algorithm with exponential complexity, so the quantum algorithm delivers an exponential speedup over the classical algorithm.
  2. Actual quantum advantage. The actual numerical advantage of a quantum algorithm over a comparable classical algorithm for specific input data, especially of a small to modest size, even if in theory a quantum algorithm would deliver an exponential speedup for larger input data.

Net quantum advantage

Three categories of quantum advantage

  1. Wall clock problems. Time is of the essence, the clock is ticking. Minutes and hours. Even a modest quantum advantage of 2X to 10X could make a great difference.
  2. Larger wall clock problem. Calendar time is significant. Days, weeks, months. A somewhat more dramatic quantum advantage of 1,000X or even a million is needed. But, for some niche applications, particularly those which have pushed classical computing to its limits, even a 20X to 100X advantage could deliver great value.
  3. Time per se is not an issue. Classical solutions are so impractical that even more months are not sufficient. Sure, maybe a classical solution can complete in many months or a year, but the significant advantage is a large factor of reduction in time and resources. A truly dramatic quantum advantage is needed — a factor of millions, billions, trillions, or even more is needed.

Wall clock problems

Two-hour business process optimization problems

Larger wall clock problems

  1. A day or two. Might be meaningful for an application which is run on the weekend, part of a weekly process.
  2. A week or two. Might be meaningful for some design process which occurs over a small number of months.
  3. A month or two. Might be meaningful for some process which occurs over many months or even a year or more.

Be sure to use the same input data when comparing quantum solutions to classical solutions

Ranges of actual quantum advantage

  1. Under 25%
  2. 25%
  3. 50%
  4. 75%
  5. 2X (100%)
  6. 4X
  7. 5X
  8. 8X
  9. 10X
  10. 20X
  11. 50X
  12. 75X
  13. 100X
  14. 250X
  15. 500X
  16. 750X
  17. 1,000X
  18. 2,500X
  19. 5,000X
  20. 7,500X
  21. 10,000X
  22. 25,000X
  23. 50,000X
  24. 75,000X
  25. 100,000X
  26. 250,000X
  27. 500,000X
  28. 750,000X
  29. 1,000,000X
  30. 10,000,000X
  31. 100,000,000X
  32. 500,000,000X
  33. Billion X
  34. 10 Billion X
  35. 100 Billion X
  36. 500 Billion X
  37. Trillion X
  38. 10 Trillion X
  39. 100 Trillion X
  40. 500 Trillion X
  41. Quadrillion X

Minimal, substantial or significant, and dramatic quantum advantage

  1. Minimal quantum advantage. A 1,000X performance advantage over classical solutions. 2X, 10X, and 100X (among others) are reasonable stepping stones.
  2. Substantial or significant quantum advantage. A 1,000,000X performance advantage over classical solutions. 20,000X, 100,000X, and 500,000X (among others) are reasonable stepping stones.
  3. Dramatic quantum advantage. A one quadrillion X (one million billion times) performance advantage over classical solutions. 100,000,000X, a billion X, and a trillion X (among others) are reasonable stepping stones.

Minimal quantum advantage — 1,000X

Substantial or significant quantum advantage — 1,000,000X

Dramatic quantum advantage — one quadrillion X

Fractional quantum advantage

  1. 1% minimum quantum advantage would be 0.01 times 1,000X or 10X.
  2. 10% minimum quantum advantage would be 0.10 times 1,000X or 100X.
  3. 50% minimum quantum advantage would be 0.50 times 1,000X or 500X.
  4. 5% substantial or significant quantum advantage would be 0.05 times 1,000,000X or 50,000X.
  5. 25% substantial or significant quantum advantage would be 0.25 times 1,000,000X or 250,000X.
  6. 1% dramatic quantum advantage would be 0.01 times one quadrillion X or ten trillion X.
  7. 0.1% dramatic quantum advantage would be 0.001 times one quadrillion X or one trillion X.
  8. 0.0001% dramatic advantage would be 0.000001 times one quadrillion X or one billion X.

One, two, and three star quantum advantage

  1. One star. Minimal quantum advantage — 1,000X.
  2. Two stars. Substantial or significant quantum advantage — 1,000,000X.
  3. Three stars. Dramatic quantum advantage — one quadrillion X.

Gold, silver, and bronze levels of quantum advantage

  1. Gold. Three stars. Dramatic quantum advantage — one quadrillion X.
  2. Silver. Two stars. Substantial or significant quantum advantage — 1,000,000X.
  3. Bronze. One star. Minimal quantum advantage — 1,000X.

Platinum, stainless steel, and brushed aluminum levels of quantum advantage

  1. Platinum. Gold. Three stars. Dramatic quantum advantage — one quadrillion X.
  2. Stainless steel. Silver. Two stars. Substantial or significant quantum advantage — 1,000,000X.
  3. Brushed aluminum. Bronze. One star. Minimal quantum advantage — 1,000X.

Why aren’t 10X to 500X considered dramatic quantum advantage?

Why aren’t 1,000X to 50,000X considered dramatic quantum advantage?

1,000,000X seems to be the best threshold for dramatic quantum advantage

One quadrillion X would be a very clear and very compelling dramatic quantum advantage

Flip a coin whether 100,000X to 750,000X should be considered significant quantum advantage?

But what about supercomputers?

Be sure to divide net quantum advantage by the number of classical processors used by an application

Special case quantum advantage: Generating random numbers

Never underestimate the cleverness of classical programmers

Don’t expect a dramatic quantum advantage from an algorithm offering only a quadratic speedup

Application categories for practical quantum algorithms

Quantum supremacy

  • quantum supremacy. A quantum computer is able to compute a solution to a particular problem when no classical computer is able to do so at all or in any reasonable amount of time. Does not imply either an advantage or supremacy for any other problems beyond the particular problem or niche of closely related problems. Alternatively, quantum advantage across a wide range of applications and computations. Or, possibly simply a synonym for quantum advantage.

What about Google’s claim of quantum supremacy?

Why is it so hard to explain quantum computing?

Standard maximum classical computer configuration for comparisons

  1. 1,000 servers. The low end.
  2. A few thousand servers.
  3. 10,000 servers. Seems like a sweet spot for a good standard size to use.
  4. 25,000 servers.
  5. 50,000 servers.
  6. 75,000 servers. A high-end maximum. The extreme. I’m unaware of anyone using more servers for a single application.
  1. Two hours.
  2. Eight hours. A single, full shift.
  3. One day.
  4. Two days.
  5. Three days.
  6. One week.
  7. Two weeks.
  8. One month.
  9. 45 days. Seems like the sweet spot for a good standard limit to use.
  10. Two months.
  11. Three months.
  12. Six months.
  13. One year. Not likely, but possible.
  • A distributed cluster of 10,000 reasonably high-end classical servers.
  • Running for a maximum of 45 days.

Asking questions about quantum advantage should be a key criteria for reviewing algorithms, applications, papers, projects, and products

  1. Have they achieved quantum advantage at all?
  2. What exactly is the quantum advantage that has been achieved?
  3. Have they examined not just the abstract theoretical quantum advantage, but also the actual net quantum advantage based on actual expected data input size?
  4. Have they clearly identified what input sizes were tested and quantified the actual net quantum advantage for those tested input sizes?
  5. Have they really only achieved a fractional quantum advantage, such as a modest advantage over classical solutions, but nothing particularly impressive and actually noteworthy?
  6. Not just claimed, but have they tested to confirm the claimed quantum advantage?
  7. Have they actually tested against a classical solution?
  8. Did the classical solution have sufficient hardware resources to fully exploit the extensive capabilities of classical computing?
  9. For what input size range have they achieved and tested quantum advantage?
  10. Does that input size represent a true, production-scale application, or is it really only for demonstration purposes and not ready for production-scale use?
  11. Has the classical solution really been optimized or may it be suboptimal so that the comparison with an optimal quantum solution is not a fair comparison?
  12. Exactly how much attention and how elite of a technical staff was placed on optimizing the classical solution?
  13. And have they really achieved dramatic quantum advantage as discussed in this paper?
  14. How scalable is their algorithm and its net quantum advantage over a broad range of input sizes?
  15. What shot count or circuit repetitions are needed, and how do they and quantum advantage scale as the input size scales? Have they taken shot count into account when calculating and measuring quantum advantage — to discount theoretical quantum advantage by shot count overhead?
  16. Do they have concise, crisp Big-O formulas for the algorithmic complexity of both the quantum and classical solutions.

We’re not there yet anyway

When will we be there?

  • This year? No way.
  • Next year? No.
  • Two years? Still not there.
  • Three to four years? Well, maybe for some narrow niche special cases, in special situations, but not generally across the board.
  • Five years? Some possibility, for some but not necessarily all application categories, but don’t bet the farm.
  • Seven years? I would hope so, but bet only very judiciously, and not for a few more years. At least for multiple application categories.
  • Ten years? A reasonable bet. For a wider range of application categories.
  • Fifteen years? A fairly sure thing. For most application categories.
  • Twenty years? Commonplace. For all application categories.

Will dramatic quantum advantage require quantum error correction and error-free logical qubits?

Is dramatic quantum advantage possible on NISQ quantum computers?

Is any quantum advantage possible on any NISQ quantum computers?

Best path to dramatic quantum advantage — Little data with a big solution space

Summary and conclusions

  1. There is no standard or even consensus as to what quantum advantage really is or what metric and what value for that metric should be used to judge quantum advantage, let alone for dramatic quantum advantage.
  2. Each user gets to decide based on their own business needs what numeric quantum advantage is sufficient to justify a quantum solution over a classical solution.
  3. Even within one organization, different projects or different business units may have different requirements or needs which result in differing thresholds for what constitutes an acceptable quantum advantage.
  4. The best to hope for is a range of expectations for each organization.
  5. Exponential speedup is the ideal, the best goal for quantum solutions. A quantum computer and quantum algorithm are not delivering on their true promise unless they deliver an exponential speedup compared to a classical algorithm running on a classical computer. Put simply, the time to execute a quantum algorithm with an exponential speedup grows much more slowly than the time to execute the comparable classical algorithm as the input size grows. Delivering an exponential speedup for a nontrivial amount of input data would certainly qualify as a dramatic quantum advantage.
  6. Regardless of the specific technical metric used to judge a dramatic quantum advantage, the real question is whether technical staff, users, managers, executives, and customers alike simply feel that the quantum solution is truly compelling — it just feels like a truly compelling advantage.
  7. But even if a quantum solution delivers something somewhat less than a strict exponential speedup, it’s still possible that the quantum solution might in fact still offer a quantum advantage of some sort, possibly a significant quantum advantage, and maybe even a dramatic quantum advantage. Anything is possible, but nothing is guaranteed — only exponential speedup for a nontrivial amount of input data provides a guarantee of dramatic quantum advantage.
  8. Whether a quantum algorithm which delivers only a quadratic speedup, such as the Grover search algorithm, delivers a dramatic quantum advantage can be problematic — some such algorithms may deliver a dramatic quantum advantage, while some may not. Generally, quadratic speedup should not be expected to deliver a significant quantum advantage, let alone a dramatic quantum advantage.
  9. I wouldn’t consider a performance advantage of 2X, 5X, 10X, 25X, 50X, or even 100X as a dramatic quantum advantage. Even 250X, 500X, and 750X just aren’t close.
  10. And anything less than 2X (25%, 50%, 75% advantage) would be hardly worth the effort since it is usually fairly easy for a skilled technical team to wring out such gains from classical computing solutions using clever tricks or just more hardware.
  11. A performance advantage of 1,000,000 X should be the primary focus as the preferred starting point threshold for dramatic quantum advantage. This is what I refer to as a substantial or significant quantum advantage.
  12. At a bare minimum, a performance advantage of 1,000X would start to be a dramatic quantum advantage, but should only be pursued if the 1,000,000X threshold cannot be achieved. It should be considered more of a distraction or mere stepping stone rather than the primary objective. This is what I refer to as a minimal quantum advantage.
  13. A performance advantage of one quadrillion X and more would be more typical of the kind of dramatic quantum advantage which we should be expecting from quantum computers. This is where the great promise of quantum computing lies. This would require the use of 50 or more qubits for the core of the quantum computation (2⁵⁰ = one quadrillion.) Even speedups of a billion or a trillion would be mere stepping stones. This is what I refer to as a dramatic quantum advantage.
  14. For some high-value niche applications a performance advantage of 5X to 10X might be sufficient to deliver significant value to an organization, but that would be more of an exception than the rule for quantum computing.
  15. Even 1,000X to 50,000X performance advantages are not necessarily truly dramatic quantum advantages since large distributed clusters of classical servers can achieve such gains without the need to completely switch from a classical mindset to a quantum mindset.
  16. Only advantages of 100,000X and more are clearly beyond even large distributed clusters of classical servers.
  17. One can consider partial achievement of a quantum advantage level, call it fractional quantum advantage, measured as a percentage or decimal fraction of the milestone metric.
  18. Direct comparisons with classical solutions can be misleading. It’s one thing if the classical solution is truly the best possible classical solution, but many classical solutions are far from optimal or best. It would be misleading to compare a great quantum solution to a mediocre classical solution. On the other hand, it would be very notable if a mediocre quantum solution greatly outperforms a great classical solution.
  19. Quantum supremacy is a special case of quantum advantage — where the quantum computer can perform a task which cannot be performed at all by a classical computer — there is no classical solution.
  20. Every algorithm, application, paper, project, and product should be carefully reviewed relative to its quantum advantage. Not just the abstract theoretical quantum advantage, but also the actual net quantum advantage based on actual expected data input size.
  21. Important caveat #1: Quantum advantage is generally nonlinear. As the size of the input grows, the advantage also grows, but not necessarily at the same rate as the input grows. Similarly, for smaller input sizes, the quantum advantage will be smaller. There will be some threshold input size where quantum advantage transitions from less than dramatic to very dramatic. Unfortunately, there can be extreme cases where the growth of the advantage eventually slows or the advantage even declines as input size grows, possibly even hitting a wall and failing. Be very cognizant of your input size to get a better handle on the actual quantum advantage.
  22. Important caveat #2: Shot count (circuit repetitions) can dramatically reduce or even eliminate the quantum advantage. Especially for noisy NISQ devices which may require a very large number of circuit repetitions to achieve a statistically meaningful result.
  23. Be sure to divide the net quantum advantage (after dividing by shot count) by the number of classical processors used by an application, so that the comparison is quantum solution to classical solution — at the application level, not simply quantum algorithm to classical algorithm at the processor level.
  24. Alas, we’re not even close to achieving any significant quantum advantage, let alone dramatic quantum advantage in the near future. The relevance of this paper is for more than a few years from now. Consider it a preview of the future of quantum computing.

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Jack Krupansky

Jack Krupansky

Freelance Consultant

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