The Case Against ‘The Case Against Quantum Computing’

By Ben Criger

January 9, 2019

Editor’s note: In this contributed piece, Ben Criger, a post-doctoral researcher at QuTech, part of the TU Delft in the Netherlands, responds to criticisms of quantum computing and offers an explanation for why such criticisms tend to garner a lot of attention.

It’s not easy to be a physicist. Richard Feynman (basically the Jimi Hendrix of physicists) once said: “The first principle is that you must not fool yourself – and you are the easiest person to fool.” This maxim motivates us to be critical of our research, even if we’re more critical when it comes to the research of others. From time to time, we even look through journals and technical magazines for arguments against the things we’re trying to do.

Last month, while I was looking for some nice criticism of quantum computing, I had the opportunity to read an article called “The Case Against Quantum Computing,” written by Mikhail Dyakonov, in IEEE Spectrum. While I was reading, I noticed two things that seemed out of the ordinary. First, all of the physics-based criticism of quantum computing was wrong, or had been addressed twenty years ago when the field was starting. The second, and perhaps more important thing, is that I could see the appeal of the article, despite its technical deficiencies.

I noticed that this article had been reviewed on the 27th of November by John Russell, here in HPCwire, so I thought that this would also be a good forum for a rebuttal (many thanks to Tiffany Trader for giving me the opportunity to write one). In the following sections, I’m going to go over two of the main technical points that Dyakonov makes, and try to give people a better idea about where we’re at in quantum computing. I’ll conclude with a comment on the article’s appeal.

Precision in Computing

Dyakonov: “A useful quantum computer needs to process a set of continuous parameters that is larger than the number of subatomic particles in the observable universe.”

No computer, classical or quantum, ever has to process even a single continuous parameter. In classical computers, we can use floating-point arithmetic to approximate continuous parameters using a finite number of bits. Most of the time, we can even manage to do it to within the desired relative precision, in order to avoid catastrophic error propagation. This is because the number of numbers which we can express using a floating-point type scales exponentially with the number of bits.

Normally, I wouldn’t belabour this point so heavily, but I’m going to do the “quantum” version of this in a minute, so let’s take a look at an animation of floating-point representations in action:

Here, I’m writing out all numbers of the form (−1)base sign×significand× 10((−1)exp sign∗exponent), when the variables significand and exponent are each n-bit integers. Now, I can’t plot the whole real line (my monitor isn’t wide enough), so I’ve used a Riemann projection, drawing a ray from the center of the semi-circle shown above to the point on the real line that I’d like to show, and instead showing where that ray intersects the semi-circle, like so:


If we begin with 0 bits in the significand and exponent, we can assign any value we like to the sign bits, and the only number we can represent is 0. There are four independent ways, therefore, to represent 0, so there’s a little inefficiency in the representation. However, by the time I get up to 9 bits each in the significand and exponent, all of the points plotted are overlapping, and it’s clear that I have enough precision for the task at hand, for any real number I care to approximate.

A similar result holds in quantum computing, though the ‘data type’ we’ll consider here is a single qubit’s state, rather than a real number. The continuous complex parameters α and β mentioned by Professor Dyakonov go in a length two vector:

These parameters can also be mapped to angles θ and φ on the Bloch sphere, like so:

α = cos(θ/2)        β = esin(θ/2)

(exercise for the reader: show that the state |0>, with α = 1 and β = 0, sits at the North Pole).

The operations we can apply in quantum computing are unitary matrices, equivalent to rotations of the Bloch sphere. For a single qubit, these matrices have two rows and two columns. Now, in fault-tolerant quantum computing, the operations which we can implement with arbitrarily low (but not exactly zero) error rates are limited to a discrete set. Let’s suppose for the sake of example, that there are two, and that they’re called H and T. Furthermore, let’s suppose that we only know how to initialise a single fixed state of our fault-tolerant qubit, the |0> state. How many qubit states can we reach with a string of Hs and Ts of fixed length n? Again, just as in floating-point arithmetic, the number of sequences I can generate scales exponentially with respect to the length of the sequence, despite a few collisions at low n (for example, HH |0> = |0>):

This animation doesn’t look quite as nice as the last one. There’s a lot more space to cover on the sphere than there is on the semi-circle that we used for floating-point arithmetic. From this, we can conclude that quantum computing is harder than classical computing, though I suspect that this does not come as a surprise.

Now, this isn’t the only thing fundamentally wrong with quantum computing, according to Professor Dyakonov. According to him, the entire discussion above is irrelevant, since imprecision and error will inevitably ruin any large-scale quantum computation before we can even think about stringing our Hs and Ts together. This is probably also not a surprise, but this was one of the first big problems that was ever solved in quantum computing, and I’ll talk about it a bit in the following section.

The Threshold Theorem

Dyakonov: “Indeed, [scientists studying quantum computing] claim that something called the threshold theorem proves it can be done. They point out that once the error per qubit per quantum gate is below a certain value, indefinitely long quantum computation becomes possible, at a cost of substantially increasing the number of qubits needed. With those extra qubits, they argue, you can handle errors by forming logical qubits using multiple physical qubits.”

The threshold theorem, initally proven by Aharonov and Ben-Or, has been around for about twenty years. The proof itself is in a 63-page paper, but the basic qualitative argument is relatively easy to grasp in a few paragraphs. At the cost of oversimplifying things, I’ll try to summarise that argument here.

Let’s define a logical gate as a small quantum computation that uses a number of physical gates acting on encoded states to simulate the effect of a single physical quantum logic gate acting on an unencoded state. Some logical gates can be made fault-tolerant by adding quantum error correction subroutines. The function of these subroutines is to correct the failure of a small number (typically one) of the physical quantum logic gates included in either the logical gate, or the error correction subroutines themselves. Each of these gadgets (that’s the technical term) contains a certain number of physical gates, let’s call it G. Also, let’s assume that, if any pair of these gates does something unanticipated, that the whole thing fails. When, then, does such a circuit have a low error probability? Let’s suppose, for the sake of simplicity, that each physical gate fails with probability p. The probability of error for the fault-tolerant gadget is , and whenever that’s less than p, we’re in business.

Now,  may not be a low enough probability of error for a given computation. In that case, we take advantage of something called concatenation, which is where you replace every physical gate in a fault-tolerant logical gate with yet another fault-tolerant logical gate, as depicted below:

If we use l levels of this concatenation, the number of gates we need to execute scales exponentially in l, but (very importantly) the final probability of error is p2l [ed. note: p^2^l] so it’s doubly-exponentially suppressed.

If this sounds clunky and inefficient to you, you’d be more or less right. The important thing for this initial proof of concept was not that the scheme be particularly efficient, but that it use simple ideas which could be widely understood. Over the past twenty years, a small community of quantum computing researchers have been concerned with finding more efficient schemes, with fewer gates, and the ability to tolerate higher error rates, and the results have been fairly positive. They’ve also been hard at work proving that quantum computing can still be made fault-tolerant if the errors are correlated, rather than independent, as I’ve assumed above (though Aharonov and Ben-Or consider weak correlations in their original work).

During this time, people like Mikhail Dyakonov (and Gil Kalai, and other noted skeptics of quantum computing) have been career researchers. If the theorem were false, we’d expect one of these skeptics, or someone they’ve inspired, to have proven that it was false, or to show that physically-reasonable correlated noise precludes quantum computing. They have not done this. Instead, Dyakonov has loosely suggested that the theorem is false, without a direct statement, or evidence. I, for one, think that the theorem is more or less correct, and that quantum computing is possible.

These are the official fact-based rebuttals that we physicists rely on when confronted with critiques from Dyakonov and the other scientists and engineers who believe that quantum computing is doomed for some reason or another. They’ve been used before, and I suspect that they’ll be used again. In one sense, they’re perfectly sufficient, but I don’t think they’ve addressed the core problem. Dyakonov’s critiques are unfounded, and yet they endure. Why?

The Important Question

So, why was Dyakonov’s article written? Why was it published? I hope I’ve argued adequately that there’s not a lot of science behind it, so why is it so appealing?

I think this article was published because, in a sense we don’t often talk about, it’s correct. People who study quantum computing don’t view it as our responsibility to oppose the unjustified hype building up in the popular press. Times are tough for scientists in every field, as the budgets for those funding agencies Dyakonov mentions dwindle. There’s a temptation not to rock the boat, especially when the critics we do have don’t do a great job of challenging us on technical grounds.

We lament the lack of well-founded criticism, but how often, and how loudly, do we lament the abundance of unfounded optimism? Are these two things not equally dangerous to the progress of science? We’re the people best able to criticise quantum computing, is it then our responsibility to do so?

So far, we’ve left editors with little selection when they look for something to stem the tide of breathless proclamations about how quantum computing is going to solve everything. We often lament the lack of good critiques of quantum computing, but in the end, the only chance we have to elevate the level of criticism is to do it ourselves.

About the Author

Ben is a post-doctoral researcher at QuTech, part of the TU Delft in the Netherlands. His research is focused on near-term implementations of fault-tolerant quantum computing. He can be reached via Twitter (@BenCriger) and GitHub ( Scripts producing the animations in this article can be found at

Subscribe to HPCwire's Weekly Update!

Be the most informed person in the room! Stay ahead of the tech trends with industy updates delivered to you every week!

SC19’s HPC Impact Showcase Chair: AI + HPC a ‘Speed Train’

November 16, 2019

This year’s chair of the HPC Impact Showcase at the SC19 conference in Denver is Lori Diachin, who has spent her career at the spearhead of HPC. Currently deputy director for the U.S. Department of Energy’s (DOE) Read more…

By Doug Black

Microsoft Azure Adds Graphcore’s IPU

November 15, 2019

Graphcore, the U.K. AI chip developer, is expanding collaboration with Microsoft to offer its intelligent processing units on the Azure cloud, making Microsoft the first large public cloud vendor to offer the IPU designe Read more…

By George Leopold

At SC19: What Is UrgentHPC and Why Is It Needed?

November 14, 2019

The UrgentHPC workshop, taking place Sunday (Nov. 17) at SC19, is focused on using HPC and real-time data for urgent decision making in response to disasters such as wildfires, flooding, health emergencies, and accidents. We chat with organizer Nick Brown, research fellow at EPCC, University of Edinburgh, to learn more. Read more…

By Tiffany Trader

China’s Tencent Server Design Will Use AMD Rome

November 13, 2019

Tencent, the Chinese cloud giant, said it would use AMD’s newest Epyc processor in its internally-designed server. The design win adds further momentum to AMD’s bid to erode rival Intel Corp.’s dominance of the glo Read more…

By George Leopold

NCSA Industry Conference Recap – Part 1

November 13, 2019

Industry Program Director Brendan McGinty welcomed guests to the annual National Center for Supercomputing Applications (NCSA) Industry Conference, October 8-10, on the University of Illinois campus in Urbana (UIUC). One hundred seventy from 40 organizations attended the invitation-only, two-day event. Read more…

By Elizabeth Leake, STEM-Trek

AWS Solution Channel

Making High Performance Computing Affordable and Accessible for Small and Medium Businesses with HPC on AWS

High performance computing (HPC) brings a powerful set of tools to a broad range of industries, helping to drive innovation and boost revenue in finance, genomics, oil and gas extraction, and other fields. Read more…

IBM Accelerated Insights

Data Management – The Key to a Successful AI Project


Five characteristics of an awesome AI data infrastructure

[Attend the IBM LSF & HPC User Group Meeting at SC19 in Denver on November 19!]

AI is powered by data

While neural networks seem to get all the glory, data is the unsung hero of AI projects – data lies at the heart of everything from model training to tuning to selection to validation. Read more…

Cray, Fujitsu Both Bringing Fujitsu A64FX-based Supercomputers to Market in 2020

November 12, 2019

The number of top-tier HPC systems makers has shrunk due to a steady march of M&A activity, but there is increased diversity and choice of processing components with Intel Xeon, AMD Epyc, IBM Power, and Arm server ch Read more…

By Tiffany Trader

SC19’s HPC Impact Showcase Chair: AI + HPC a ‘Speed Train’

November 16, 2019

This year’s chair of the HPC Impact Showcase at the SC19 conference in Denver is Lori Diachin, who has spent her career at the spearhead of HPC. Currently Read more…

By Doug Black

Cray, Fujitsu Both Bringing Fujitsu A64FX-based Supercomputers to Market in 2020

November 12, 2019

The number of top-tier HPC systems makers has shrunk due to a steady march of M&A activity, but there is increased diversity and choice of processing compon Read more…

By Tiffany Trader

Intel AI Summit: New ‘Keem Bay’ Edge VPU, AI Product Roadmap

November 12, 2019

At its AI Summit today in San Francisco, Intel touted a raft of AI training and inference hardware for deployments ranging from cloud to edge and designed to support organizations at various points of their AI journeys. The company revealed its Movidius Myriad Vision Processing Unit (VPU)... Read more…

By Doug Black

IBM Adds Support for Ion Trap Quantum Technology to Qiskit

November 11, 2019

After years of percolating in the shadow of quantum computing research based on superconducting semiconductors – think IBM, Rigetti, Google, and D-Wave (quant Read more…

By John Russell

Tackling HPC’s Memory and I/O Bottlenecks with On-Node, Non-Volatile RAM

November 8, 2019

On-node, non-volatile memory (NVRAM) is a game-changing technology that can remove many I/O and memory bottlenecks and provide a key enabler for exascale. That’s the conclusion drawn by the scientists and researchers of Europe’s NEXTGenIO project, an initiative funded by the European Commission’s Horizon 2020 program to explore this new... Read more…

By Jan Rowell

MLPerf Releases First Inference Benchmark Results; Nvidia Touts its Showing

November 6, 2019, the young AI-benchmarking consortium, today issued the first round of results for its inference test suite. Among organizations with submissions wer Read more…

By John Russell

Azure Cloud First with AMD Epyc Rome Processors

November 6, 2019

At Ignite 2019 this week, Microsoft's Azure cloud team and AMD announced an expansion of their partnership that began in 2017 when Azure debuted Epyc-backed instances for storage workloads. The fourth-generation Azure D-series and E-series virtual machines previewed at the Rome launch in August are now generally available. Read more…

By Tiffany Trader

Nvidia Launches Credit Card-Sized 21 TOPS Jetson System for Edge Devices

November 6, 2019

Nvidia has launched a new addition to its Jetson product line: a credit card-sized (70x45mm) form factor delivering up to 21 trillion operations/second (TOPS) o Read more…

By Doug Black

Supercomputer-Powered AI Tackles a Key Fusion Energy Challenge

August 7, 2019

Fusion energy is the Holy Grail of the energy world: low-radioactivity, low-waste, zero-carbon, high-output nuclear power that can run on hydrogen or lithium. T Read more…

By Oliver Peckham

Using AI to Solve One of the Most Prevailing Problems in CFD

October 17, 2019

How can artificial intelligence (AI) and high-performance computing (HPC) solve mesh generation, one of the most commonly referenced problems in computational engineering? A new study has set out to answer this question and create an industry-first AI-mesh application... Read more…

By James Sharpe

Cray Wins NNSA-Livermore ‘El Capitan’ Exascale Contract

August 13, 2019

Cray has won the bid to build the first exascale supercomputer for the National Nuclear Security Administration (NNSA) and Lawrence Livermore National Laborator Read more…

By Tiffany Trader

DARPA Looks to Propel Parallelism

September 4, 2019

As Moore’s law runs out of steam, new programming approaches are being pursued with the goal of greater hardware performance with less coding. The Defense Advanced Projects Research Agency is launching a new programming effort aimed at leveraging the benefits of massive distributed parallelism with less sweat. Read more…

By George Leopold

AMD Launches Epyc Rome, First 7nm CPU

August 8, 2019

From a gala event at the Palace of Fine Arts in San Francisco yesterday (Aug. 7), AMD launched its second-generation Epyc Rome x86 chips, based on its 7nm proce Read more…

By Tiffany Trader

D-Wave’s Path to 5000 Qubits; Google’s Quantum Supremacy Claim

September 24, 2019

On the heels of IBM’s quantum news last week come two more quantum items. D-Wave Systems today announced the name of its forthcoming 5000-qubit system, Advantage (yes the name choice isn’t serendipity), at its user conference being held this week in Newport, RI. Read more…

By John Russell

Ayar Labs to Demo Photonics Chiplet in FPGA Package at Hot Chips

August 19, 2019

Silicon startup Ayar Labs continues to gain momentum with its DARPA-backed optical chiplet technology that puts advanced electronics and optics on the same chip Read more…

By Tiffany Trader

Crystal Ball Gazing: IBM’s Vision for the Future of Computing

October 14, 2019

Dario Gil, IBM’s relatively new director of research, painted a intriguing portrait of the future of computing along with a rough idea of how IBM thinks we’ Read more…

By John Russell

Leading Solution Providers

ISC 2019 Virtual Booth Video Tour


Intel Confirms Retreat on Omni-Path

August 1, 2019

Intel Corp.’s plans to make a big splash in the network fabric market for linking HPC and other workloads has apparently belly-flopped. The chipmaker confirmed to us the outlines of an earlier report by the website CRN that it has jettisoned plans for a second-generation version of its Omni-Path interconnect... Read more…

By Staff report

Kubernetes, Containers and HPC

September 19, 2019

Software containers and Kubernetes are important tools for building, deploying, running and managing modern enterprise applications at scale and delivering enterprise software faster and more reliably to the end user — while using resources more efficiently and reducing costs. Read more…

By Daniel Gruber, Burak Yenier and Wolfgang Gentzsch, UberCloud

Dell Ramps Up HPC Testing of AMD Rome Processors

October 21, 2019

Dell Technologies is wading deeper into the AMD-based systems market with a growing evaluation program for the latest Epyc (Rome) microprocessors from AMD. In a Read more…

By John Russell

Rise of NIH’s Biowulf Mirrors the Rise of Computational Biology

July 29, 2019

The story of NIH’s supercomputer Biowulf is fascinating, important, and in many ways representative of the transformation of life sciences and biomedical res Read more…

By John Russell

Xilinx vs. Intel: FPGA Market Leaders Launch Server Accelerator Cards

August 6, 2019

The two FPGA market leaders, Intel and Xilinx, both announced new accelerator cards this week designed to handle specialized, compute-intensive workloads and un Read more…

By Doug Black

When Dense Matrix Representations Beat Sparse

September 9, 2019

In our world filled with unintended consequences, it turns out that saving memory space to help deal with GPU limitations, knowing it introduces performance pen Read more…

By James Reinders

With the Help of HPC, Astronomers Prepare to Deflect a Real Asteroid

September 26, 2019

For years, NASA has been running simulations of asteroid impacts to understand the risks (and likelihoods) of asteroids colliding with Earth. Now, NASA and the European Space Agency (ESA) are preparing for the next, crucial step in planetary defense against asteroid impacts: physically deflecting a real asteroid. Read more…

By Oliver Peckham

Cerebras to Supply DOE with Wafer-Scale AI Supercomputing Technology

September 17, 2019

Cerebras Systems, which debuted its wafer-scale AI silicon at Hot Chips last month, has entered into a multi-year partnership with Argonne National Laboratory and Lawrence Livermore National Laboratory as part of a larger collaboration with the U.S. Department of Energy... Read more…

By Tiffany Trader

  • arrow
  • Click Here for More Headlines
  • arrow
Do NOT follow this link or you will be banned from the site!
Share This