The Quantum Confidence Trick: Encryption, Fraud, and the Constitutional Consequences of a Manufactured Threat

The Quantum Confidence Trick: Encryption, Fraud, and the Constitutional Consequences of a Manufactured Threat

Billions of dollars have been raised, federal statutes enacted, and constitutional privacy arguments restructured on the premise that quantum computers will soon shatter modern encryption. The physics disagrees. The law should catch up.

I. The Architecture of the Claim

There is a particular species of technological fraud that is especially dangerous precisely because it is not entirely false. The claim need only be sufficiently true to be unsatisfying as a prosecution target, yet sufficiently exaggerated to extract the maximum value from a credulous investor, a frightened legislator, or a federal agency writing a procurement contract. The quantum computing sector has perfected this technique. Call it the adjacent truth: a real physical phenomenon, a real mathematical algorithm, a real academic literature — wrapped around a commercial and policy claim that the underlying science does not support.

The claim is this: quantum computers will, within the near to medium term, break the public-key encryption that protects banking, communications, digital identity, and national security infrastructure. This claim has become the organizing premise of a multi-billion dollar investment ecosystem, of Congressional legislation,1 of Executive Branch mandates,2 and of a growing body of Fourth Amendment scholarship arguing that the government's ability to decrypt communications changes the constitutional calculus under Katz v. United States3 and its progeny. If the claim is substantially false — not merely premature, but fraudulently overstated — then everything built upon it deserves scrutiny, and the law has tools to apply it.

This essay undertakes three tasks. First, it examines what the physics actually says about quantum computing and encryption — not the press release, not the venture pitch, but the peer-reviewed engineering constraint. Second, it surveys the documented pattern of material misrepresentation in the quantum sector, applying securities fraud doctrine under Section 10(b) of the Securities Exchange Act of 19344 and Rule 10b-5 promulgated thereunder. Third, it considers the constitutional dimension: how manufactured technological panic shapes Fourth Amendment jurisprudence, executive surveillance doctrine, and the structural relationship between government power and individual privacy.

II. What Quantum Computing Actually Is — and Is Not

A. The Physical Reality of Qubits

A quantum bit, or qubit, is a two-state quantum-mechanical system. Unlike a classical bit, which is deterministically either 0 or 1, a qubit can exist in a superposition of both states simultaneously. Two or more qubits can become entangled, meaning their states are correlated in ways that have no classical analogue. These properties are the foundation of Shor's algorithm,5 which demonstrates that a sufficiently large quantum computer could factor the product of two large prime numbers in polynomial time — directly attacking the computational hardness assumption underlying RSA encryption.

The words "sufficiently large" are doing enormous work in that sentence. Here is what they conceal.

Every physical implementation of a qubit — whether superconducting circuits, trapped ions, neutral atoms, photonic systems, or semiconductor spin qubits — suffers from decoherence: the irreversible loss of quantum information through interaction with the environment.6 A qubit's quantum state is extraordinarily fragile. Thermal fluctuations, electromagnetic noise, stray photons, mechanical vibrations, even the act of measuring an adjacent qubit — all collapse the superposition. A 2024 study found that vibrations from cryogenic cooling systems created error bursts in superconducting qubits by perturbing two-level system defects in the chip substrate, cutting qubit lifetime in half intermittently.7 Superconducting systems currently achieve coherence times on the order of microseconds to milliseconds — the window within which a quantum computation must complete before noise renders the result meaningless.

The engineering response to decoherence is quantum error correction: encoding one logical qubit across many physical qubits, so that the logical state can be recovered even as individual physical qubits fail. The ratio of physical to logical qubits is not cosmetic. Using the dominant approach — surface codes — early estimates placed the requirement at 1,000 to 10,000 physical qubits per logical qubit.8 More recent work using Low-Density Parity Check (LDPC) codes claims to compress this ratio, but LDPC codes impose their own engineering constraint: they require non-local qubit measurements that are structurally incompatible with the nearest-neighbor connectivity of most superconducting architectures.9

B. What Breaking RSA-2048 Actually Requires

The canonical target for quantum cryptanalysis is RSA-2048, the 2048-bit public key standard that underpins most online banking, secure email, and digital certificates. Breaking it requires finding the prime factors of a 617-digit number — a task that would take a classical supercomputer longer than the age of the observable universe.

The theoretical qubit requirements to run Shor's algorithm against RSA-2048 have been refined substantially over the past three decades. Stéphane Beauregard's 2003 circuit required 4,099 logical qubits but extremely deep circuits.10 The 2021 Gidney-Ekerå analysis required 20 million noisy physical qubits running for eight hours.11 A May 2025 preprint by Google Quantum AI researcher Craig Gidney reduced the estimate to fewer than one million noisy physical qubits — a genuine algorithmic advance — but at the cost of five days of continuous operation at a gate error rate of 0.1% or better, a coherence specification "well beyond today's systems."12 A February 2026 preprint from Sydney researchers claimed 100,000 physical qubits were theoretically sufficient using LDPC architectures — but the paper itself noted that the decoder speed required for real-time hardware control was outside its scope, and that the LDPC connectivity requirements remain a formidable engineering problem.13

To be precise about where the hardware stands: as of early 2026, IBM's Heron R2 processor has 156 physical qubits with improved coherence and gate fidelity.14 No publicly demonstrated system has achieved fault-tolerant logical qubits at scale. The largest number ever factored on a quantum device using Shor's algorithm is 21.15 The gap between 21 and 2048-bit RSA is not a matter of engineering optimization schedules. It is a gap of multiple orders of magnitude in every relevant metric simultaneously — qubit count, error rate, coherence time, and circuit depth — all of which must be achieved together, not sequentially.

"The largest number ever factored on a quantum device using Shor's algorithm is 21. RSA-2048 is a 617-digit number."

An expert consensus study cited by the U.S. National Security Agency concluded that a cryptanalytically relevant quantum computer is unlikely to exist before 2030, and the NSA stated it "does not know when or even if such a quantum computer will be built."16 A benchmark analysis published in late 2025 estimated that the field was "perhaps on the order of one-tenth of the way there" in capability terms, with a plausible timeline of five to seven years to reach the necessary logical qubit threshold — assuming no further engineering obstacles, a historically improbable assumption in this domain.17

C. The Microsoft Case Study in Manufactured Milestones

No single episode better illustrates the gap between quantum claim and quantum reality than Microsoft's February 2025 announcement of the Majorana 1 chip and its purported topological qubit. Microsoft's press release announced "the world's first Quantum Processing Unit powered by a Topological Core" and predicted that "useful quantum computers were just years away."18

Buried in the peer review materials accompanying the supporting Nature paper, the journal's own editorial team wrote: "the results in this manuscript do not represent evidence for the presence of Majorana zero modes in the reported devices."19 Two of four peer reviewers opposed publication even after the authors responded to initial comments. Physicist Sergei Frolov of the University of Pittsburgh, whose earlier investigations had contributed to Microsoft's 2018 retraction of a prior Majorana claim from Nature, characterized the 2025 announcement similarly: the improvement, he stated, lay in "the quality of the PR campaign" rather than the quality of the devices, and noted that independent experts in condensed matter physics broadly agreed.20 Winfried Hensinger of the University of Sussex stated plainly that topological quantum computing was "probably 20 to 30 years behind the other platforms."21

Microsoft has had two high-profile Nature publications in this domain retracted or editorially disclaimed. The company nonetheless raised the spectacle into mainstream headlines as a breakthrough. The press release was not peer-reviewed. The underlying paper was.

A. The Elements of 10b-5 Liability

Section 10(b) of the Securities Exchange Act of 1934 makes it unlawful "to use or employ, in connection with the purchase or sale of any security . . . any manipulative or deceptive device or contrivance in contravention of such rules and regulations as the Commission may prescribe."22 Rule 10b-5, promulgated thereunder, prohibits making any untrue statement of a material fact, omitting a material fact necessary to prevent existing statements from being misleading, or engaging in any act or practice that operates as a fraud or deceit upon any person, in connection with the purchase or sale of a security.23

A private plaintiff — or the SEC — must establish: (1) a material misrepresentation or omission; (2) scienter; (3) a connection with the purchase or sale of a security; (4) reliance; (5) economic loss; and (6) loss causation.24 The Supreme Court in Basic Inc. v. Levinson25 established that materiality requires a substantial likelihood that a reasonable investor would consider the information important in the total mix of available information. In Ernst & Ernst v. Hochfelder,26 the Court held that scienter requires intent to deceive, manipulate, or defraud — something above negligence but encompassing severe recklessness, defined as an extreme departure from ordinary care presenting a danger the defendant must have been aware of.

The question for quantum technology companies is whether overstatements of technical capability, made in securities filings or in connection with equity offerings, constitute material misrepresentations knowingly made. In Virginia Bankshares v. Sandberg,27 the Court held that knowingly false statements of opinion are actionable under Rule 10b-5 even if conclusory in form. A forward-looking statement about technology timelines, made by a CEO who has been briefed by technical staff on the actual engineering constraints, is not pure puffery. It is an opinion about fact. If the opinion is false and the speaker knows the underlying facts contradict it, it is actionable.

B. The Documented Pattern

The quantum sector has produced documented instances of the full spectrum from aggressive puffery to alleged outright fabrication. These are not editorial characterizations. They are the subject of filed or announced securities fraud class actions.

Quantum Computing Inc. (NASDAQ: QUBT) announced it was building "the nation's first dedicated quantum photonic chip foundry" in Arizona, claimed a "longstanding relationship" with NASA, and described multiple "NASA contract awards." Investigative research firms Iceberg Research and Capybara Research found that the foundry address corresponded to a small lab facility, that NASA had confirmed no land purchase, and that the company's "strategic partnership" with NASA consisted of a single $26,000 sole-source contract for basic programming work.28 Former employees described the company's quantum products as "glorified lab projects" that were nowhere near producing useful results. The company generated under $400,000 in total revenue across all of 2023 and 2024 combined — approximately $39,000 in Q1 2025.29 Multiple securities fraud class actions were filed by law firms including KSF Law, Glancy Prongay & Murray, and Gross Law Firm.30 The stock fell approximately 15% over two days following the Capybara report.

IonQ (NYSE: IONQ) faced allegations from Wolfpack Research in early 2026 that the company had consistently misled investors about the organic demand for its technology — in particular, that revenues were substantially dependent on "backdoor earmarks" inserted into the Pentagon budget by friendly legislators, that those earmarks were canceled after the 2025 Congressional transition, and that the company had failed to disclose the revenue impact of their loss until insiders had sold approximately $396.6 million in stock under 10b5-1 plans.31 Kerrisdale Capital had separately labeled the company as "hype" in March 2025, characterizing its systems as "limited, error-prone" and the company as "far from being on the verge of a new era of commercial success."32 IonQ disputes these characterizations. The underlying question — whether the company disclosed all material facts about the composition of its revenue — is now squarely presented.

Quantum Corporation (NASDAQ: QMCO) announced a delay in its Form 10-K filing in June 2025 due to an ongoing review of revenue contracts and accounting practices, triggering a 15% stock drop and a subsequent class action covering purchasers between November 2024 and August 2025.33

These cases share a structural pattern: the complexity and novelty of quantum technology creates an information asymmetry that permits corporate insiders to make claims that retail investors cannot independently evaluate. The physics is genuinely hard. The gap between what the engineering permits and what the press release asserts is therefore difficult to close without specialized expertise. This is precisely the condition that securities fraud doctrine exists to address. The law does not require retail investors to be quantum physicists. It requires corporate executives to be honest.

C. The Puffery Defense and Its Limits

Defendants in quantum fraud litigation will predictably invoke the puffery doctrine: vague expressions of optimism about future performance are not actionable because no reasonable investor would rely on them as statements of fact. In re Donald J. Trump Casino Securities Litigation34 and subsequent circuit authority confirm that generalized, non-specific predictions — "this technology will be transformative," "we are leaders in a revolutionary field" — fall outside the ambit of Rule 10b-5.

The puffery defense has recognized limits. A statement is not puffery when it is specific, when it concerns a present state of affairs rather than a speculative future, and when the speaker possesses information contradicting the statement. A company that announces its foundry is "now operational and fulfilling orders" when no foundry exists has not uttered puffery. A company that claims a "strategic partnership" with NASA when it has a $26,000 clerical contract has not uttered puffery. A company that represents its technology as capable of producing commercially useful quantum results when its own engineers know the hardware is a demonstrator has not uttered puffery. These are statements of present fact. Their falsity, if proved, is actionable.

The Supreme Court's admonition in Omnicare, Inc. v. Laborers District Council Construction Industry Pension Fund35 is directly relevant: a statement of opinion may be false and misleading if it omits facts that, if disclosed, would have made the opinion's basis apparent as false. An executive who states that the company's quantum hardware "will break RSA within five years" while in possession of engineering reports concluding that the hardware cannot sustain even a hundred coherent gate operations has not expressed genuine optimism. The omitted facts contradict the opinion's implied premise.

IV. Wire Fraud, Criminal Exposure, and the FTC

The securities fraud analysis applies to public companies with securities traded on national exchanges. The conduct in the broader quantum technology ecosystem — including private fundraising, grant applications, and government contracting — implicates a distinct set of federal provisions.

18 U.S.C. § 1343 prohibits using wire communications in furtherance of any scheme to defraud. A company that emails investors a pitch deck containing fabricated technical specifications has, assuming the other elements of wire fraud are present, violated the statute. The elements are: (1) a scheme to defraud; (2) use of wire communications; (3) in furtherance of the scheme; (4) with intent to defraud.36 The "scheme to defraud" element is satisfied by a plan to obtain money by false representations, including false representations about technical capability. Courts have held that willful blindness — the deliberate avoidance of knowledge of relevant facts — satisfies the intent requirement.37

False statements in federal grant applications implicate 18 U.S.C. § 1001, which prohibits knowingly and willfully making materially false statements in any matter within the jurisdiction of the executive branch. A company that overstates its technical accomplishments in a Department of Energy or DARPA application for quantum computing research funding has committed a federal crime if the overstatement is material and knowing. The materiality standard in § 1001 does not require that the government actually rely on the false statement; it requires only that the statement has a natural tendency to influence the relevant determination.38

The Federal Trade Commission has pursued "AI-washing" cases under Section 5 of the FTC Act — unfair or deceptive acts or practices — against companies that misrepresented the capabilities of artificial intelligence products to consumers and business customers.39 The logic applies with equal force to quantum technology. A cybersecurity vendor that represents its product as "quantum-safe" without meaningful technical basis for the claim, or that sells "quantum encryption" services using classical technology with a quantum brand, engages in unfair or deceptive trade practices. Multiple regulatory bodies internationally have issued formal warnings about exactly this pattern — investment platforms using the word "quantum" as a magical signifier with no underlying technical content, documented by the Australian Competition and Consumer Commission, the Central Bank of Ireland, Germany's BaFin, Denmark's DFSA, and others.40

V. The Constitutional Dimension: How Quantum Panic Restructures Rights

A. The Surveillance State's Quantum Dividend

The practical consequences of the quantum threat narrative extend beyond financial markets. They reach the structure of constitutional law. Executive Branch surveillance programs, legislative mandates, and Fourth Amendment doctrine have all been shaped — and will be further shaped — by the claim that quantum computers are an imminent threat to encrypted communications. If that claim is substantially overstated, the constitutional architecture built upon it rests on a manufactured premise.

The Foreign Intelligence Surveillance Act, the USA PATRIOT Act, and their successors have consistently been defended, in part, on the ground that foreign adversaries possess or will shortly possess capabilities that make current surveillance authorities essential to national security. The quantum threat has been incorporated into this rhetorical structure: if adversarial states will soon be able to decrypt communications collected today — the so-called "harvest now, decrypt later" strategy — then bulk collection of encrypted data acquires a urgency it would otherwise lack. The argument is that data collected today, even if currently unintelligible, will become intelligible when a quantum cryptanalytic capability matures.

This argument is not frivolous. The harvest-now-decrypt-later threat is the most technically credible quantum security concern, precisely because it requires no current quantum capability — only the eventual development of one. NIST finalized its first post-quantum cryptography standards in August 2024, and the NSA's Commercial National Security Algorithm Suite 2.0 mandates quantum-safe cryptography for new national security systems by January 2027.41 These are appropriate precautionary responses. They do not, however, require accepting the broader claim that a cryptanalytically relevant quantum computer is imminent, nor do they justify surveillance authorities predicated on a threat that the relevant technical agencies themselves acknowledge may never materialize.

B. Katz and the Technological Expectation

The Fourth Amendment prohibits unreasonable searches and seizures. Under Katz v. United States,42 the Amendment protects people, not places — and specifically, those people's reasonable expectations of privacy. The reasonableness of a privacy expectation is evaluated against the backdrop of what technology makes practically concealed versus practically exposed. This creates a structural feedback loop: as technology changes what can be known, it changes what can be reasonably expected to remain private.

End-to-end encryption currently creates a category of practical privacy: communications that are, as a factual matter, inaccessible to third parties including government actors without the decryption key. The Supreme Court's recognition in Carpenter v. United States43 that the Fourth Amendment must account for the seismic shifts wrought by digital technology opens the question of how quantum cryptanalytic capability, if it materialized, would affect the privacy calculus. If encrypted communications became as accessible to government actors as plaintext telephone calls, the privacy expectations currently recognized in Riley v. California44 and Carpenter would require substantial revision.

The problem is that legal doctrine does not wait for technology to arrive. Doctrinal anticipation of technological change — reasoning from a claimed near-future capability to a present adjustment of rights — has a poor track record. The government argued in the early 2000s that new communications technologies required updating surveillance authority before rights-protective doctrine caught up with capability. The result was a decade of contested surveillance programs, retroactive immunization statutes, and FISA Court opinions written in the dark.

If the quantum computing threat is substantially overstated — if the relevant physics makes a cryptanalytically relevant quantum computer a decade or more away and not within the five-to-ten-year horizon consistently implied by industry and government sources — then constitutional doctrine adjusted in anticipation of imminent quantum capability will have been adjusted on false premises. Doctrinal change made in response to manufactured technological panic is not a neutral error. It is a structural transfer: rights are diminished, surveillance powers are expanded, and the population lives under a legal regime shaped by a claim that was not true.

C. Congressional Action and the Constitutional Economy of Fear

The Quantum Computing Cybersecurity Preparedness Act of 202245 requires federal agencies to inventory cryptographic systems, assess vulnerability to quantum attack, and develop migration plans for post-quantum cryptographic standards. This is defensible prudential legislation — the harvest-now-decrypt-later concern is real, and cryptographic agility is a genuine engineering value regardless of the exact timeline. The legislation can be justified on its own terms without reference to any claim about the imminence of a cryptanalytically relevant quantum computer.

The constitutional concern arises when quantum threat claims are used not to justify cryptographic migration but to justify expanded governmental power over private communications, weakened encryption standards, or backdoor access mandates. The FBI and other agencies have periodically advanced "going dark" arguments: that strong encryption, increasingly ubiquitous, is creating law enforcement blind spots that must be addressed through technical mandates. If quantum computing is falsely characterized as being about to render encryption obsolete anyway, the argument becomes: you will lose your encryption soon enough; concede government access now in exchange for nothing. This is the constitutional economy of fear — voluntary surrender of rights in response to a threat that is not what it has been represented to be.

The Framers did not build a republic on the premise that government claims about security threats should be taken on faith. The Federalist Papers are replete with warnings about exactly this dynamic. James Madison's observation in Federalist No. 51 — that men are not angels, and that government must therefore be controlled — extends naturally to government characterizations of technological threats. A threat claim that is materially false, advanced to support expanded governmental authority, is precisely the kind of claim the constitutional structure was designed to scrutinize. Courts have tools. They should use them.

A. What Counsel Should Know

Attorneys advising quantum technology companies should understand that the science sets the floor for permissible representation, and that floor is considerably lower than what the industry's promotional discourse suggests. The following are statements of engineering fact, not legal opinion, that counsel should internalize:

No quantum computer has demonstrated fault-tolerant logical qubits at a scale relevant to cryptographic attack. The best-characterized systems operate in what researchers call the Noisy Intermediate Scale Quantum (NISQ) regime — fifty to a thousand qubits with meaningful but uncorrected error rates. The gap between NISQ systems and a cryptanalytically relevant machine is not a linear extrapolation problem. It involves simultaneous breakthroughs in error correction overhead, coherence time, gate fidelity at scale, and control system engineering, all of which interact with each other in non-linear ways.

A company that represents its NISQ hardware as a near-term threat to RSA-2048 in a materials document used to solicit investment, or in an SEC filing, has made a material misrepresentation. A company that fails to disclose, in relevant filings, that its claimed revenue is substantially dependent on non-recurring governmental earmarks that are subject to political cancellation has omitted a material fact. A company whose CEO makes public statements about imminent quantum capability while possessing internal engineering assessments to the contrary has satisfied the scienter requirement for securities fraud.

B. What Litigants and Courts Should Know

Plaintiffs' counsel in quantum securities litigation should retain experts who can translate the engineering constraint into the materiality analysis. The question is not whether a defendant used the right technical vocabulary. It is whether a reasonable investor, if informed of the actual engineering status — the decoherence times, the error rates, the physical-to-logical qubit ratios, the specific gap between demonstrated capability and claimed capability — would have considered that information significant. The answer, for any competent securities lawyer who has read the technical literature, is yes.

Courts should approach quantum technology expert testimony with the same rigor required under Daubert v. Merrell Dow Pharmaceuticals46 for any scientific claim offered in evidence. The field is characterized by extraordinary marketing incentives, publication bias toward optimistic results, and a press ecosystem that systematically fails to distinguish algorithmic improvement in theory from hardware capability in practice. An expert who testifies that a given quantum company's representations were technically accurate bears the burden of demonstrating that opinion on reliable methodology, not on the company's press releases.

C. The Regulatory Gap and Legislative Response

The current regulatory framework does not specifically address quantum technology claims. The SEC's general antifraud authority applies, as does the FTC's unfair and deceptive practices jurisdiction. But neither agency has issued guidance specifically addressing what quantum companies may represent about their capabilities in connection with securities offerings, consumer marketing, or government contracting.

The analogy to AI regulation is instructive. The FTC's 2023 AI guidance and subsequent enforcement actions targeting "AI washing" — the attribution of artificial intelligence capabilities to products that do not possess them — created a framework that both deterred false claims and provided companies with clearer guidance about permissible representation. A parallel framework for quantum technology claims, specifying that representations about cryptographic threat capability must be grounded in peer-reviewed engineering consensus rather than pre-publication announcements or corporate white papers, would serve the same function.

Congress, which has already legislated on quantum preparedness, could mandate that federal contractors making quantum capability claims in connection with government solicitations provide independent technical verification. The False Claims Act, 31 U.S.C. § 3729, already imposes liability for knowingly presenting false claims to the federal government; application to quantum capability claims in government contracts requires no new statute, only enforcement will.

VII. Conclusion: The Law's Obligation to Demand Honesty About the Future

The quantum computing industry is not uniformly fraudulent. There is genuine scientific progress — genuine improvements in error correction, genuine demonstrations of quantum advantage in narrow computational tasks, genuine advances in algorithmic efficiency. The fault-tolerant quantum computer may eventually exist. Post-quantum cryptographic standards are worth developing now, regardless of the exact timeline, because the harvest-now-decrypt-later risk is real and cryptographic migration takes time.

None of this licenses the misrepresentation that has characterized substantial portions of the quantum investment ecosystem. The law does not permit raising capital by making claims that the underlying physics cannot support. The law does not permit omitting from securities filings the material fact that revenue depends on earmarks that can be legislatively canceled. The law does not permit telling investors that a foundry is operational and fulfilling orders when it is a small laboratory. These are not questions of technological optimism. They are questions of factual honesty, and the legal framework is clear.

The constitutional dimension adds urgency. When the government invokes a technological threat to justify expanded surveillance authority, weakened encryption mandates, or doctrinal adjustment of Fourth Amendment protections, it is making a factual claim that courts are entitled — and obligated — to examine. The quantum threat is real in some dimensions and manufactured in others. A legal system committed to constraining governmental power must be capable of distinguishing between them. That requires lawyers who understand the physics, judges willing to interrogate the science, and a legislative culture that does not treat the word "quantum" as a talisman that dissolves the ordinary burden of proof.

The confidence trick works because the mark cannot easily verify the claim. The mark — the investor, the legislator, the federal judge — does not know enough physics to push back. The solution is not to learn quantum mechanics. It is to apply, rigorously, the tools the law already provides: the materiality standard, the scienter requirement, the Daubert framework, and the constitutional warrant that government claims about threats to public safety must be honest, verifiable, and proportionate. Physics is hard. Honesty is not.

Notes

1. Quantum Computing Cybersecurity Preparedness Act, Pub. L. No. 117-260, 136 Stat. 2375 (2022).

2. National Security Memorandum 10 (NSM-10), "Promoting United States Leadership in Quantum Computing While Mitigating Risks to Vulnerable Cryptographic Systems" (May 4, 2022); Exec. Order 14156 (June 2025) (referencing NSM-10 as foundational document for post-quantum cryptography transition).

3. Katz v. United States, 389 U.S. 347 (1967).

4. Securities Exchange Act of 1934, 15 U.S.C. § 78j(b).

5. Peter W. Shor, "Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer," SIAM Journal on Computing 26, no. 5 (1997): 1484–1509.

6. See generally Wojciech H. Zurek, "Decoherence, Einselection, and the Quantum Origins of the Classical," Reviews of Modern Physics 75 (2003): 715.

7. "The Many Faces of Decoherence," PostQuantum.com (Sept. 3, 2025) (citing 2024 study linking pulse-tube cooler vibrations to TLS-induced error bursts in superconducting qubits).

8. See Luminaryera, "Quantum Computing in 2026: Separating Real Progress from a Decade of Hype" (Feb. 12, 2026) ("early estimates suggested 1,000–10,000 physical qubits per logical qubit").

9. Scott Aaronson, "On Reducing the Cost of Breaking RSA-2048 to 100,000 Physical Qubits," Shtetl-Optimized (Feb. 15, 2026) ("LDPC codes are harder to engineer than the surface code (especially for superconducting qubits) because you need wildly nonlocal measurements of the error syndromes").

10. Stéphane Beauregard, "Circuit for Shor's Algorithm Using 2n+3 Qubits," Quantum Information & Computation 3, no. 2 (2003): 175–185.

11. Craig Gidney & Martin Ekerå, "How to Factor 2048 Bit RSA Integers in 8 Hours Using 20 Million Noisy Qubits," Quantum 5 (2021): 433.

12. Craig Gidney, "How to Factor 2048 Bit RSA Integers with Less Than a Million Noisy Qubits," arXiv:2505.15917 (May 21, 2025).

13. "New Architecture Could Cut Quantum Hardware Needed to Break RSA-2048 by Tenfold, Study Finds," The Quantum Insider (Feb. 13, 2026) (describing Sydney research group's Pinnacle architecture using generalized bicycle QLDPC codes).

14. "Understanding and Solving Quantum Decoherence," BlueQubit (July 17, 2025) (noting IBM Heron R2, a 156-qubit processor with improved coherence, introduced late 2024).

15. Classiq, "Shor's Algorithm Explained" (noting the largest number factored to date with Shor's algorithm is 21).

16. "The Enormous Energy Cost of Breaking RSA-2048 with Quantum Computers," PostQuantum.com (Sept. 23, 2025) (citing NSA statement and expert consensus study). See also NSA, "Quantum Computing and Post-Quantum Cryptography FAQ" (2021).

17. "CRQC Readiness Benchmark," PostQuantum.com (Dec. 1, 2025).

18. Microsoft press release, "Microsoft Unveils Majorana 1" (Feb. 19, 2025).

19. Nature peer review file accompanying M. Aghaee et al., "Interferometric Single-Shot Parity Measurement in InAs–Al Hybrid Devices," Nature 638, 651–655 (2025), quoted in "Experts Weigh in on Microsoft's Topological Qubit Claim," Physics World (Feb. 27, 2025); "FAQ on Microsoft's Topological Qubit Thing," Shtetl-Optimized (Feb. 20, 2025) (Aaronson quoting the editorial disclaimer).

20. "Microsoft's Quantum Breakthrough Claim Labeled 'Unreliable,'" The Register (Mar. 12, 2025) (quoting Frolov: "The only improvement there has been is in the quality of the PR campaign . . . and I would say almost everyone in the field agrees with that").

21. "Experts Weigh in on Microsoft's Topological Qubit Claim," Physics World (Feb. 27, 2025) (quoting Hensinger).

22. 15 U.S.C. § 78j(b).

23. 17 C.F.R. § 240.10b-5.

24. Dura Pharmaceuticals, Inc. v. Broudo, 544 U.S. 336 (2005).

25. Basic Inc. v. Levinson, 485 U.S. 224 (1988).

26. Ernst & Ernst v. Hochfelder, 425 U.S. 185 (1976).

27. Virginia Bankshares, Inc. v. Sandberg, 501 U.S. 1083 (1991).

28. "Quantum Winter Warning: Why Overhype and the QCI Saga Could Chill Quantum Computing," PostQuantum.com (Sept. 3, 2025); "Quantum Computing Inc (QUBT) Under Investigation for Potential Securities Law Violations," GuruFocus (Jan. 16, 2025).

29. "Quantum Winter Warning," supra note 28 (noting revenues under $0.4 million for 2023 and 2024 combined, $39,000 in Q1 2025).

30. Id.

31. "IonQ Disputes Claims from Short Seller That Lost Gov't Contracts Have Left $54.6M 'Black Hole' in Revenue," Data Center Dynamics (Feb. 2026); "IonQ Misled Investors About Its Dependence on Backdoor Earmarks, Short-Seller Report Says," Fortune (Feb. 4, 2026). IonQ disputes these characterizations.

32. Kerrisdale Capital, short report on IonQ (Mar. 2025), quoted in Fortunesupra note 31.

33. The Portnoy Law Firm, class action announcement (Jan. 19, 2026); "When Quantum Promises Collide: Red Flags in Financial Reporting," ainvest.com (July 1, 2025).

34. In re Donald J. Trump Casino Securities Litigation, 7 F.3d 357 (3d Cir. 1993).

35. Omnicare, Inc. v. Laborers District Council Construction Industry Pension Fund, 575 U.S. 175 (2015).

36. Neder v. United States, 527 U.S. 1 (1999).

37. Global-Tech Appliances, Inc. v. SEB S.A., 563 U.S. 754 (2011).

38. United States v. Gaudin, 515 U.S. 506 (1995).

39. See FTC, "Guidance on AI Claims" (2023); DLA Piper client alert on FTC "AI-washing" cases (cited in "We Need to Disentangle Hype from AI and Quantum Computing," TechPolicy.Press, Mar. 5, 2026).

40. ACCC warning on "Quantum AI" (Mar. 1, 2024); Central Bank of Ireland warning (Dec. 2, 2024); BaFin (Feb. 2025); DFSA (Oct. 30, 2025). Compiled at FinanceFraudMonitor.com (Mar. 2026).

41. NSA, "CNSA Suite 2.0" (2022); NIST, "Post-Quantum Cryptography Standardization: Final Standards" (Aug. 2024); "Q-Day Just Got Closer," The Quantum Insider (Mar. 31, 2026).

42. Katz v. United States, 389 U.S. 347 (1967).

43. Carpenter v. United States, 585 U.S. 296 (2018).

44. Riley v. California, 573 U.S. 373 (2014).

45. Quantum Computing Cybersecurity Preparedness Act, Pub. L. No. 117-260 (2022).

46. Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579 (1993).

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