Research

Technical work and legal analysis on cryptography, patent eligibility and the law of new technology.

Selected research October 29, 2026

Where is post-quantum work heading, and who is driving it?

PQScope connects 4,444 research items with standards, implementations, contributors, policy, and patent evidence to investigate the technical and commercial decisions facing post-quantum teams.

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Fig. 1. Post-quantum work at the IETF

Individual proposals: —
Working-group development: —
Publication review: —
Published RFCs: —

Tracked documents · PQScope, .
Current statuses, not a conversion funnel.

Sources and definitions

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All analysis

November 1, 2026Post-quantum cryptography · PQScope
Why Post-Quantum Standards Still Raise Patent Questions
A new practice area focused on tracking research, standards, and patents so technology companies can implement or contribute to post-quantum cryptography without creating avoidable IP problems.
November 1, 2026Quantum computing · Patents
What investors read in a quantum startup's patent portfolio
Investor counsel reads a quantum startup's patent families twice, in the data room and in the public record at the USPTO and EPO. How to spend a limited patent budget so both tell the same story.
October 29, 2026Post-quantum cryptography · PQScope
Where is post-quantum work heading, and who is driving it?
PQScope connects 4,444 research items with standards, implementations, contributors, policy, and patent evidence to investigate the technical and commercial decisions facing post-quantum teams.
September 20, 2026Quantum computing · Licensing
University and startup: the license terms that matter in quantum
Many quantum computing companies begin with a university license. The terms that most often need working out between the two, and why several of them are harder in quantum than in other fields.
August 30, 2026Quantum cryptography · QKD
Quantum key distribution (QKD) patents: open strategic opportunities
The USPTO has granted more than 600 QKD patents and the EPO about 180. What those patents cover, who holds them, and where the field is still open.
August 5, 2026Quantum computing · Patents
Where to spend a quantum patent budget: what the USPTO and the EPO actually grant
The USPTO and the EPO grant quantum applications at different rates and for different reasons. What the examination records of 16,896 quantum applications mean for where a limited patent budget should go.
May 14, 2026Post-quantum cryptography · Patents
Post-quantum cryptography has one PTAB precedent. What it means for a post-quantum patent portfolio
The USPTO Patent Trial and Appeal Board has ruled on a quantum-resistant cryptographic construction exactly once, in 2018, and the applicant won. What the near-empty record means for how a post-quantum patent portfolio should be drafted and prosecuted.
November 17, 2025AI · Section 101
AI Patent Eligibility Dramatically Expanded at USPTO
The precedential Ex parte Desjardins decision recalibrates how the USPTO examines AI and machine learning applications under Section 101, and what it means for claiming and specification strategy.
October 13, 2025AI · Section 101
USPTO Shifts Tone on AI Patents with August 2025 Eligibility Memo
The August 4, 2025 USPTO memorandum sets a "close call" standard for Section 101 rejections, limits the mental process grouping, and restores broad neural network training claims. What it means for filing and drafting decisions.

Papers & experiments

Technical paper · PDF

Self-supervised training for patent prior-art search: leveraging internal document structure without examiner labels

J. M. Denaro
Case Studies in Machine Learning
The University of Texas at Austin

Trains BERT to match patent claims with passages from their own descriptions; 96% matching accuracy on 6,447 USPTO patents, with no examiner citations.

Read the paper (PDF)

Interactive figure

From a measurement to factors

A small experiment in quantum order finding. Examine the distribution, sample a measurement, and reconstruct a period.

View the experiment

Research methods

Inside PQScope

Which post-quantum ideas are gaining ground, who is behind them, and where they stand in the standards. Proprietary research tooling used in CipherLaw’s legal work.

Read about the research

Post-quantum research

The mathematics behind the transition

Shor’s algorithm connects quantum computation to the mathematics underlying RSA and other widely used public-key systems. A sufficiently large, fault-tolerant quantum computer would change their security assumptions.

This small experiment makes one part of that idea tangible: how quantum order finding can help reveal the factors of a number. Measurements and continued fractions illustrate the underlying mathematics.

A view across the field

PQScope follows research, standards discussions and the people and organizations behind them. These figures describe PQScope’s coverage.

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Where post-quantum work is heading →
Standards and IP Strategy →

Shor’s algorithm · a small experiment

From a measurement to factors

Measurements from a quantum Fourier distribution provide evidence of the hidden period.

N =

a =

Fourier measurementQ = 64 · 6 control qubits

TheoryObserved frequency0 runs

Each run returns one value, not the whole distribution.

01 · MeasureNo measurements yet.

02 · ReconstructA continued fraction will suggest a denominator.

03 · Verify & factorThe period is not supplied to the reconstruction.

Mathematical details

ExampleFourier register size

Q = 64 is below N² = 225. Small registers can work here, but lack the usual general precision guarantee.

Remove coherence before the Fourier transform

This models complete dephasing of the exponent register in its computational basis. Its Fourier outcomes become uniform. Chance samples may still yield factors in these tiny examples; they no longer concentrate near the useful phases.

Changing the instance, register size, or coherence starts a new experiment.

The modular function

The first 16 values of a^x mod N. Equal values label the same state of the output register; their exponent amplitudes can interfere.

The Fourier chart is not a transform of these bar heights. It sums amplitudes within each group of equal function values, then adds the groups’ probabilities.

From a sample to an order

A sample gives y/Q ≈ k/r. Continued fractions produce possible reduced fractions; their denominators may be divisors of r. We keep candidates within half a Fourier bin, combine denominator hypotheses by least common multiples, and test aᴿ mod N = 1. A verified exponent is reduced by removing redundant prime factors to obtain the order r.

This is a bounded teaching implementation for N = 15 and 21. The usual textbook choice N² ≤ Q < 2N² gives Q = 256 and 512 respectively. Finite precision can produce incorrect candidates; the modular check is essential.

The latest continued fraction appears after a measurement.

Most recent measurements (0)
Run	y	Candidate k/r	aᵈ mod N
No measurements yet.

The ideal distribution

P (y) = \frac{1}{Q^{2}} \sum_{z} {| \sum_{x : f (x) = z} e^{2 π i x y / Q} |}^{2}

Here f(x) = aˣ mod N, 0 ≤ x < Q, and 0 ≤ z < N. This is the normalized distribution when the output register is ignored, with no postselection. The simulator computes it from f(x), without using a known period. In the dephased model, P(y) = 1/Q.

An even order helps only when aʳᐟ² is a nontrivial square root of 1 modulo N. An odd order or aʳᐟ² ≡ −1 calls for a different base.

Shor’s paper · Order finding explained

A classical simulation of quantum order finding at toy size. Applying Shor’s algorithm to an RSA-2048 modulus would require a sufficiently large, fault-tolerant quantum computer.