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Christopher K. Long @christopher-k-long.ac · 11/06/2026

In our recent arXiv (arxiv.org/abs/2605.28936) we benchmarked QEC and magic state factories for spin qubits. By computing magic state production overheads as a function of initialization, gate, measurement, and decoherence times we estimated the runtimes for typical algorithms—see Fig.

$Figure 2 from Songqinghao Yang, Christopher K. Long, Rubén M. Otxoa, Prakash Murali, Crispin H. W. Barnes, & David R. M. Arvidsson-Shukur, Hardware-Tailored Resource Estimation for Magic-State Distillation on Silicon Spin Qubits, arXiv preprint arXiv:2605.28936 (2026). Used under a CC-BY-4.0 license: https://creativecommons.org/licenses/by/4.0/ Caption: Algorithmic resource requirements. We plot the wall-clock time (horizontal axis) and the number of physical qubits (vertical axis) needed to run three different quantum algorithms. The color map indicates the fraction of the qubits used for MSD. The circles label the sparse SpinBus architecture with the standard surface code; the triangles label the SpinBus architecture with the XZZX surface code; and the squares label the dense architecture with the standard surface code. The logical operations are implemented with lattice surgery and the ‘grow-and-distill’ MSD protocol is chosen to minimize the space-time overhead.$

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Christopher K. Long @christopher-k-long.ac · 28/10/2025

It looks like Bluesky doesn't like transparent images. Here is take two:

Taken from: https://en.wikipedia.org/wiki/Quantum_phase_estimation_algorithm#/media/File:PhaseCircuit.svg

Under CC BY-SA 4.0 License.
Author: Omrika
Created: 14 April 2023
Uploaded: 14 April 2023
Caption:
"The circuit of the quantum phase estimation algorithm, which estimates the phase of an eigenvector of a unitary matrix."

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Christopher K. Long @christopher-k-long.ac · 28/10/2025

I meant the one with the QFT (diagram from Wikipedia below). I've always heard it called Kitaev's QPEA. In the thread is some history—it looks like many worked on it. The algorithm is HSP with the hiding function given by the sequence of controlled unitaries, and the period being the phase. (1/4)

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Christopher K. Long @christopher-k-long.ac · 08/10/2025

If a Python package has a pyproject.toml you can look for the requires-python line: `requires-python = ">=3.8"`. If you check the package on PyPI the requirements are also listed under Project Details > Unverified Details > Meta > Requires.

A screenshot of https://pypi.org/project/py-ste/#data showing the required Python version under Project Details > Unverified Details > Meta > Requires as `Python >=3.8`

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Christopher K. Long @christopher-k-long.ac · 18/09/2025

Example pulse distortions: (Top row) The modulation of a virtual Pauli-Z term in the system Hamiltonian. (2nd row) The time dilation required to implement the virtual Pauli-Z term without actually introducing it to the Hamiltonian. (3rd and 4th rows) The distorted two- and one-qubit control pulses.

Figure 2 from:

C. K. Long and C. H. W. Barnes, From virtual Z gates to virtual Z pulses, 2025. arXiv: 2509.13453 [quant-ph]. https://arxiv.org/abs/2509.13453.

Caption:
FIG. 2. Dilated pulses corresponding to virtual Z pulses. (Top row) The desired virtual Z pulses in units with ℏ = 1, with varying amplitudes: (left) derivative of Gaussian and (centre and right) derivative of hyperbolic tangent. The centre and right-hand columns differ only by the amplitude, with the right-hand column displaying larger amplitudes. (Second row from the top) The time-dilation required to implement the virtual Z pulse in the top row. The black curve in the centre column is an example of a virtual Z pulse that requires time compression. (Third row from the top) The distorted J pulse that implements a Gaussian (standard deviation 0.3) J pulse in the presence of the desired simultaneous virtual Z pulse. The purple curve corresponds to no virtual Z pulse—i.e., the undistorted pulse. (Bottom row) The distorted I′ (solid) and Q′ (dashed) pulses that implement a Gaussian (standard deviation 0.3) I pulse in the presence of the desired simultaneous virtual Z pulse—assuming the virtual Z pulse is applied only to qubit 1. Note that the J, I, and Q pulses can all be implemented simultaneously.

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Christopher K. Long @christopher-k-long.ac · 05/07/2025

Even accounting for this, we find the effect persists: the separation of the black curve from the blue vertical line for (X±Y)/√2 increases with qubit number. We conjecture this is due to the use of the fast two-qubit operation to aid in implementing single-qubit operations in some entangled basis.

The black solid curves represent numerically estimated cumulative probability distributions. The shaded region corresponds to a 99.99% confidence interval (CI) estimated via 105 bootstrap resamples (see “Methods” section). Vertical blue lines mark typical gate times. The dashed purple and orange curves are the homogeneous and isotropic (HI) fits and higher-order fits, respectively. For details on the fitting, see “Methods” section.

Taken from:
Long, C.K., Mayhall, N.J., Economou, S.E. et al. Minimal state-preparation times for silicon spin qubits. npj Quantum Inf 11, 113 (2025). https://doi.org/10.1038/s41534-025-01027-8
Under http://creativecommons.org/licenses/by/4.0/
No changes were made.

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Christopher K. Long @christopher-k-long.ac · 05/07/2025

Further, we consider random state transitions to bound the performance of arbitrary quantum algorithms. Finally, we study the robustness of the pulse-based approach to device imperfections and leakage:

Curves show the probability of occupying the computational, valley, double-, triple-, and quadruple-occupation subspaces of a 4-site Hubbard model with valleys. The applied pulse achieves the ground-state of LiH at the equilibrium bound distance of 1.59 Å in the corresponding 4-spin Heisenberg model [21] within 20 ns.

Taken from:
Long, C.K., Mayhall, N.J., Economou, S.E. et al. Minimal state-preparation times for silicon spin qubits. npj Quantum Inf 11, 113 (2025). https://doi.org/10.1038/s41534-025-01027-8
Under http://creativecommons.org/licenses/by/4.0/
No changes were made.

[21] Burkard, G., Ladd, T. D., Pan, A., Nichol, J. M. & Petta, J. R. Semiconductor spin qubits. Rev. Mod. Phys. 95, 025003 (2023).

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Christopher K. Long @christopher-k-long.ac · 05/07/2025

Preparing molecular ground states for H₂, HeH⁺, and LiH in 2.3, 4.6, and 26.8 ns:

(top) Molecular energy C(T) as a function of bond distance for a range of evolution times. At zero evolution time, C(0) corresponds to the (yellow) Hartree-Fock disassociation curve of the initial state. At the MET, the energy C(T = MET) (blue dissociation curve) converges to the full configuration interaction (FCI) energy C0 (dashed black curve). (bottom) Energy error Δ(T) := C(T) − C0 on a logarithmic color scale as a function of bond distance and evolution time. A white line shows the silicon METs. A dashed (gray) curve marks transmon METs [11].

Taken from:
Long, C.K., Mayhall, N.J., Economou, S.E. et al. Minimal state-preparation times for silicon spin qubits. npj Quantum Inf 11, 113 (2025). https://doi.org/10.1038/s41534-025-01027-8
Under http://creativecommons.org/licenses/by/4.0/
No changes were made.

[11] Meitei, O. R. et al. Gate-free state preparation for fast variational quantum eigensolver simulations. npj Quantum Inf. 7, 1–11 (2021).

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Christopher K. Long @christopher-k-long.ac · 17/06/2025

Please reach out if you have any issues with the libraries. And in Bluesky tradition, I will finish on a meme: (7/7)

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Christopher K. Long @christopher-k-long.ac · 17/06/2025

Hi all! I am excited to finally share this suite of quantum optimal control libraries that run up to 100× faster than QuTiP for some tasks. We developed these libraries while working on our preprint arxiv.org/abs/2406.10913, which was recently accepted into npj Quantum Information—keep tuned! (1/7)

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