About
I design quantum error-correcting codes that are high-rate, single-shot decodable and ready for real hardware.
PhD student at UMass Amherst (Manning CICS), advised by Stefan Krastanov; I also work with Owen Gwilliam. I build quantum LDPC codes from algebra, simulate them at circuit level, and lead the code library in QuantumClifford.jl.
Seeking research internships
Quantum error correction and fault-tolerant architectures, with flexible timing. Happy to chat: fmian@umass.edu
Papers
Koszul-complex description of abelian multicycle codes, with explicit metachecks.
$K_\bullet(F_1,\dots,F_t;S)$ with $F_i\in S$, $\;t=2q\ge 4$, $\;\operatorname{rank}K_k=\binom{t}{k}$, $\;M_XP_X=0=M_ZP_Z$
Explicit quantum Tanner codes from non-abelian groups at moderate blocklength.
on $\mathrm{Cay}_2(G,A,B)$ with $G$ non-abelian, $\;n\in[500,1000]$, $\;d_{\min}>\sqrt{n}$ for 7 of 8 highlighted codes, $\;p_{\mathrm{th}}^{\mathrm{circ}}\approx 0.14\text{–}0.27\%$
I wrote the Codes Tested section and contributed the code implementations through QuantumClifford.jl.
Compiling syndrome extraction for any CSS code onto two parallel quantum-dot arrays with few shuttles.
for column-regular qLDPC codes with Shor-style extraction; minimizing shuttles for general CSS codes is NP-hard.
Earlier, in hardware: SoC-Based Implementation of 1D Convolutional Neural Network for 3-Channel ECG Arrhythmia Classification via HLS4ML. Feroz Ahmed Mian, Saima Zafar. IEEE Embedded Systems Letters, 2024. cited by 28
Contributions I'm proud of
LPCode built non-commuting stabilizers whenever the group was non-abelian, because only the left regular representation was used. I switched one factor to the right regular representation, following Panteleev and Kalachev, which restores CSS orthogonality for any finite group.
“This is great, a really solid improvement.” (Stefan Krastanov, review)
Oscar's homology raised an error for chain complexes of modules over finite fields such as GF(2). I extended it upstream, then used Oscar chain complexes to build D-dimensional surface and toric codes in QuantumClifford.jl.
Used in QuantumClifford.jl #534
Generalized the 2D, 3D and 4D surface and toric codes to arbitrary D, built as tensor products of repetition-code chain complexes in Oscar. The boundary maps give both parity checks and metachecks.
Multi-sector homological product codes from classical and quasi-cyclic codes, and the double homological product, built on the same Oscar homological algebra. I also wrote the Double Homological Product entry for the Error Correction Zoo.
Also in the Error Correction Zoo
A hypergraph-product-style family built from a structured classical LDPC code with parity-check matrix [C | M]. I also contributed it to the Error Correction Zoo.
Also in the Error Correction Zoo
A solver-agnostic MILP formulation that certifies the distance of quantum LDPC codes. It is now the library's exact distance method, and I use it to certify code distances in my own work.
In-place Pauli measurement for generalized stabilizer states, following Yoder's algorithm, so circuits with T gates can be simulated with measurements, without the state's inverse sparsity Λ growing.
The reference implementation of MM codes: Koszul matrices with each variable replaced by its circulant, and a metacheck interface so decoders can use the check redundancy.
News
QuantumExpanders.jl library.Software
Lead contributor of the error-correcting-code library: MM, generalized toric, D-dimensional surface and toric, non-abelian lifted product, two-block group algebra and tile codes, plus an exact MILP distance solver.
Quantum Tanner codes from Cayley complexes and lifts, search heuristics, and explicit Ramanujan graphs. Reproduces every code in the QT paper.
Contributions to AWS Braket tooling and quantum optimal control in Julia (unitaryHack 2024, 3rd globally).
Collaborators
Amherst, through my lens
Photographs coming soon.