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Nouédyn Baspin

Publications and source records attributed to Nouédyn Baspin.

At least 19 recordsLinked to original sources
arXiv2026

2 Fast 2 Surgery: Fast surgery on QLDPC codes with $\tilde{O}(n(k + d))$ space overhead

We show that the fast surgery framework of Baspin-Berent-Cohen can be instantiated using at most $\tilde{O}(n(k + d))$ ancilla qubits, improving on the previously achievable $O(n\cdot k \cdot d)$ overhead. This result also establishes that fast surgery can be performed at a cost comparable to the $\tilde{O}(nk)$ overhead required for regular surgery. We build the surgery ancilla by first starting with a dense, but expanding system; and then applying expansion-preserving sparsification methods from gauging and code embeddings.

quant-ph↗
arXiv2026

A lower bound on the overhead of addressable surgery on sparse stabiliser codes

We show that, for stabilisers codes, there always exists a logical subspace requiring $\tildeΩ(k^2)$ ancillary qubits to be measured with a sparse surgery ancilla. For CSS codes the hard subspace can be taken to be generated by all-X, or all-Z operators. As a result, for codes with large $k$, constant overhead ancillas can only realise a small fraction of possible measurements.

quant-ph↗
arXiv2026

4D and 5D Layer Codes through Color Routing

We introduce and explicit Calderbank-Shor-Steane (CSS) code construction that generalizes the Layer codes to $D=4,5$ dimensions. Much like its predecessor, the present construction is based on embedding quantum low-density parity check (qLDPC) codes; from an $[[n,k,d]]$ code with energy barrier $Δ$, we obtain a $D=4,5$ dimensional Layer code with parameters $[[Θ(n^{D/(D-2)}), k, Θ(dn^{1/(D-2)})]]$ and energy barrier $Ω(Δ)$. Using good qLDPC codes as input, our construction saturates the $D=4,5$ dimensional BPT bounds exactly. The higher dimensional Layer Codes are modular, and thus well suited to architectures composed of modular network patches, despite our physical limitation to three dimensions. We overcome the hurdles encountered by previous generalization attempts through the use of \textit{color routing}, allowing us to resolve the structure of the check layers and line defects.

quant-ph↗
arXiv2026

Non-CSS Quantum Code Embedding

We generalize the unified framework in [Phys. Rev. A 113, 022438 (2026)] to accommodate arbitrary stabilizer codes (referred as non-CSS for emphasis). The generalization has immediate consequences in areas including logical measurement, quantum weight reduction and Euclidean embedding. For example, currently CSS (pure $X,Z$-type) logical measurements are well-understood based on the (height-1) cone, while non-CSS (e.g., $Y$-type) logical measurements are ad hoc (e.g., rely on local Clifford transform). Similarly, quantum weight reduction and optimal Euclidean embeddings only exist for CSS input codes. Here, we show that our generalized framework addresses this issue, and thus many constructions, including qLDPC surgery, Layer Codes and quantum weight reduction generalize to non-CSS codes in a relatively straightforward fashion. The previously mentioned examples are derived in detail for clarity.

quant-ph↗
arXiv2026

The Pinnacle Architecture: Reducing the cost of breaking RSA-2048 to 100 000 physical qubits using quantum LDPC codes

The realisation of utility-scale quantum computing inextricably depends on the design of practical, low-overhead fault-tolerant architectures. We introduce the Pinnacle Architecture, which uses quantum low-density parity check (QLDPC) codes to allow for universal, fault-tolerant quantum computation with a spacetime overhead significantly smaller than that of any competing architecture. With this architecture, we show that 2048-bit RSA integers can be factored with fewer than one hundred thousand physical qubits, given a physical error rate of $10^{-3}$, code cycle time of $1$ microsecond and a reaction time of $10$ microseconds. We thereby demonstrate the feasibility of utility-scale quantum computing with an order of magnitude fewer physical qubits than has previously been believed necessary.

quant-ph↗
arXiv2026

Wire Codes

Quantum information is fragile and must be protected by a quantum error-correcting code for large-scale practical applications. Recently, highly efficient quantum codes have been discovered which require a high degree of spatial connectivity. This raises the question of how to realize these codes with minimal overhead under physical hardware connectivity constraints. Here, we introduce a general recipe to transform any quantum stabilizer code into a subsystem code that has local interactions, with weight and degree three, on a given graph. We call the subsystem codes produced by our recipe wire codes, and their code parameters depend on the input code and the given graph. Wire codes can be adapted to have a local implementation on any graph that supports a low-density embedding of the input Tanner graph, with an overhead that depends on the embedding. In particular, applying our results to a stabilizer code and a subdivision of its own Tanner graph, yields a quantum weight reduction procedure with a multiplicative qubit overhead and distance reduction that are linear in the input check degree and weight, respectively. Applying our results to hypercubic lattices leads to a construction of local subsystem codes with optimal scaling code parameters in any fixed spatial dimension. Similarly, applying our results to families of expanding graphs leads to local codes on these graphs with code parameters that depend on the degree of expansion. Our results constitute a general method to construct low-overhead subsystem codes on general graphs, which can be applied to adapt highly efficient quantum error correction procedures to hardware with restricted connectivity.

quant-ph↗
arXiv2026

Quantum Weight Reduction with Layer Codes

Quantum weight reduction procedures ease the implementation of quantum codes by sparsifying them, resulting in low-weight checks and low-degree qubits. However, to date, only few quantum weight reduction methods have been explored. In this work we introduce a simple and general procedure for quantum weight reduction that achieves check weight 6 and total qubit degree 6, lower than existing procedures at the cost of a potentially larger qubit overhead. Our quantum weight reduction procedure replaces each qubit and check in an arbitrary Calderbank-Shor-Steane code with an ample patch of surface code, these patches are then joined together to form a geometrically nonlocal Layer Code. This is a quantum analog of the simple classical weight reduction procedure where each bit and check is replaced by a repetition code. Due to the simplicity of our weight reduction procedure, bounds on the weight and degree of the resulting code follow directly from the Layer Code construction and hence are easily verified by inspection. Our procedure is well suited for implementation in modular architectures that consist of surface code patches networked via long-range interconnects.

quant-ph↗
arXiv2025

Fast surgery for quantum LDPC codes

Quantum LDPC codes promise significant reductions in physical qubit overhead compared with topological codes. However, many existing constructions for performing logical operations come with distance-dependent temporal overheads. We introduce a scheme for performing generalized surgery on quantum LDPC codes using a constant number of rounds of syndrome measurement. The merged code in our scheme is constructed by taking the total complex of the base code and a suitably chosen homomorphic chain complex. We demonstrate the applicability of our scheme on an example multi-cycle code and assess the performance under a phenomenological noise model, showing that fast surgery performs comparably to standard generalized surgery with multiple rounds. Our results pave the way towards fault-tolerant quantum computing with LDPC codes with both low spatial and temporal overheads.

quant-ph↗
arXiv2025

The Free Energy Barrier: An Eyring-Polanyi bound for stabilizer Hamiltonians, with applications to quantum error correction

The lack of an energy barrier in stabilizer Hamiltonians is well known to be an indication of short thermalisation times; and serves as a simple criteria to rule out self-correction. Its applicability has recently been challenged by the discovery of stabilizer codes with maximal energy barriers whose self-correcting status remains unclear. We address this question by introducing the more general notion of a free energy barrier, whose absence is also demonstrated to guarantee fast thermalisation. Applying these new results to the Layer codes, we prove that they lack self-correction.

quant-ph↗
arXiv2024

Layer Codes

The surface code is a two-dimensional topological code with code parameters that scale optimally with the number of physical qubits, under the constraint of two-dimensional locality. In three spatial dimensions an analogous simple yet optimal code was not previously known. Here, we introduce a construction that takes as input a stabilizer code and produces as output a three-dimensional topological code with related code parameters. The output codes have the special structure of being topological defect networks formed by layers of surface code joined along one-dimensional junctions, with a maximum stabilizer check weight of six. When the input is a family of good low-density parity-check codes, the output is a three-dimensional topological code with optimal scaling code parameters and a polynomial energy barrier.

quant-ph↗
arXiv2023

On combinatorial structures in linear codes

In this work we show that given a connectivity graph $G$ of a $[[n,k,d]]$ quantum code, there exists $\{K_i\}_i, K_i \subset G$, such that $\sum_i |K_i|\in Ω(k), \ |K_i| \in Ω(d)$, and the $K_i$'s are $\tildeΩ( \sqrt{{k}/{n}})$-expander. If the codes are classical we show instead that the $K_i$'s are $\tildeΩ\left({{k}/{n}}\right)$-expander. We also show converses to these bounds. In particular, we show that the BPT bound for classical codes is tight in all Euclidean dimensions. Finally, we prove structural theorems for graphs with no "dense" subgraphs which might be of independent interest.

cs.IT↗
arXiv2023

Simulating LDPC code Hamiltonians on 2D lattices

While LDPC codes have been demonstrated with desirable error correcting properties, this has come at a cost of diverging from the geometrical constraints of many hardware platforms. Viewing codes as the groundspace of a Hamiltonian, we consider engineering a simulation Hamiltonian reproducing some relevant features of the code. Techniques from Hamiltonian simulation theory are used to build a simulation of LDPC codes using only 2D nearest-neighbour interactions at the cost of an energy penalty polynomial in the system size. We derive guarantees for the simulation that allows us to approximately reproduce the ground state of the code Hamiltonian, approximating a $[[N, Ω(\sqrt{N}), Ω(\sqrt{N})]]$ code in 2D. The key ingredient is a new constructive tool to simulate an $l$-long interaction between two qubits by a 1D chain of $l$ nearest-neighbour interacting qubits using $\mathrm{poly}( l)$ interaction strengths. This is an exponential advantage over the existing gadgets for this routine which facilitates the first $ε$-simulation of \emph{arbitrary sparse} Hamiltonian on $n$ qubits with a Hamiltonian on a 2D lattice of $O(n^2)$ qubits with interaction strengths scaling as $O\left(\mathrm{poly}(n,1/ε)\right)$.

quant-ph↗
arXiv2023

Improved rate-distance trade-offs for quantum codes with restricted connectivity

For quantum error-correcting codes to be realizable, it is important that the qubits subject to the code constraints exhibit some form of limited connectivity. The works of Bravyi & Terhal (BT) and Bravyi, Poulin & Terhal (BPT) established that geometric locality constrains code properties -- for instance $[[n,k,d]]$ quantum codes defined by local checks on the $D$-dimensional lattice must obey $k d^{2/(D-1)} \le O(n)$. Baspin and Krishna studied the more general question of how the connectivity graph associated with a quantum code constrains the code parameters. These trade-offs apply to a richer class of codes compared to the BPT and BT bounds, which only capture geometrically-local codes. We extend and improve this work, establishing a tighter dimension-distance trade-off as a function of the size of separators in the connectivity graph. We also obtain a distance bound that covers all stabilizer codes with a particular separation profile, rather than only LDPC codes.

quant-ph↗
arXiv2023

A lower bound on the overhead of quantum error correction in low dimensions

We show that a quantum architecture with an error correction procedure limited to geometrically local operations incurs an overhead that grows with the system size, even if arbitrary error-free classical computation is allowed. In particular, we prove that in order to operate a quantum error correcting code in 2D at a logical error rate of $δ$, a space overhead of $Ω(\sqrt{\log(1/δ)})$ is needed for any constant depolarizing noise $p > 0$.

quant-ph↗
arXiv2022

Connectivity constrains quantum codes

Quantum low-density parity-check (LDPC) codes are an important class of quantum error correcting codes. In such codes, each qubit only affects a constant number of syndrome bits, and each syndrome bit only relies on some constant number of qubits. Constructing quantum LDPC codes is challenging. It is an open problem to understand if there exist good quantum LDPC codes, i.e. with constant rate and relative distance. Furthermore, techniques to perform fault-tolerant gates are poorly understood. We present a unified way to address these problems. Our main results are a) a bound on the distance, b) a bound on the code dimension and c) limitations on certain fault-tolerant gates that can be applied to quantum LDPC codes. All three of these bounds are cast as a function of the graph separator of the connectivity graph representation of the quantum code. We find that unless the connectivity graph contains an expander, the code is severely limited. This implies a necessary, but not sufficient, condition to construct good codes. This is the first bound that studies the limitations of quantum LDPC codes that does not rely on locality. As an application, we present novel bounds on quantum LDPC codes associated with local graphs in $D$-dimensional hyperbolic space.

quant-ph↗
arXiv2021

Quantifying nonlocality: how outperforming local quantum codes is expensive

Quantum low-density parity-check (LDPC) codes are a promising avenue to reduce the cost of constructing scalable quantum circuits. However, it is unclear how to implement these codes in practice. Seminal results of Bravyi & Terhal, and Bravyi, Poulin & Terhal have shown that quantum LDPC codes implemented through local interactions obey restrictions on their dimension $k$ and distance $d$. Here we address the complementary question of how many long-range interactions are required to implement a quantum LDPC code with parameters $k$ and $d$. In particular, in 2D we show that a quantum LDPC with distance $n^{1/2 + ε}$ code requires $Ω(n^{1/2 + ε})$ interactions of length $\widetildeΩ(n^ε)$. Further a code satisfying $k \propto n$ with distance $d \propto n^α$ requires $\widetildeΩ(n)$ interactions of length $\widetildeΩ(n^{α/2})$. Our results are derived using bounds on quantum codes from graph metrics. As an application of these results, we consider a model called a stacked architecture, which has previously been considered as a potential way to implement quantum LDPC codes. In this model, although most interactions are local, a few of them are allowed to be very long. We prove that limited long-range connectivity implies quantitative bounds on the distance and code dimension.

quant-ph↗
arXiv2020

Detecting topological edge states with the dynamics of a qubit

We consider the Su-Schrieffer-Heeger (SSH) chain, which has 0, 1, or 2 topological edge states depending on the ratio of the hopping parameters and the parity of the chain length. We couple a qubit to one edge of the SSH chain and a semi-infinite undimerized chain to the other, and evaluate the dynamics of the qubit. By evaluating the decoherence rate of the qubit we can probe the edge states of the SSH chain. The rate shows strong even-odd oscillations with the number of sites reflecting the presence or absence of edge states. Hence, the qubit acts as an efficient detector of the topological edge states of the SSH model. This can be generalized to other topological systems.

cond-mat.mes-hall↗