Karthik Seetharam | Searcharxiv

arXiv2026

Macromux: scalable postselection for high-threshold fault-tolerant quantum computation

We introduce a new resource-efficient scheme for fault-tolerant quantum computation known as `macroscale multiplexing' (or simply `Macromux'), that utilizes scalable postselection to significantly improve the threshold of a given fault-tolerant protocol against both Pauli and erasure errors. Macromux is a hierarchical method for postselecting on constant-size space-time windows of a fault tolerant protocol, requiring only constant additional overheads. The method can be straightforwardly implemented for any fault-tolerant protocol and in any architecture that has access to routing and memory, such as linear-optical fusion-based architectures. We construct fault-tolerant protocols that, to our knowledge, have the highest thresholds in the literature; we perform simulations of fusion-based schemes based on the surface code, showing a maximum possible increase in Pauli thresholds of up to a factor of $\sim6$ (from $1.0\%$ to $5.9\%$). Our schemes are highly-resource efficient, and can for example, double the loss thresholds of some photonic fusion-based protocols using as little as $3 \times$ overhead.

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arXiv2024

Quantum sampling algorithms for quantum state preparation and matrix block-encoding

The problems of quantum state preparation and matrix block-encoding are ubiquitous in quantum computing: they are crucial parts of various quantum algorithms for the purpose for initial state preparation as well as loading problem relevant data. We first present an algorithm based on QRS that prepares a quantum state $|ψ_f\rangle \propto \sum^N_{x=1} f(x)|x\rangle$. When combined with efficient reference states the algorithm reduces the cost of quantum state preparation substantially, if certain criteria on $f$ are met. When the preparation of the reference state is not the dominant cost, and the function $f$ and relevant properties are efficiently computable or provided otherwise with cost $o(N)$, the QRS-based method outperforms the generic state preparation algorithm, which has cost $O(N)$. We demonstrate the detailed performance (in terms of the number of Toffoli gates) of the QRS-based algorithm for quantum states commonly appearing in quantum applications, e.g., those with coefficients that obey power law decay, Gaussian, and hyperbolic tangent, and compare it with other methods. Then, we adapt QRS techniques to the matrix block-encoding problem and introduce a QRS-based algorithm for block-encoding a given matrix $A = \sum_{ij} A_{ij} |i\rangle \langle j|$. We work out rescaling factors for different access models, which encode how the information about the matrix is provided to the quantum computer. We exemplify these results for a particular Toeplitz matrix with elements $A_{\mathbf{ij}}= 1/\|{\mathbf{i}}-{\mathbf{j}}\|^2$, which appears in quantum chemistry, and PDE applications, e.g., when the Coulomb interaction is involved. Our work unifies, and in certain ways goes beyond, various quantum state preparation and matrix block-encoding methods in the literature, and gives detailed performance analysis of important examples that appear in quantum applications.

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