Tensor Decomposition for Non-Clifford Gate Minimization

• URL: http://arxiv.org/abs/2602.15285v1
• Date: Tue, 17 Feb 2026 01:11:07 GMT
• Title: Tensor Decomposition for Non-Clifford Gate Minimization
• Authors: Kirill Khoruzhii, Patrick Gelß, Sebastian Pokutta,
• Abstract summary: Fault-tolerant quantum computation requires minimizing non-Clifford gates, whose implementation via magic state distillation dominates resource costs.<n>We develop methods for this problem, building on a connection between Toffoli count and tensor decomposition over $bbF$.<n>On standard benchmarks, these methods match or improve all reported results for both Toffoli and $T$-count, with most circuits completing in under a minute on a single CPU instead of thousands of TPUs used by prior work.
• Score: 17.808896175242644
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Fault-tolerant quantum computation requires minimizing non-Clifford gates, whose implementation via magic state distillation dominates the resource costs. While $T$-count minimization is well-studied, dedicated $CCZ$ factories shift the natural target to direct Toffoli minimization. We develop algebraic methods for this problem, building on a connection between Toffoli count and tensor decomposition over $\mathbb{F}_2$. On standard benchmarks, these methods match or improve all reported results for both Toffoli and $T$-count, with most circuits completing in under a minute on a single CPU instead of thousands of TPUs used by prior work.

Related papers

• Adaptive Quantum Homeopathy [0.0]
  We present a protocol, named Quantum Homeopathy, able to generate unitary $k$-designs on $n$ qubits.<n>Inspired by the principle of homeopathy, our method applies a $k$-design only to a subsystem of size $Theta(k)$, independent of $n$.<n>We prove that this construction achieves full quantum security against adaptive adversaries using only $tildeO(k2 logvarepsilon-1)$ non-Clifford gates.
  arXiv  Detail & Related papers  (2025-10-09T12:14:58Z)
• Tensor Decomposition Networks for Fast Machine Learning Interatomic Potential Computations [48.46721044282335]
  tensor decomposition networks (TDNs) achieve competitive performance with dramatic speedup in computations.<n>We evaluate TDNs on PubChemQCR, a newly curated molecular relaxation dataset containing 105 million DFT-calculated snapshots.<n>Results show that TDNs achieve competitive performance with dramatic speedup in computations.
  arXiv  Detail & Related papers  (2025-07-01T18:46:27Z)
• Proving the Limited Scalability of Centralized Distributed Optimization via a New Lower Bound Construction [57.93371273485736]
  We consider a centralized distributed learning setup where all workers jointly find an unbiased bound LDeltaepsilon2,$ better poly-logarithmically in $n$, even in the homogeneous (i.i.d.) case, where all workers access the same distribution.
  arXiv  Detail & Related papers  (2025-06-30T13:27:39Z)
• Reducing T Gates with Unitary Synthesis [0.41873449350124814]
  This work presents a novel FT synthesis algorithm that directly synthesizes arbitrary single-qubit unitaries.<n>By leveraging tensor network-based search, our approach enables native $U3$ synthesis, reducing the $T$ count, Clifford gate count, and approximation error.
  arXiv  Detail & Related papers  (2025-03-20T04:53:54Z)
• LDC-MTL: Balancing Multi-Task Learning through Scalable Loss Discrepancy Control [48.98651927356094]
  Multi-task learning (MTL) has been widely adopted for its ability to simultaneously learn multiple tasks.<n>We propose LDC-MTL, a simple and scalable loss discrepancy control approach for MTL, formulated from a bilevel optimization perspective.<n>Our method incorporates two key components: (i) a bilevel formulation for fine-grained loss discrepancy control, and (ii) a scalable first-order bilevel algorithm that requires only $mathcalO(1)$ time and memory.
  arXiv  Detail & Related papers  (2025-02-12T17:18:14Z)
• Non-Clifford diagonalization for measurement shot reduction in quantum expectation value estimation [1.2754578699685275]
  Estimating expectation values on near-term quantum computers often requires a prohibitively large number of measurements.<n>We introduce a method that relaxes this constraint of commutativity, instead allowing for entirely arbitrary terms to be grouped together.<n>We show that $k$-NoCliD reduces the number of circuit shots, often by a very large margin, and often even for $k$ as small as 2.
  arXiv  Detail & Related papers  (2024-08-21T18:00:03Z)
• Minimal entanglement for injecting diagonal gates [0.0]
  We show that the connectivity between the computational space and magic state factories forms a fundamental bottleneck on the rate at which non-Clifford operations can be implemented. We construct local stabilizer circuits that use only $nu(|Drangle)$ ebits to implement $D$ in the computational space.
  arXiv  Detail & Related papers  (2024-03-27T18:00:03Z)
• Nearly Minimax Optimal Regret for Learning Linear Mixture Stochastic Shortest Path [80.60592344361073]
  We study the Shortest Path (SSP) problem with a linear mixture transition kernel. An agent repeatedly interacts with a environment and seeks to reach certain goal state while minimizing the cumulative cost. Existing works often assume a strictly positive lower bound of the iteration cost function or an upper bound of the expected length for the optimal policy.
  arXiv  Detail & Related papers  (2024-02-14T07:52:00Z)
• Efficiently Learning One-Hidden-Layer ReLU Networks via Schur Polynomials [50.90125395570797]
  We study the problem of PAC learning a linear combination of $k$ ReLU activations under the standard Gaussian distribution on $mathbbRd$ with respect to the square loss. Our main result is an efficient algorithm for this learning task with sample and computational complexity $(dk/epsilon)O(k)$, whereepsilon>0$ is the target accuracy.
  arXiv  Detail & Related papers  (2023-07-24T14:37:22Z)
• Early fault-tolerant simulations of the Hubbard model [3.988614978933934]
  Simulation of the Hubbard model is a leading candidate for the first useful applications of a fault-tolerant quantum computer. We present a new analytic approach to bounding the simulation error due to Trotterization that provides much tighter bounds for the split-operator FFFT method. We find there is a potentially useful application for fault-tolerant quantum computers using around one million Toffoli gates.
  arXiv  Detail & Related papers  (2020-12-16T20:07:54Z)
• Learning Halfspaces with Tsybakov Noise [50.659479930171585]
  We study the learnability of halfspaces in the presence of Tsybakov noise. We give an algorithm that achieves misclassification error $epsilon$ with respect to the true halfspace.
  arXiv  Detail & Related papers  (2020-06-11T14:25:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.