Synthesis of Single Qutrit Circuits from Clifford+R

• URL: http://arxiv.org/abs/2503.20203v1
• Date: Wed, 26 Mar 2025 03:55:43 GMT
• Title: Synthesis of Single Qutrit Circuits from Clifford+R
• Authors: Erik J. Gustafson, Henry Lamm, Diyi Liu, Edison M. Murairi, Shuchen Zhu,
• Abstract summary: Two deterministic algorithms are presented to approximate single-qutrit gates.<n>The first algorithm exhaustively searches over the Clifford + $mathbfR$ group.<n>The second algorithm searches for Householder reflections.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present two deterministic algorithms to approximate single-qutrit gates. These algorithms utilize the Clifford + $\mathbf{R}$ group to find the best approximation of diagonal rotations. The first algorithm exhaustively searches over the group; while the second algorithm searches only for Householder reflections. The exhaustive search algorithm yields an average $\mathbf{R}$ count of $2.193(11) + 8.621(7) \log_{10}(1 / \varepsilon)$, albeit with a time complexity of $\mathcal{O}(\varepsilon^{-4.4})$. The Householder search algorithm results in a larger average $\mathbf{R}$ count of $3.20(13) + 10.77(3) \log_{10}(1 / \varepsilon)$ at a reduced time complexity of $\mathcal{O}(\varepsilon^{-0.42})$, greatly extending the reach in $\varepsilon$. These costs correspond asymptotically to 35% and 69% more non-Clifford gates compared to synthesizing the same unitary with two qubits. Such initial results are encouraging for using the $\mathbf{R}$ gate as the non-transversal gate for qutrit-based computation.

Related papers

• Implicit High-Order Moment Tensor Estimation and Learning Latent Variable Models [39.33814194788341]
  We study the task of learning latent-variable models. Motivated by such applications, we develop a general efficient algorithm for implicit moment computation. By leveraging our general algorithm, we obtain the first-time learners for the following models.
  arXiv  Detail & Related papers  (2024-11-23T23:13:24Z)
• A Sub-Quadratic Time Algorithm for Robust Sparse Mean Estimation [6.853165736531941]
  We study the algorithmic problem of sparse mean estimation in the presence of adversarial outliers. Our main contribution is an algorithm for robust sparse mean estimation which runs in emphsubquadratic time using $mathrmpoly(k,log d,1/epsilon)$ samples.
  arXiv  Detail & Related papers  (2024-03-07T18:23:51Z)
• A Scalable Algorithm for Individually Fair K-means Clustering [77.93955971520549]
  We present a scalable algorithm for the individually fair ($p$, $k$)-clustering problem introduced by Jung et al. and Mahabadi et al. A clustering is then called individually fair if it has centers within distance $delta(x)$ of $x$ for each $xin P$. We show empirically that not only is our algorithm much faster than prior work, but it also produces lower-cost solutions.
  arXiv  Detail & Related papers  (2024-02-09T19:01:48Z)
• Do you know what q-means? [45.810803542748495]
  We present an improved version of the quantum algorithm originally proposed by Kerenidis, Landman, Luongo, and Prakash (NeurIPS')<n>Our algorithm does not rely on quantum linear algebra primitives of prior work, but instead only uses QRAM to prepare simple states.<n>We also present a "dequantized" algorithm for $varepsilon$-$k$-means which runs in $Obig.
  arXiv  Detail & Related papers  (2023-08-18T17:52:12Z)
• 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)
• Near-Optimal Bounds for Learning Gaussian Halfspaces with Random Classification Noise [50.64137465792738]
  We show that any efficient SQ algorithm for the problem requires sample complexity at least $Omega(d1/2/(maxp, epsilon)2)$. Our lower bound suggests that this quadratic dependence on $1/epsilon$ is inherent for efficient algorithms.
  arXiv  Detail & Related papers  (2023-07-13T18:59:28Z)
• Near-Optimal Quantum Coreset Construction Algorithms for Clustering [15.513270929560088]
  We give quantum algorithms that find coresets for $k$-clustering in $mathbbRd$ with $tildeO(sqrtnkd3/2)$ query complexity. Our coreset reduces the input size from $n$ to $mathrmpoly(kepsilon-1d)$, so that existing $alpha$-approximation algorithms for clustering can run on top of it.
  arXiv  Detail & Related papers  (2023-06-05T12:22:46Z)
• Fast $(1+\varepsilon)$-Approximation Algorithms for Binary Matrix Factorization [54.29685789885059]
  We introduce efficient $(1+varepsilon)$-approximation algorithms for the binary matrix factorization (BMF) problem. The goal is to approximate $mathbfA$ as a product of low-rank factors. Our techniques generalize to other common variants of the BMF problem.
  arXiv  Detail & Related papers  (2023-06-02T18:55:27Z)
• Linear Query Approximation Algorithms for Non-monotone Submodular Maximization under Knapsack Constraint [16.02833173359407]
  This work introduces two constant factor approximation algorithms with linear query complexity for non-monotone submodular over a ground set of size $n$ subject to a knapsack constraint. $mathsfDLA$ is a deterministic algorithm that provides an approximation factor of $6+epsilon$ while $mathsfRLA$ is a randomized algorithm with an approximation factor of $4+epsilon$.
  arXiv  Detail & Related papers  (2023-05-17T15:27:33Z)
• Sketching Algorithms and Lower Bounds for Ridge Regression [65.0720777731368]
  We give a sketching-based iterative algorithm that computes $1+varepsilon$ approximate solutions for the ridge regression problem. We also show that this algorithm can be used to give faster algorithms for kernel ridge regression.
  arXiv  Detail & Related papers  (2022-04-13T22:18:47Z)
• Well Separated Pair Decomposition and power weighted shortest path metric algorithm fusion [0.0]
  We consider an algorithm that computes all $s$-well separated pairs in certain point sets in $mathbbRn$, $n$ $>$ $1$. We also consider an algorithm that is a permutation of Dijkstra's algorithm, that computes $K$-nearest neighbors using a certain power weighted shortest path metric in $mathbbRn$, $n$ $>$ $1$.
  arXiv  Detail & Related papers  (2021-03-20T17:38:13Z)
• Practical and Parallelizable Algorithms for Non-Monotone Submodular Maximization with Size Constraint [20.104148319012854]
  We present and parallelizable for a submodular function, not necessarily a monotone, with respect to a size constraint. We improve the best approximation factor achieved by an algorithm that has optimal adaptivity and nearly optimal complexity query to $0.193 - varepsilon$.
  arXiv  Detail & Related papers  (2020-09-03T22:43:55Z)
• Exact Quantum Query Algorithms Outperforming Parity -- Beyond The Symmetric functions [3.652509571098291]
  We first obtain optimal exact quantum query algorithms ($Q_algo(f)$) for a direct sum based class of $Omega left( 2fracsqrtn2 right)$ non-symmetric functions. We show that query complexity of $Q_algo$ is $lceil frac3n4 rceil$ whereas $D_oplus(f)$ varies between $n-1$ and $lceil frac3n4 rce
  arXiv  Detail & Related papers  (2020-08-14T12:17:48Z)
• Streaming Complexity of SVMs [110.63976030971106]
  We study the space complexity of solving the bias-regularized SVM problem in the streaming model. We show that for both problems, for dimensions of $frac1lambdaepsilon$, one can obtain streaming algorithms with spacely smaller than $frac1lambdaepsilon$.
  arXiv  Detail & Related papers  (2020-07-07T17:10:00Z)

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.