Multi-Qubit Golden Gates

• URL: http://arxiv.org/abs/2509.09047v1
• Date: Wed, 10 Sep 2025 22:52:19 GMT
• Title: Multi-Qubit Golden Gates
• Authors: Rahul Dalal, Shai Evra, Ori Parzanchevski,
• Abstract summary: We extend the work of a letter of Sarnak and arXiv:1704.02106 on golden and super-golden gates to higher dimensions.<n>Our main motivation is to construct efficient multi-qubit universal gate sets for quantum computers.
• Score: 0.5097809301149341
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Our goal in this paper is to construct optimal topological generators for compact unitary Lie groups, extending the work of a letter of Sarnak and arXiv:1704.02106 on golden and super-golden gates to higher dimensions. To do so we consider a variant of the Sarnak--Xue Density Hypotheses in the weight aspect for definite projective unitary groups and prove it using the endoscopic classification of automorphic representations. Our main motivation is to construct efficient multi-qubit universal gate sets for quantum computers. For example, we find a set of universal gates that, for a given accuracy, can heuristically approximate arbitrary unitary operations on 2 qubits with $\approx$10 times fewer ``expensive'' $T$-type gates than the standard Clifford+$T$ set. Our framework also covers the 2-qubit Clifford+CS gate set, well-known for being particularly friendly to fault-tolerant implementation. We thereby prove tight upper bounds on the required CS count for approximations (specifically, $4.8$x fewer non-Clifford gates than Clifford+$T$).

Related papers

• BPDQ: Bit-Plane Decomposition Quantization on a Variable Grid for Large Language Models [56.504879072674015]
  We propose Bit-Plane Decomposition Quantization (BPDQ), which constructs a variable quantization grid via bit-planes and scalar coefficients.<n>BPDQ enables serving Qwen2.5-72B on a single GTX 3090 with 83.85% GSM8K accuracy (vs. 90.83% at 16-bit)
  arXiv  Detail & Related papers  (2026-02-04T02:54:37Z)
• Transversal Clifford-Hierarchy Gates via Non-Abelian Surface Codes [0.0]
  We present a purely 2D realization of phase gates at any level of the Clifford hierarchy.<n>Our construction encodes a logical qubit in the quantum double $D(G)$ of a non-Abelian group $G$ on a triangular spatial patch.
  arXiv  Detail & Related papers  (2025-12-15T19:00:00Z)
• Clifford+V synthesis for multi-qubit unitary gates [0.0]
  We develop a general framework for synthesizing target gates by using a finite set of basic gates.<n>We introduce a suboptimal but short run-time algorithm for synthesizing multi-qubit controlled gates.
  arXiv  Detail & Related papers  (2025-10-09T14:57:55Z)
• Efficient unitary designs and pseudorandom unitaries from permutations [35.66857288673615]
  We show that products exponentiated sums of $S(N)$ permutations with random phases match the first $2Omega(n)$ moments of the Haar measure. The heart of our proof is a conceptual connection between the large dimension (large-$N$) expansion in random matrix theory and the method.
  arXiv  Detail & Related papers  (2024-04-25T17:08:34Z)
• Low-depth Clifford circuits approximately solve MaxCut [44.99833362998488]
  We introduce a quantum-inspired approximation algorithm for MaxCut based on low-depth Clifford circuits. Our algorithm finds an approximate solution of MaxCut on an $N$-vertex graph by building a depth $O(N)$ Clifford circuit.
  arXiv  Detail & Related papers  (2023-10-23T15:20:03Z)
• Characterising semi-Clifford gates using algebraic sets [0.0]
  We study the sets of gates of the third-level of the Clifford hierarchy and their distinguished subsets of nearly diagonal' semi-Clifford gates. Semi-Clifford gates are important because they can be implemented with far more efficient use of these resource states.
  arXiv  Detail & Related papers  (2023-09-26T18:41:57Z)
• Quantum control landscape for generation of $H$ and $T$ gates in an open qubit with both coherent and environmental drive [57.70351255180495]
  An important problem in quantum computation is generation of single-qubit quantum gates such as Hadamard ($H$) and $pi/8$ ($T$) Here we consider the problem of optimal generation of $H$ and $T$ gates using coherent control and the environment as a resource acting on the qubit via incoherent control.
  arXiv  Detail & Related papers  (2023-09-05T09:05:27Z)
• Shorter quantum circuits via single-qubit gate approximation [1.2463824156241843]
  We give a novel procedure for approximating general single-qubit unitaries from a finite universal gate set. We show that taking probabilistic mixtures of channels to solve (arXiv:1409.3552) and magnitude approximation problems saves factor of two in approximation costs.
  arXiv  Detail & Related papers  (2022-03-18T17:14:35Z)
• Finding the disjointness of stabilizer codes is NP-complete [77.34726150561087]
  We show that the problem of calculating the $c-disjointness, or even approximating it to within a constant multiplicative factor, is NP-complete. We provide bounds on the disjointness for various code families, including the CSS codes,$d codes and hypergraph codes. Our results indicate that finding fault-tolerant logical gates for generic quantum error-correcting codes is a computationally challenging task.
  arXiv  Detail & Related papers  (2021-08-10T15:00:20Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• Solving correlation clustering with QAOA and a Rydberg qudit system: a full-stack approach [94.37521840642141]
  We study the correlation clustering problem using the quantum approximate optimization algorithm (QAOA) and qudits. Specifically, we consider a neutral atom quantum computer and propose a full stack approach for correlation clustering. We show the qudit implementation is superior to the qubit encoding as quantified by the gate count.
  arXiv  Detail & Related papers  (2021-06-22T11:07:38Z)
• Efficient unitary designs with a system-size independent number of non-Clifford gates [2.387952453171487]
  It takes exponential resources to produce Haar-random unitaries drawn from the full $n$-qubit group. Unitary $t-designs mimic the Haar-$-th moments. We derive novel bounds on the convergence time of random Clifford circuits to the $t$-th moment of the uniform distribution on the Clifford group.
  arXiv  Detail & Related papers  (2020-02-21T19:41:07Z)

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.