Linear-Time T-Gate Optimization via Random Abstraction

• URL: http://arxiv.org/abs/2605.13929v1
• Date: Wed, 13 May 2026 15:54:13 GMT
• Title: Linear-Time T-Gate Optimization via Random Abstraction
• Abstract summary: Quantum computers promise exponential speedups for problems in cryptography, chemistry, and optimization.<n>T-gate count can dominate the resource budget of large-scale quantum computations.<n>We present theoretical and practical results on T-gate optimization.
• Score: 6.345523830122166
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Quantum computers promise exponential speedups for problems in cryptography, chemistry, and optimization. Realizing this promise requires fault tolerance: physical qubits are noisy, so logical qubits must be encoded redundantly across many physical ones using quantum error-correcting codes. In most practical fault-tolerance schemes, T gates cannot be implemented transversally and instead require costly magic-state distillation protocols involving a complex set of operations. As a result, T-gate count can dominate the resource budget of large-scale quantum computations, making T-count minimization a central bottleneck on the path to quantum advantage. Existing T-count optimization tools, however, do not scale to the circuits that quantum advantage demands. We present theoretical and practical results on T-gate optimization. On the theoretical side, we give a linear-time randomized algorithm for phase folding, based on a novel randomized static analysis. Our static analysis soundly approximates the set of reachable quantum states with an arbitrarily high probability. Our key insight is a static analysis that does not track symbolic expressions, but propagates constant-width bitstrings down the circuit. On the practical side, our implementation, TZAP, is multiple orders of magnitude faster than state-of-the-art tools -- such as PyZX, VOQC, and Feynman -- closely matches their T-count reductions on standard benchmarks, and within seconds on a laptop computer can optimize circuits with millions of gates.

Related papers

• Verifiable quantum advantage in extremely low depth [52.51019642214249]
  We give a problem that is solvable by shallow quantum circuits, hard for computation in time under lattice-based assumptions.<n>We prove that shallow quantum circuits have sufficient structure to solve certain classically hard tasks whose solutions can be verified efficiently.
  arXiv  Detail & Related papers  (2026-09-01T15:54:34Z)
• General circuit mapping algorithm for neutral atom quantum computers [1.047947389293086]
  Neutral atom quantum computers (NAQC) are emerging as a promising, scalable quantum computing platform.<n> circuit execution often requires physically moving qubits, making compilation a critical optimization challenge.<n>We propose a circuit independent mathematical framework built on graph-theoretic optimization that determines the minimal number of required qubit transfers.
  arXiv  Detail & Related papers  (2026-06-18T17:21:23Z)
• Quantum Compiling with Reinforcement Learning on a Superconducting Processor [55.135709564322624]
  We develop a reinforcement learning-based quantum compiler for a superconducting processor. We demonstrate its capability of discovering novel and hardware-amenable circuits with short lengths. Our study exemplifies the codesign of the software with hardware for efficient quantum compilation.
  arXiv  Detail & Related papers  (2024-06-18T01:49:48Z)
• T-Count Optimizing Genetic Algorithm for Quantum State Preparation [0.05999777817331316]
  We present and utilize a genetic algorithm for state preparation circuits consisting of gates from the Clifford + T gate set. Our algorithm does automatically generate fault tolerantly implementable solutions where the number of the most error prone components is reduced.
  arXiv  Detail & Related papers  (2024-06-06T12:26:14Z)
• Quantum Circuit Optimization with AlphaTensor [47.9303833600197]
  We develop AlphaTensor-Quantum, a method to minimize the number of T gates that are needed to implement a given circuit. Unlike existing methods for T-count optimization, AlphaTensor-Quantum can incorporate domain-specific knowledge about quantum computation and leverage gadgets. Remarkably, it discovers an efficient algorithm akin to Karatsuba's method for multiplication in finite fields.
  arXiv  Detail & Related papers  (2024-02-22T09:20:54Z)
• QuantumSEA: In-Time Sparse Exploration for Noise Adaptive Quantum Circuits [82.50620782471485]
  QuantumSEA is an in-time sparse exploration for noise-adaptive quantum circuits. It aims to achieve two key objectives: (1) implicit circuits capacity during training and (2) noise robustness. Our method establishes state-of-the-art results with only half the number of quantum gates and 2x time saving of circuit executions.
  arXiv  Detail & Related papers  (2024-01-10T22:33:00Z)
• Optimizing quantum gates towards the scale of logical qubits [78.55133994211627]
  A foundational assumption of quantum gates theory is that quantum gates can be scaled to large processors without exceeding the error-threshold for fault tolerance. Here we report on a strategy that can overcome such problems. We demonstrate it by choreographing the frequency trajectories of 68 frequency-tunablebits to execute single qubit while superconducting errors.
  arXiv  Detail & Related papers  (2023-08-04T13:39:46Z)
• Scalable noisy quantum circuits for biased-noise qubits [37.69303106863453]
  We consider biased-noise qubits affected only by bit-flip errors, which is motivated by existing systems of stabilized cat qubits. For realistic noise models, phase-flip will not be negligible, but in the Pauli-Twirling approximation, we show that our benchmark could check the correctness of circuits containing up to $106$ gates.
  arXiv  Detail & Related papers  (2023-05-03T11:27:50Z)
• Synthesizing Quantum-Circuit Optimizers [7.111661677477926]
  QUESO is an efficient approach for automatically synthesizing a quantum-circuit for a given quantum device. For an instance, in 1.2 minutes, QUESO can synthesize an correctness with high-probability guarantees.
  arXiv  Detail & Related papers  (2022-11-17T17:30:20Z)
• Quantum Gate Pattern Recognition and Circuit Optimization for Scientific Applications [1.6329956884407544]
  We introduce two ideas for circuit optimization and combine them in a multi-tiered quantum circuit optimization protocol called AQCEL. AQCEL is deployed on an iterative and efficient quantum algorithm designed to model final state radiation in high energy physics. Our technique is generic and can be useful for a wide variety of quantum algorithms.
  arXiv  Detail & Related papers  (2021-02-19T16:20:31Z)
• Space-efficient binary optimization for variational computing [68.8204255655161]
  We show that it is possible to greatly reduce the number of qubits needed for the Traveling Salesman Problem. We also propose encoding schemes which smoothly interpolate between the qubit-efficient and the circuit depth-efficient models.
  arXiv  Detail & Related papers  (2020-09-15T18:17:27Z)

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.