Topological quantum compilation of two-qubit gates

• URL: http://arxiv.org/abs/2408.07132v1
• Date: Tue, 13 Aug 2024 18:02:54 GMT
• Title: Topological quantum compilation of two-qubit gates
• Authors: Phillip C. Burke, Christos Aravanis, Johannes Aspman, Jakub Mareček, Jiří Vala,
• Abstract summary: We generate gates that are leakage-free and equivalent to the controlled-NOT gate up to single-qubit operations. Most of the generated classes are located near the edges of the Weyl chamber representation of two-qubit gates.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the topological quantum compilation of two-qubit operations within a system of Fibonacci anyons. Our primary goal is to generate gates that are approximately leakage-free and equivalent to the controlled-NOT (CNOT) gate up to single-qubit operations. These gates belong to the local equivalence class [CNOT]. Additionally, we explore which local equivalence classes of two-qubit operations can be naturally generated by braiding Fibonacci anyons. We discovered that most of the generated classes are located near the edges of the Weyl chamber representation of two-qubit gates, specifically between the local equivalence classes of the identity [1] and [CNOT], and between those of the double-controlled-NOT [DCNOT] and [SWAP]. Furthermore, we found a numerically exact implementation of a local equivalent of the SWAP gate using a sequence of only nine elements from the Fibonacci braiding gate set.

Related papers

• Scalable modular architecture for universal quantum computation [49.1574468325115]
  We show that it is sufficient to connect two qubit arrays that are evolution operator controllable by a single entangling two-qubit gate.<n>Our proof provides a template to build up modular QPUs from smaller building blocks with reduced numbers of local controls and couplings.
  arXiv  Detail & Related papers  (2025-07-19T16:45:47Z)
• Geometric structure and transversal logic of quantum Reed-Muller codes [51.11215560140181]
  In this paper, we aim to characterize the gates of quantum Reed-Muller (RM) codes by exploiting the well-studied properties of their classical counterparts. A set of stabilizer generators for a RM code can be described via $X$ and $Z$ operators acting on subcubes of particular dimensions.
  arXiv  Detail & Related papers  (2024-10-10T04:07:24Z)
• Linear Circuit Synthesis using Weighted Steiner Trees [45.11082946405984]
  CNOT circuits are a common building block of general quantum circuits. This article presents state-of-the-art algorithms for optimizing the number of CNOT gates. A simulated evaluation shows that the suggested is almost always beneficial and reduces the number of CNOT gates by up to 10%.
  arXiv  Detail & Related papers  (2024-08-07T19:51:22Z)
• Control landscapes for high-fidelity generation of C-NOT and C-PHASE gates with coherent and environmental driving [41.94295877935867]
  We consider the problem of high fidelity generation of two-qubit C-NOT and C-PHASE (with a detailed study of C-Z) gates in presence of the environment. We study quantum control landscapes which describe the behaviour of the fidelity as a function of the controls.
  arXiv  Detail & Related papers  (2024-05-23T00:04:19Z)
• Decomposition Algorithm of an Arbitrary Pauli Exponential through a Quantum Circuit [5.800032532382661]
  We review the staircase algorithm to decompose the exponential of a generalized Pauli matrix. We propose two alternative methods which offer more efficient quantum circuits.
  arXiv  Detail & Related papers  (2023-05-08T16:05:27Z)
• Decomposition of Multi-controlled Special Unitary Single-Qubit Gates [1.412197703754359]
  Multi-controlled unitary gates have been a subject of interest in quantum computing since its inception. Current state-of-the-art approach to implementing n-qubit multi-controlled gates involves the use of a quadratic number of single-qubit and CNOT gates. We present a new decomposition of n-qubit multi-controlled SU(2) gates that requires a circuit with a number of CNOT gates proportional to 20n.
  arXiv  Detail & Related papers  (2023-02-13T14:08:53Z)
• Controlled Gate Networks Applied to Eigenvalue Estimation [0.28106259549258145]
  We introduce a new scheme for quantum circuit design called controlled gate networks. Rather than trying to reduce the complexity of individual unitary operations, the new strategy is to toggle between all of the unitary operations needed with the fewest number of gates.
  arXiv  Detail & Related papers  (2022-08-29T12:46:46Z)
• Software mitigation of coherent two-qubit gate errors [55.878249096379804]
  Two-qubit gates are important components of quantum computing. But unwanted interactions between qubits (so-called parasitic gates) can degrade the performance of quantum applications. We present two software methods to mitigate parasitic two-qubit gate errors.
  arXiv  Detail & Related papers  (2021-11-08T17:37:27Z)
• Quantum simulation of $\phi^4$ theories in qudit systems [53.122045119395594]
  We discuss the implementation of quantum algorithms for lattice $Phi4$ theory on circuit quantum electrodynamics (cQED) system. The main advantage of qudit systems is that its multi-level characteristic allows the field interaction to be implemented only with diagonal single-qudit gates.
  arXiv  Detail & Related papers  (2021-08-30T16:30:33Z)
• Compiling single-qubit braiding gate for Fibonacci anyons topological quantum computation [0.0]
  Topological quantum computation is an implementation of a quantum computer in a way that radically reduces decoherence. Topological qubits are encoded in the topological evolution of two-dimensional quasi-particles called anyons.
  arXiv  Detail & Related papers  (2020-08-08T15:34:03Z)
• Improving the Performance of Deep Quantum Optimization Algorithms with Continuous Gate Sets [47.00474212574662]
  Variational quantum algorithms are believed to be promising for solving computationally hard problems. In this paper, we experimentally investigate the circuit-depth-dependent performance of QAOA applied to exact-cover problem instances. Our results demonstrate that the use of continuous gate sets may be a key component in extending the impact of near-term quantum computers.
  arXiv  Detail & Related papers  (2020-05-11T17:20:51Z)
• Efficient Two-Qubit Pulse Sequences Beyond CNOT [0.0]
  We design efficient controlled-rotation gates with arbitrary angle acting on three-spin encoded qubits for exchange-only quantum computation. We build two-qubit sequences out of subsequences with special properties that render each step of the construction analytically tractable.
  arXiv  Detail & Related papers  (2020-01-25T17:38:14Z)

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.