Unitary tetrahedron quantum gates

• URL: http://arxiv.org/abs/2407.10731v2
• Date: Thu, 25 Jul 2024 14:10:55 GMT
• Title: Unitary tetrahedron quantum gates
• Authors: Vivek Kumar Singh, Akash Sinha, Pramod Padmanabhan, Vladimir Korepin,
• Abstract summary: Quantum simulations of many-body systems using 2-qubit Yang-Baxter gates offer a benchmark for quantum hardware. This can be extended to the higher dimensional case with $n$-qubit generalisations of Yang-Baxter gates called $n$-simplex operators. Finding them amounts to identifying unitary solutions of the $n$-simplex equations, the building blocks of higher dimensional integrable systems.
• Score: 3.117417023918577
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Quantum simulations of many-body systems using 2-qubit Yang-Baxter gates offer a benchmark for quantum hardware. This can be extended to the higher dimensional case with $n$-qubit generalisations of Yang-Baxter gates called $n$-simplex operators. Such multi-qubit gates potentially lead to shallower and more efficient quantum circuits as well. Finding them amounts to identifying unitary solutions of the $n$-simplex equations, the building blocks of higher dimensional integrable systems. These are a set of highly non-linear and over determined system of equations making it notoriously hard to solve even when the local Hilbert spaces are spanned by qubits. We systematically overcome this for higher simplex operators constructed using two methods: from Clifford algebras and by lifting Yang-Baxter operators. The $n=3$ or the tetrahedron case is analyzed in detail. For the qubit case our methods produce 13 inequivalent families of unitary tetrahedron operators. 12 of these families are obtained by appending the 5 unitary families of 4 by 4 constant Yang-Baxter operators of Dye-Hietarinta, with a single qubit operator. As applications, universal sets of single, two and three qubit gates are realized using such unitary tetrahedron operators. The ideas presented in this work can be naturally extended to the higher simplex cases.

Related papers

• 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)
• Hietarinta's classification of $4\times 4$ constant Yang-Baxter operators using algebraic approach [1.429979512794144]
  Classifying Yang-Baxter operators is an essential first step in the study of integrable quantum systems on quantum computers. We use four different algebraic structures that reproduce 10 of the 11 Hietarinta families when the qubit representation is chosen.
  arXiv  Detail & Related papers  (2024-09-09T07:16:16Z)
• Toffoli gates solve the tetrahedron equations [1.8434042562191815]
  In particular, factorised scattering operators result in integrable quantum circuits that provide universal quantum computation. A natural question is to extend this construction to higher qubit gates, like the Toffoli gates. We show that unitary families of such operators are constructed by the 3-dimensional generalizations of the Yang-Baxter operators.
  arXiv  Detail & Related papers  (2024-05-26T08:03:24Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• Optimal synthesis of general multi-qutrit quantum computation [1.556591713973462]
  Quantum circuits of a general quantum gate acting on multiple $d$-level quantum systems play a prominent role in quantum computation. We propose a new Cartan decomposition of semi-simple unitary Lie group $U(n)$ (arbitrary $n$-qutrit gate) We design an explicit quantum circuit for implementing arbitrary two-qutrit gates, and the cost of our construction is 21 generalized controlled X (GCX) and controlled increment (CINC) gates less than the earlier best result of 26 GGXs.
  arXiv  Detail & Related papers  (2023-10-18T14:28:31Z)
• 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)
• Universal qudit gate synthesis for transmons [44.22241766275732]
  We design a superconducting qudit-based quantum processor. We propose a universal gate set featuring a two-qudit cross-resonance entangling gate. We numerically demonstrate the synthesis of $rm SU(16)$ gates for noisy quantum hardware.
  arXiv  Detail & Related papers  (2022-12-08T18:59:53Z)
• Optimised Trotter Decompositions for Classical and Quantum Computing [0.0]
  Suzuki-Trotter decompositions of exponential operators like $exp(Ht)$ are required in almost every branch of numerical physics. We show how highly optimised schemes originally derived for exactly two operators $A_1,2$ can be applied to such generic Suzuki-Trotter decompositions.
  arXiv  Detail & Related papers  (2022-11-04T18:21:00Z)
• Construction and local equivalence of dual-unitary operators: from dynamical maps to quantum combinatorial designs [0.0]
  We study the map analytically for the two-qubit case describing the basins of attraction, fixed points, and rates of approach to dual unitaries. A subset of dual-unitary operators having maximum entangling power are 2-unitary operators or perfect tensors. A necessary criterion for their local unitary equivalence to distinguish classes is also introduced and used to display various concrete results.
  arXiv  Detail & Related papers  (2022-05-18T10:13:56Z)
• Constrained mixers for the quantum approximate optimization algorithm [55.41644538483948]
  We present a framework for constructing mixing operators that restrict the evolution to a subspace of the full Hilbert space. We generalize the "XY"-mixer designed to preserve the subspace of "one-hot" states to the general case of subspaces given by a number of computational basis states. Our analysis also leads to valid Trotterizations for "XY"-mixer with fewer CX gates than is known to date.
  arXiv  Detail & Related papers  (2022-03-11T17:19:26Z)
• 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)

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.