Multi-controlled single-qubit unitary gates based on the quantum Fourier transform

• URL: http://arxiv.org/abs/2408.00935v2
• Date: Fri, 23 Aug 2024 23:10:30 GMT
• Title: Multi-controlled single-qubit unitary gates based on the quantum Fourier transform
• Authors: Vladimir V. Arsoski,
• Abstract summary: Multi-controlled (MC) unitary (U) gates are widely employed in quantum algorithms and circuits. Few state-of-the-art decompositions of MCU gates use non-elementary $C-R_x$ and $C-U1/2m-1$ gates. Our approach is based on two generalizations of the multi-controlled X (MCX) gate.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Multi-controlled (MC) unitary (U) gates are widely employed in quantum algorithms and circuits. Few state-of-the-art decompositions of MCU gates use non-elementary $C-R_x$ and $C-U^{1/2^{m-1}}$ gates resulting in a linear function for the depths of an implemented circuit on the number of these gates. Our approach is based on two generalizations of the multi-controlled X (MCX) gate that uses the quantum Fourier transform (QFT) comprised of Hadamard and controlled-phase gates. For the native gate set used in a genuine quantum computer, the decomposition of the controlled-phase gate is twice as less complex as $C-R_x$, which can result in an approximately double advantage of circuits derived from the QFT. The first generalization of QFT-MCX is based on altering the controlled gates acting on the target qubit. These gates are the most complex and are also used in the state-of-the-art circuits. The second generalization relies on the ZYZ decomposition and uses only one extended QFT-based circuit to implement the two multi-controlled X gates needed for the decomposition. Since the complexities of this circuit are approximately equal to the QFT-based MCX, our MCU implementation is more advanced than any known existing. The supremacy over the best-known optimized algorithm will be demonstrated by comparing transpiled circuits assembled for execution in a genuine quantum device. One may note that our implementations use approximately half the number of elementary gates compared to the most efficient one, potentially resulting in a smaller error. Additionally, we elaborated optimization steps to simplify the state-of-the-art linear-depth decomposition (LDD) MCU circuit to one of our implementations.

Related papers

• Implementing multi-controlled X gates using the quantum Fourier transform [0.0]
  We show how a quantum arithmetic-based approach can be efficiently used to implement many complex quantum gates. We show how the depth of the circuit can be significantly reduced using only a few ancilla qubits.
  arXiv  Detail & Related papers  (2024-07-25T13:22:00Z)
• Multi-controlled Phase Gate Synthesis with ZX-calculus applied to Neutral Atom Hardware [2.536162003546062]
  We present an approach to synthesize multi controlled phase gates using ZX calculus. By representing quantum circuits as graph like ZX diagrams, one can utilize the distinct graph structure of diagonal gates.
  arXiv  Detail & Related papers  (2024-03-16T09:06:49Z)
• 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)
• 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)
• Quantum Fourier Addition, Simplified to Toffoli Addition [92.18777020401484]
  We present the first systematic translation of the QFT-addition circuit into a Toffoli-based adder. Instead of using approximate decompositions of the gates from the QFT circuit, it is more efficient to merge gates.
  arXiv  Detail & Related papers  (2022-09-30T02:36:42Z)
• On the role of entanglement in qudit-based circuit compression [0.0]
  Gate-based universal quantum computation is formulated in terms of two types of operations: local single-qubit gates, and two-qubit entangling gates. We show how the complexity of multi-qubit circuits can be lowered significantly by employing qudit encodings.
  arXiv  Detail & Related papers  (2022-09-29T06:48:48Z)
• Applications of Universal Parity Quantum Computation [0.0]
  We demonstrate the applicability of a universal gate set in the parity encoding, which is a dual to the standard gate model. Embedding these algorithms in the parity encoding reduces the circuit depth compared to conventional gate-based implementations. We propose simple implementations of multiqubit gates in tailored encodings and an efficient strategy to prepare graph states.
  arXiv  Detail & Related papers  (2022-05-19T12:31:46Z)
• 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)
• Accurate methods for the analysis of strong-drive effects in parametric gates [94.70553167084388]
  We show how to efficiently extract gate parameters using exact numerics and a perturbative analytical approach. We identify optimal regimes of operation for different types of gates including $i$SWAP, controlled-Z, and CNOT.
  arXiv  Detail & Related papers  (2021-07-06T02:02:54Z)
• 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)

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.