Quantum Computing with Hermitian Gates

• URL: http://arxiv.org/abs/2402.12356v1
• Date: Mon, 19 Feb 2024 18:36:09 GMT
• Title: Quantum Computing with Hermitian Gates
• Authors: Ben Zindorf and Sougato Bose
• Abstract summary: We show that any single-qubit operator may be implemented as two Hermitian gates. We show that a gate set comprised of pi rotations about two fixed axes, along with the CNOT gate, is universal for quantum computation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Universal gate sets for quantum computation, when single and two qubit operations are accessible, include both Hermitian and non-Hermitian gates. Here we show that any single-qubit operator may be implemented as two Hermitian gates, and thus a purely Hermitian universal set is possible. An implementational convenience can be that non-identity single-qubit Hermitian gates are equivalent to pi rotations up to a global phase. We show that a gate set comprised of pi rotations about two fixed axes, along with the CNOT gate, is universal for quantum computation. Moreover, we show that two pi rotations can transform the axis of any multi-controlled unitary, a special case being a single CNOT sufficing for any controlled pi rotation. These gates simplify the process of circuit compilation in view of their Hermitian nature. Further, the insights are used to design an efficient circuit for a controlled-U(4) gate with any arbitrary operator on two target qubits.

Related papers

• A diverse set of two-qubit gates for spin qubits in semiconductor quantum dots [5.228819198411081]
  We propose and verify a fast composite two-qubit gate scheme to extend the available two-qubit gate types. Our gate scheme limits the parameter requirements of all essential two-qubit gates to a common JDeltaE_Z region. With this versatile composite gate scheme, broad-spectrum two-qubit operations allow us to efficiently utilize the hardware and the underlying physics resources.
  arXiv  Detail & Related papers  (2024-04-29T13:37:43Z)
• One Gate Scheme to Rule Them All: Introducing a Complex Yet Reduced Instruction Set for Quantum Computing [8.478982715648547]
  Scheme for qubits with $XX+YY$ coupling realizes any two-qubit gate up to single-qubit gates. We observe marked improvements across various applications, including generic $n$-qubit gate synthesis, quantum volume, and qubit routing.
  arXiv  Detail & Related papers  (2023-12-09T19:30:31Z)
• 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)
• Cat-qubit-inspired gate on cos($2\theta$) qubits [77.34726150561087]
  We introduce a single-qubit $Z$ gate inspired by the noise-bias preserving gate of the Kerr-cat qubit. This scheme relies on a $pi$ rotation in phase space via a beamsplitter-like transformation between a qubit and ancilla qubit.
  arXiv  Detail & Related papers  (2023-04-04T23:06:22Z)
• Two qubits in one transmon -- QEC without ancilla hardware [68.8204255655161]
  We show that it is theoretically possible to use higher energy levels for storing and controlling two qubits within a superconducting transmon. The additional qubits could be used in algorithms which need many short-living qubits in error correction or by embedding effecitve higher connectivity in qubit networks.
  arXiv  Detail & Related papers  (2023-02-28T16:18:00Z)
• Extensive characterization of a family of efficient three-qubit gates at the coherence limit [0.4471952592011114]
  We implement a three-qubit gate by simultaneously applying two-qubit operations. We generate two classes of entangled states, the GHZ and W states, by applying the new gate only once. We analyze the experimental and statistical errors on the fidelity of the gates and of the target states.
  arXiv  Detail & Related papers  (2022-07-06T19:42:29Z)
• A Complete Equational Theory for Quantum Circuits [58.720142291102135]
  We introduce the first complete equational theory for quantum circuits. Two circuits represent the same unitary map if and only if they can be transformed one into the other using the equations.
  arXiv  Detail & Related papers  (2022-06-21T17:56:31Z)
• 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)
• Approaching the theoretical limit in quantum gate decomposition [0.0]
  We propose a novel numerical approach to decompose general quantum programs in terms of single- and two-qubit quantum gates with a $CNOT$ gate count. Our approach is based on a sequential optimization of parameters related to the single-qubit rotation gates involved in a pre-designed quantum circuit used for the decomposition.
  arXiv  Detail & Related papers  (2021-09-14T15:36:22Z)
• 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)
• Constructing quantum circuits with global gates [0.0]
  A particularly popular gate set in the literature on quantum computing consists of arbitrary single-qubit gates and 2-qubit CNOT gates. A CNOT gate is however not always the natural multi-qubit interaction that can be implemented on a given physical quantum computer. This calls for an entirely different approach to constructing efficient circuits.
  arXiv  Detail & Related papers  (2020-12-16T16:29:23Z)

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.