Geometrical Formalism for Dynamically Corrected Gates in Multiqubit Systems

• URL: http://arxiv.org/abs/2008.01168v1
• Date: Thu, 30 Jul 2020 18:00:19 GMT
• Title: Geometrical Formalism for Dynamically Corrected Gates in Multiqubit Systems
• Authors: Donovan Buterakos, Sankar Das Sarma, Edwin Barnes
• Abstract summary: We show that cancellation of noise errors to leading order corresponds to closure of a curve in a multi-dimensional Euclidean space. We propose this geometric formalism as a general technique for pulse-induced error suppression in quantum computing gate operations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The ability to perform gates in multiqubit systems that are robust to noise is of crucial importance for the advancement of quantum information technologies. However, finding control pulses that cancel noise while performing a gate is made difficult by the intractability of the time-dependent Schrodinger equation, especially in multiqubit systems. Here, we show that this issue can be sidestepped by using a formalism in which the cumulative error during a gate is represented geometrically as a curve in a multi-dimensional Euclidean space. Cancellation of noise errors to leading order corresponds to closure of the curve, a condition that can be satisfied without solving the Schrodinger equation. We develop and uncover general properties of this geometric formalism, and derive a recursion relation that maps control fields to curvatures for Hamiltonians of arbitrary dimension. We demonstrate examples by using the geometric method to design dynamically corrected gates for a class of two-qubit Hamiltonians that is relevant for both superconducting transmon qubits and semiconductor spin qubits. We propose this geometric formalism as a general technique for pulse-induced error suppression in quantum computing gate operations.

Related papers

• Geometric Quantum Machine Learning with Horizontal Quantum Gates [41.912613724593875]
  We propose an alternative paradigm for the symmetry-informed construction of variational quantum circuits. We achieve this by introducing horizontal quantum gates, which only transform the state with respect to the directions to those of the symmetry. For a particular subclass of horizontal gates based on symmetric spaces, we can obtain efficient circuit decompositions for our gates through the KAK theorem.
  arXiv  Detail & Related papers  (2024-06-06T18:04:39Z)
• Geodesic Algorithm for Unitary Gate Design with Time-Independent Hamiltonians [1.9106435311144372]
  We present an algorithm that finds the strengths of the Hamiltonian terms by using the direction of the geodesic to the target quantum gate. We numerically compare our algorithm to gradient descent methods and show that it finds solutions with considerably fewer steps for standard multi-qubit gates.
  arXiv  Detail & Related papers  (2024-01-11T15:20:16Z)
• Completely Positive Map for Noisy Driven Quantum Systems Derived by Keldysh Expansion [39.58317527488534]
  We introduce a decoherence model based on the Keldysh formalism. This formalism allows us to include non-periodic drives and correlated quantum noise in our model. We demonstrate that this strategy generates pulses that mitigate correlated quantum noise in qubit state-transfer and gate operations.
  arXiv  Detail & Related papers  (2023-03-20T23:05:24Z)
• Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent and Incoherent Photons Found with Gradient Search [77.34726150561087]
  We consider an environment formed by incoherent photons as a resource for controlling open quantum systems via an incoherent control. We exploit a coherent control in the Hamiltonian and an incoherent control in the dissipator which induces the time-dependent decoherence rates.
  arXiv  Detail & Related papers  (2023-02-28T07:36:02Z)
• Dynamical-Corrected Nonadiabatic Geometric Quantum Computation [9.941657239723108]
  We present an effective geometric scheme combined with a general dynamical-corrected technique. Our scheme represents a promising way to explore large-scale fault-tolerant quantum computation.
  arXiv  Detail & Related papers  (2023-02-08T16:18:09Z)
• Universal robust quantum gates by geometric correspondence of noisy quantum dynamics [0.0]
  We develop a theory to capture quantum dynamics due to various noises graphically, obtaining the quantum erroneous evolution diagrams (QEED) We then develop a protocol to engineer a universal set of single- and two-qubit robust gates that correct the generic errors. Our approach offers new insights into the geometric aspects of noisy quantum dynamics and several advantages over existing methods.
  arXiv  Detail & Related papers  (2022-10-26T07:21:02Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
  Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
  arXiv  Detail & Related papers  (2021-08-06T19:38:01Z)
• Nonadiabatic geometric quantum gates that are insensitive to qubit-frequency drifts [8.750801670077806]
  In the current implementation of nonadiabatic geometric phases, operational and/or random errors tend to destruct the conditions that induce geometric phases. Here, we apply the path-design strategy to explain in detail why both configurations can realize universal quantum gates in a single-loop way. Our scheme provides a promising way towards practical realization of high-fidelity and robust nonadiabatic geometric quantum gates.
  arXiv  Detail & Related papers  (2021-03-16T12:05:45Z)
• Doubly geometric quantum control [0.0]
  In holonomic quantum computation, single-qubit gates are performed using driving protocols that trace out closed loops on the Bloch sphere. We present a general procedure that combines two types of geometry to design gates that simultaneously suppress pulse errors and transverse noise errors.
  arXiv  Detail & Related papers  (2021-03-14T20:41:37Z)
• Simulating nonnative cubic interactions on noisy quantum machines [65.38483184536494]
  We show that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware. On noisy devices without error correction, we show that simulation results are significantly improved when the quantum program is compiled using modular gates.
  arXiv  Detail & Related papers  (2020-04-15T05:16:24Z)

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.