Universal quantum computation and quantum error correction using discrete holonomies

• URL: http://arxiv.org/abs/2109.03692v2
• Date: Mon, 7 Feb 2022 17:11:57 GMT
• Title: Universal quantum computation and quantum error correction using discrete holonomies
• Authors: Cornelis J. G. Mommers, Erik Sj\"oqvist
• Abstract summary: Holonomic quantum computation exploits a quantum state's non-trivial, matrix-valued geometric phase (holonomy) to perform fault-tolerant computation. We show that quantum error correction codes integrate naturally in our scheme, providing a model for measurement-based quantum computation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Holonomic quantum computation exploits a quantum state's non-trivial, matrix-valued geometric phase (holonomy) to perform fault-tolerant computation. Holonomies arising from systems where the Hamiltonian traces a continuous path through parameter space have been well-researched. Discrete holonomies, on the other hand, where the state jumps from point to point in state space, have had little prior investigation. Using a sequence of incomplete projective measurements of the spin operator, we build an explicit approach to universal quantum computation. We show that quantum error correction codes integrate naturally in our scheme, providing a model for measurement-based quantum computation that combines the passive error resilience of holonomic quantum computation and active error correction techniques. In the limit of dense measurements we recover known continuous-path holonomies.

Related papers

• Quantum data learning for quantum simulations in high-energy physics [55.41644538483948]
  We explore the applicability of quantum-data learning to practical problems in high-energy physics. We make use of ansatz based on quantum convolutional neural networks and numerically show that it is capable of recognizing quantum phases of ground states. The observation of non-trivial learning properties demonstrated in these benchmarks will motivate further exploration of the quantum-data learning architecture in high-energy physics.
  arXiv  Detail & Related papers  (2023-06-29T18:00:01Z)
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
  We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
  arXiv  Detail & Related papers  (2022-06-03T18:00:02Z)
• Circuit Symmetry Verification Mitigates Quantum-Domain Impairments [69.33243249411113]
  We propose circuit-oriented symmetry verification that are capable of verifying the commutativity of quantum circuits without the knowledge of the quantum state. In particular, we propose the Fourier-temporal stabilizer (STS) technique, which generalizes the conventional quantum-domain formalism to circuit-oriented stabilizers.
  arXiv  Detail & Related papers  (2021-12-27T21:15:35Z)
• Model-Independent Error Mitigation in Parametric Quantum Circuits and Depolarizing Projection of Quantum Noise [1.5162649964542718]
  Finding ground states and low-lying excitations of a given Hamiltonian is one of the most important problems in many fields of physics. quantum computing on Noisy Intermediate-Scale Quantum (NISQ) devices offers the prospect to efficiently perform such computations. Current quantum devices still suffer from inherent quantum noise.
  arXiv  Detail & Related papers  (2021-11-30T16:08:01Z)
• Error-mitigated deep-circuit quantum simulation: steady state and relaxation rate problems [4.762232147934851]
  We show that digital quantum simulation of closed quantum systems are robust against the accumulation of Trotter errors. We propose a new error-mitigation technique based on the scaling behavior in the vicinity of the critical point of a quantum phase transition.
  arXiv  Detail & Related papers  (2021-11-18T11:01:45Z)
• Characterizing quantum instruments: from non-demolition measurements to quantum error correction [48.43720700248091]
  In quantum information processing quantum operations are often processed alongside measurements which result in classical data. Non-unitary dynamical processes can take place on the system, for which common quantum channel descriptions fail to describe the time evolution. Quantum measurements are correctly treated by means of so-called quantum instruments capturing both classical outputs and post-measurement quantum states.
  arXiv  Detail & Related papers  (2021-10-13T18:00:13Z)
• Quantum Computation Using Action Variables [4.087043981909747]
  We argue quantum computation using action variables as fault-tolerant quantum computation, whose fault-tolerance is guaranteed by the quantum KAM theorem. Besides, we view the Birkhoff norm form as a mathematical framework of the extended harmonic oscillator quantum computation.
  arXiv  Detail & Related papers  (2021-09-24T12:04:27Z)
• Quantum computing critical exponents [0.0]
  We show that the Variational Quantum-Classical Simulation algorithm admits a finite circuit depth scaling collapse when targeting the critical point of the transverse field Ising chain. The order parameter only collapses on one side of the transition due to a slowdown of the quantum algorithm when crossing the phase transition.
  arXiv  Detail & Related papers  (2021-04-02T17:38:20Z)
• Continuous-time dynamics and error scaling of noisy highly-entangling quantum circuits [58.720142291102135]
  We simulate a noisy quantum Fourier transform processor with up to 21 qubits. We take into account microscopic dissipative processes rather than relying on digital error models. We show that depending on the dissipative mechanisms at play, the choice of input state has a strong impact on the performance of the quantum algorithm.
  arXiv  Detail & Related papers  (2021-02-08T14:55:44Z)
• Quantum information spreading in a disordered quantum walk [50.591267188664666]
  We design a quantum probing protocol using Quantum Walks to investigate the Quantum Information spreading pattern. We focus on the coherent static and dynamic disorder to investigate anomalous and classical transport. Our results show that a Quantum Walk can be considered as a readout device of information about defects and perturbations occurring in complex networks.
  arXiv  Detail & Related papers  (2020-10-20T20:03:19Z)
• Variational Quantum Algorithms for Steady States of Open Quantum Systems [2.740982822457262]
  We propose a variational quantum algorithm to find the steady state of open quantum systems. The fidelity between the optimal mixed state and the true steady state is over 99%. This algorithm is derived from the natural idea of expressing mixed states with purification.
  arXiv  Detail & Related papers  (2020-01-08T14:47:36Z)

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.