Phases and phase transition in Grover's algorithm with systematic noise

• URL: http://arxiv.org/abs/2406.10344v1
• Date: Fri, 14 Jun 2024 18:00:06 GMT
• Title: Phases and phase transition in Grover's algorithm with systematic noise
• Authors: Sasanka Dowarah, Chuanwei Zhang, Vedika Khemani, Michael H. Kolodrubetz,
• Abstract summary: We consider a canonical quantum algorithm - Grover's algorithm for unordered search on $L$ qubits - in the presence of systematic noise. The RMT analysis enables analytical predictions for phases and phase transitions of the many-body dynamics. We comment on relevance to non-systematic noise in realistic quantum computers, including cold atom, trapped ion, and superconducting platforms.
• Score: 0.027042267806481293
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: While limitations on quantum computation by Markovian environmental noise are well-understood in generality, their behavior for different quantum circuits and noise realizations can be less universal. Here we consider a canonical quantum algorithm - Grover's algorithm for unordered search on $L$ qubits - in the presence of systematic noise. This allows us to write the behavior as a random Floquet unitary, which we show is well-characterized by random matrix theory (RMT). The RMT analysis enables analytical predictions for phases and phase transitions of the many-body dynamics. We find two separate transitions. At moderate disorder $\delta_{c,\mathrm{gap}}\sim L^{-1}$, there is a ergodicity breaking transition such that a finite-dimensional manifold remains non-ergodic for $\delta < \delta_{c,\mathrm{gap}}$. Computational power is lost at a much smaller disorder, $\delta_{c,\mathrm{comp}} \sim L^{-1/2}2^{-L/2}$. We comment on relevance to non-systematic noise in realistic quantum computers, including cold atom, trapped ion, and superconducting platforms.

Related papers

• On encoded quantum gate generation by iterative Lyapunov-based methods [0.0]
  The problem of encoded quantum gate generation is studied in this paper. The emphReference Input Generation Algorithm (RIGA) is generalized in this work.
  arXiv  Detail & Related papers  (2024-09-02T10:41:15Z)
• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• Efficient Quantum Simulation Algorithms in the Path Integral Formulation [0.5729426778193399]
  We provide two novel quantum algorithms based on Hamiltonian versions of the path integral formulation and another for Lagrangians of the form $fracm2dotx2 - V(x)$. We show that our Lagrangian simulation algorithm requires a number of queries to an oracle that computes the discrete Lagrangian that scales for a system with $eta$ particles in $D+1$ dimensions, in the continuum limit, as $widetildeO(eta D t2/epsilon)$ if $V(x)$ is bounded
  arXiv  Detail & Related papers  (2024-05-11T15:48:04Z)
• Error-mitigated fermionic classical shadows on noisy quantum devices [0.3775283002059579]
  Classical shadow (CS) algorithms offer a solution by reducing the number of quantum state copies needed. We propose an error-mitigated CS algorithm assuming gate-independent, time-stationary, and Markovian (GTM) noise. Our algorithm efficiently estimates $k$-RDMs with $widetildemathcal O(knk)$ state copies and $widetildemathcal O(sqrtn)$ calibration measurements for GTM noise.
  arXiv  Detail & Related papers  (2023-10-19T13:27:19Z)
• Emergence of noise-induced barren plateaus in arbitrary layered noise models [44.99833362998488]
  In variational quantum algorithms the parameters of a parameterized quantum circuit are optimized in order to minimize a cost function that encodes the solution of the problem. We discuss how, and in which sense, the phenomenon of noise-induced barren plateaus emerges in parameterized quantum circuits with a layered noise model.
  arXiv  Detail & Related papers  (2023-10-12T15:18:27Z)
• Simulating Noisy Variational Quantum Algorithms: A Polynomial Approach [1.806183113759115]
  Large-scale variational quantum algorithms are widely recognized as a potential pathway to achieve quantum advantages. We present a novel $gammaPPP method based on the integral path of observables back-propagation on paths. We conduct classical simulations of IBM's zeronoised experimental results on the 127-qubit Eagle processor.
  arXiv  Detail & Related papers  (2023-06-09T10:42:07Z)
• Unimon qubit [42.83899285555746]
  Superconducting qubits are one of the most promising candidates to implement quantum computers. Here, we introduce and demonstrate a superconducting-qubit type, the unimon, which combines the desired properties of high non-linearity, full insensitivity to dc charge noise, insensitivity to flux noise, and a simple structure consisting only of a single Josephson junction in a resonator.
  arXiv  Detail & Related papers  (2022-03-11T12:57:43Z)
• A lower bound on the space overhead of fault-tolerant quantum computation [51.723084600243716]
  The threshold theorem is a fundamental result in the theory of fault-tolerant quantum computation. We prove an exponential upper bound on the maximal length of fault-tolerant quantum computation with amplitude noise.
  arXiv  Detail & Related papers  (2022-01-31T22:19:49Z)
• Random quantum circuits transform local noise into global white noise [118.18170052022323]
  We study the distribution over measurement outcomes of noisy random quantum circuits in the low-fidelity regime. For local noise that is sufficiently weak and unital, correlations (measured by the linear cross-entropy benchmark) between the output distribution $p_textnoisy$ of a generic noisy circuit instance shrink exponentially. If the noise is incoherent, the output distribution approaches the uniform distribution $p_textunif$ at precisely the same rate.
  arXiv  Detail & Related papers  (2021-11-29T19:26:28Z)
• Interactive quantum advantage with noisy, shallow Clifford circuits [0.0]
  We show a strategy for adding noise tolerance to the interactive protocols of Grier and Schaeffer. A key component of this reduction is showing average-case hardness for the classical simulation tasks. We show that is true even for quantum tasks which are $oplus$L-hard to simulate.
  arXiv  Detail & Related papers  (2021-02-13T00:54:45Z)
• Quantum Algorithms for Simulating the Lattice Schwinger Model [63.18141027763459]
  We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x-1/2$ and electric field cutoff $x-1/2Lambda$. We estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density.
  arXiv  Detail & Related papers  (2020-02-25T19:18:36Z)

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.