Unified framework for efficiently computable quantum circuits

• URL: http://arxiv.org/abs/2401.08187v2
• Date: Tue, 21 May 2024 20:16:21 GMT
• Title: Unified framework for efficiently computable quantum circuits
• Authors: Igor Ermakov, Oleg Lychkovskiy, Tim Byrnes,
• Abstract summary: Quantum circuits consisting of Clifford and matchgates are two classes of circuits that are known to be efficiently simulatable on a classical computer. We introduce a unified framework that shows in a transparent way the special structure that allows these circuits can be efficiently simulatable.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum circuits consisting of Clifford and matchgates are two classes of circuits that are known to be efficiently simulatable on a classical computer. We introduce a unified framework that shows in a transparent way the special structure that allows these circuits can be efficiently simulatable. The approach relies on analyzing the operator spread within a network of basis operators during the evolution of quantum circuit. Quantifying the complexity of a calculation by the number of operators with amplitude above a threshold value, we show that there is a generic form of the complexity curve involving an initial exponential growth, saturation, then exponential decay in the presence of decoherence. Our approach is naturally adaptable into a numerical procedure, where errors can be consistently controlled as a function of the complexity of the simulation.

Related papers

• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Simulating Quantum Circuits by Model Counting [0.0]
  We show for the first time that a strong simulation of universal quantum circuits can be efficiently tackled through weighted model counting. Our work paves the way to apply the existing array of powerful classical reasoning tools to realize efficient quantum circuit compilation.
  arXiv  Detail & Related papers  (2024-03-11T22:40:15Z)
• Tensor Networks or Decision Diagrams? Guidelines for Classical Quantum Circuit Simulation [65.93830818469833]
  tensor networks and decision diagrams have independently been developed with differing perspectives, terminologies, and backgrounds in mind. We consider how these techniques approach classical quantum circuit simulation, and examine their (dis)similarities with regard to their most applicable abstraction level. We provide guidelines for when to better use tensor networks and when to better use decision diagrams in classical quantum circuit simulation.
  arXiv  Detail & Related papers  (2023-02-13T19:00:00Z)
• Efficient estimation of trainability for variational quantum circuits [43.028111013960206]
  We find an efficient method to compute the cost function and its variance for a wide class of variational quantum circuits. This method can be used to certify trainability for variational quantum circuits and explore design strategies that can overcome the barren plateau problem.
  arXiv  Detail & Related papers  (2023-02-09T14:05:18Z)
• Exploring the role of parameters in variational quantum algorithms [59.20947681019466]
  We introduce a quantum-control-inspired method for the characterization of variational quantum circuits using the rank of the dynamical Lie algebra. A promising connection is found between the Lie rank, the accuracy of calculated energies, and the requisite depth to attain target states via a given circuit architecture.
  arXiv  Detail & Related papers  (2022-09-28T20:24:53Z)
• A single $T$-gate makes distribution learning hard [56.045224655472865]
  This work provides an extensive characterization of the learnability of the output distributions of local quantum circuits. We show that for a wide variety of the most practically relevant learning algorithms -- including hybrid-quantum classical algorithms -- even the generative modelling problem associated with depth $d=omega(log(n))$ Clifford circuits is hard.
  arXiv  Detail & Related papers  (2022-07-07T08:04:15Z)
• Quasi-Chaotic Oscillators Based on Modular Quantum Circuits [3.383942690870476]
  We propose the implementation of a quasi-chaotic oscillator based on quantum modular addition and multiplication. We prove that quantum computing allows the parallel processing of data, paving the way for a fast and robust multi-channel encryption/decryption scheme.
  arXiv  Detail & Related papers  (2022-03-26T09:14:29Z)
• Numerical Simulations of Noisy Quantum Circuits for Computational Chemistry [51.827942608832025]
  Near-term quantum computers can calculate the ground-state properties of small molecules. We show how the structure of the computational ansatz as well as the errors induced by device noise affect the calculation.
  arXiv  Detail & Related papers  (2021-12-31T16:33:10Z)
• Quantum Circuits in Additive Hilbert Space [0.0]
  We show how conventional circuits can be expressed in the additive space and how they can be recovered. In particular in our formalism we are able to synthesize high-level multi-controlled primitives from low-level circuit decompositions. Our formulation also accepts a circuit-like diagrammatic representation and proposes a novel and simple interpretation of quantum computation.
  arXiv  Detail & Related papers  (2021-11-01T19:05:41Z)
• Optimized Low-Depth Quantum Circuits for Molecular Electronic Structure using a Separable Pair Approximation [0.0]
  We present a classically solvable model that leads to optimized low-depth quantum circuits leveraging separable pair approximations. The obtained circuits are well suited as a baseline circuit for emerging quantum hardware and can, in the long term, provide significantly improved initial states for quantum algorithms.
  arXiv  Detail & Related papers  (2021-05-09T05:10:59Z)
• Efficient classical simulation of random shallow 2D quantum circuits [104.50546079040298]
  Random quantum circuits are commonly viewed as hard to simulate classically. We show that approximate simulation of typical instances is almost as hard as exact simulation. We also conjecture that sufficiently shallow random circuits are efficiently simulable more generally.
  arXiv  Detail & Related papers  (2019-12-31T19:00:00Z)

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.