Classical simulation of non-Gaussian fermionic circuits
- URL: http://arxiv.org/abs/2307.12912v3
- Date: Mon, 6 May 2024 13:47:49 GMT
- Title: Classical simulation of non-Gaussian fermionic circuits
- Authors: Beatriz Dias, Robert Koenig,
- Abstract summary: We argue that this problem is analogous to that of simulating Clifford circuits with non-stabilizer initial states.
Our construction is based on an extension of the covariance matrix formalism which permits to efficiently track relative phases in superpositions of Gaussian states.
It yields simulation algorithms with complexity in the number of fermions, the desired accuracy, and certain quantities capturing the degree of non-Gaussianity of the initial state.
- Score: 0.4972323953932129
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We propose efficient algorithms for classically simulating fermionic linear optics operations applied to non-Gaussian initial states. By gadget constructions, this provides algorithms for fermionic linear optics with non-Gaussian operations. We argue that this problem is analogous to that of simulating Clifford circuits with non-stabilizer initial states: Algorithms for the latter problem immediately translate to the fermionic setting. Our construction is based on an extension of the covariance matrix formalism which permits to efficiently track relative phases in superpositions of Gaussian states. It yields simulation algorithms with polynomial complexity in the number of fermions, the desired accuracy, and certain quantities capturing the degree of non-Gaussianity of the initial state. We study one such quantity, the fermionic Gaussian extent, and show that it is multiplicative on tensor products when the so-called fermionic Gaussian fidelity is. We establish this property for the tensor product of two arbitrary pure states of four fermions with positive parity.
Related papers
- The quantum magic of fermionic Gaussian states [0.0]
We introduce an efficient method to quantify nonstabilizerness in fermionic Gaussian states.
We reveal an extensive leading behavior equal to that of Haar random states, with logarithmic subleading corrections.
Applying the sampling algorithm to a two-dimensional free-fermionic topological model, we uncover a sharp transition in magic at the phase boundaries.
arXiv Detail & Related papers (2024-12-06T19:00:16Z) - Displaced Fermionic Gaussian States and their Classical Simulation [0.0]
This work explores displaced fermionic Gaussian operators with nonzero linear terms.
We first demonstrate equivalence between several characterizations of displaced Gaussian states.
We also provide an efficient classical simulation protocol for displaced Gaussian circuits.
arXiv Detail & Related papers (2024-11-27T17:05:04Z) - Classical simulation and quantum resource theory of non-Gaussian optics [1.3124513975412255]
We propose efficient algorithms for simulating Gaussian unitaries and measurements applied to non-Gaussian initial states.
From the perspective of quantum resource theories, we investigate the properties of this type of non-Gaussianity measure and compute optimal decomposition for states relevant to continuous-variable quantum computing.
arXiv Detail & Related papers (2024-04-10T15:53:41Z) - Classical simulation of non-Gaussian bosonic circuits [0.4972323953932129]
We propose efficient classical algorithms to simulate bosonic linear optics circuits applied to superpositions of Gaussian states.
We present an exact simulation algorithm whose runtime is in the number of modes and the size of the circuit.
We also present a faster approximate randomized algorithm whose runtime is quadratic in this number.
arXiv Detail & Related papers (2024-03-27T23:52:35Z) - Fermionic approach to variational quantum simulation of Kitaev spin
models [50.92854230325576]
Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions.
We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation.
We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
arXiv Detail & Related papers (2022-04-11T18:00:01Z) - Deterministic Gaussian conversion protocols for non-Gaussian single-mode
resources [58.720142291102135]
We show that cat and binomial states are approximately equivalent for finite energy, while this equivalence was previously known only in the infinite-energy limit.
We also consider the generation of cat states from photon-added and photon-subtracted squeezed states, improving over known schemes by introducing additional squeezing operations.
arXiv Detail & Related papers (2022-04-07T11:49:54Z) - Efficient simulation of Gottesman-Kitaev-Preskill states with Gaussian
circuits [68.8204255655161]
We study the classical simulatability of Gottesman-Kitaev-Preskill (GKP) states in combination with arbitrary displacements, a large set of symplectic operations and homodyne measurements.
For these types of circuits, neither continuous-variable theorems based on the non-negativity of quasi-probability distributions nor discrete-variable theorems can be employed to assess the simulatability.
arXiv Detail & Related papers (2022-03-21T17:57:02Z) - Pathwise Conditioning of Gaussian Processes [72.61885354624604]
Conventional approaches for simulating Gaussian process posteriors view samples as draws from marginal distributions of process values at finite sets of input locations.
This distribution-centric characterization leads to generative strategies that scale cubically in the size of the desired random vector.
We show how this pathwise interpretation of conditioning gives rise to a general family of approximations that lend themselves to efficiently sampling Gaussian process posteriors.
arXiv Detail & Related papers (2020-11-08T17:09:37Z) - Local optimization on pure Gaussian state manifolds [63.76263875368856]
We exploit insights into the geometry of bosonic and fermionic Gaussian states to develop an efficient local optimization algorithm.
The method is based on notions of descent gradient attuned to the local geometry.
We use the presented methods to collect numerical and analytical evidence for the conjecture that Gaussian purifications are sufficient to compute the entanglement of purification of arbitrary mixed Gaussian states.
arXiv Detail & Related papers (2020-09-24T18:00:36Z) - Efficient construction of tensor-network representations of many-body
Gaussian states [59.94347858883343]
We present a procedure to construct tensor-network representations of many-body Gaussian states efficiently and with a controllable error.
These states include the ground and thermal states of bosonic and fermionic quadratic Hamiltonians, which are essential in the study of quantum many-body systems.
arXiv Detail & Related papers (2020-08-12T11:30:23Z)
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.