Efficient Classical Simulation of Clifford Circuits from Framed Wigner
Functions
- URL: http://arxiv.org/abs/2307.16688v1
- Date: Mon, 31 Jul 2023 14:02:33 GMT
- Title: Efficient Classical Simulation of Clifford Circuits from Framed Wigner
Functions
- Authors: Guedong Park, Hyukjoon Kwon, and Hyunseok Jeong
- Abstract summary: Wigner function formalism serves as crucial tool for simulating continuous-variable and odd-prime dimensional quantum circuits.
We introduce a novel classical simulation method for non-adaptive Clifford circuits based on the framed Wigner function.
- Score: 4.282159812965446
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The Wigner function formalism serves as a crucial tool for simulating
continuous-variable and odd-prime dimensional quantum circuits, as well as
assessing their classical hardness. However, applying such a formalism to qubit
systems is limited due to the negativity in the Wigner function induced by
Clifford operations. In this work, we introduce a novel classical simulation
method for non-adaptive Clifford circuits based on the framed Wigner function,
an extended form of the qubit Wigner function characterized by a binary-valued
frame function. Our approach allows for updating phase space points under
Clifford circuits without inducing negativity in the Wigner function by
switching to a suitable frame when applying each Clifford gate. By leveraging
this technique, we establish a sufficient condition for efficient classical
simulation of Clifford circuits even with non-stabilizer inputs, where direct
application of the Gottesmann-Knill tableau method is not feasible. We further
develop a graph-theoretical approach to identify classically simulatable
marginal outcomes of Clifford circuits and explore the number of simulatable
qubits of log-depth circuits. We also present the Born probability estimation
scheme using the framed Wigner function and discuss its precision. Our approach
opens new avenues for quasi-probability simulation of quantum circuits, thereby
expanding the boundary of classically simulatable circuits.
Related papers
- Disentangling unitary dynamics with classically simulable quantum circuits [0.0]
We study both quantum circuit and Hamiltonian dynamics.
We find that expectations of Pauli operators can be simulated efficiently even for deep Clifford circuits.
For the Hamiltonian dynamics we find that the classical simulation generically quickly becomes inefficient.
arXiv Detail & Related papers (2024-10-11T17:18:26Z) - Efficient classical simulation of quantum computation beyond Wigner positivity [0.0]
We present the generalization of the CNC formalism, based on closed and noncontextual sets of Pauli observables, to the setting of odd-prime-dimensional qudits.
arXiv Detail & Related papers (2024-07-14T22:25:13Z) - Simulating quantum circuit expectation values by Clifford perturbation
theory [0.0]
We consider the expectation value problem for circuits composed of Clifford gates and non-Clifford Pauli rotations.
We introduce a perturbative approach based on the truncation of the exponentially growing sum of Pauli terms in the Heisenberg picture.
Results indicate that this systematically improvable perturbative method offers a viable alternative to exact methods for approxing expectation values of large near-Clifford circuits.
arXiv Detail & Related papers (2023-06-07T21:42:10Z) - Partitioning Quantum Chemistry Simulations with Clifford Circuits [1.0286890995028481]
Current quantum computing hardware is restricted by the availability of only few, noisy qubits.
We investigate the limits of their classical and near-classical treatment while staying within the framework of quantum circuits.
arXiv Detail & Related papers (2023-03-02T13:05:19Z) - Third quantization of open quantum systems: new dissipative symmetries
and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
We reformulate the technique of third quantization in a way that explicitly connects all three methods.
We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians.
For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
arXiv Detail & Related papers (2023-02-27T18:56:40Z) - 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) - 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) - Learnability of the output distributions of local quantum circuits [53.17490581210575]
We investigate, within two different oracle models, the learnability of quantum circuit Born machines.
We first show a negative result, that the output distributions of super-logarithmic depth Clifford circuits are not sample-efficiently learnable.
We show that in a more powerful oracle model, namely when directly given access to samples, the output distributions of local Clifford circuits are computationally efficiently PAC learnable.
arXiv Detail & Related papers (2021-10-11T18:00:20Z) - Error mitigation and quantum-assisted simulation in the error corrected
regime [77.34726150561087]
A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations.
We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
arXiv Detail & Related papers (2021-03-12T20:58:41Z) - Quadratic Clifford expansion for efficient benchmarking and
initialization of variational quantum algorithms [0.8808007156832224]
Variational quantum algorithms are considered to be appealing applications of near-term quantum computers.
We propose a perturbative approach for efficient benchmarking of variational quantum algorithms.
arXiv Detail & Related papers (2020-11-19T16:09:00Z) - Efficient simulatability of continuous-variable circuits with large
Wigner negativity [62.997667081978825]
Wigner negativity is known to be a necessary resource for computational advantage in several quantum-computing architectures.
We identify vast families of circuits that display large, possibly unbounded, Wigner negativity, and yet are classically efficiently simulatable.
We derive our results by establishing a link between the simulatability of high-dimensional discrete-variable quantum circuits and bosonic codes.
arXiv Detail & Related papers (2020-05-25T11:03:42Z)
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.