Quantum Magic via Perfect Pauli Sampling of Matrix Product States
- URL: http://arxiv.org/abs/2303.05536v2
- Date: Wed, 19 Apr 2023 10:43:28 GMT
- Title: Quantum Magic via Perfect Pauli Sampling of Matrix Product States
- Authors: Guglielmo Lami, Mario Collura
- Abstract summary: We consider the recently introduced Stabilizer R'enyi Entropies (SREs)
We show that the exponentially hard evaluation of the SREs can be achieved by means of a simple perfect sampling of the many-body wave function over the Pauli string configurations.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We introduce a novel breakthrough approach to evaluate the nonstabilizerness
of an $N$-qubits Matrix Product State (MPS) with bond dimension $\chi$. In
particular, we consider the recently introduced Stabilizer R\'enyi Entropies
(SREs). We show that the exponentially hard evaluation of the SREs can be
achieved by means of a simple perfect sampling of the many-body wave function
over the Pauli string configurations. The sampling is achieved with a novel MPS
technique, which enables to compute each sample in an efficient way with a
computational cost $O(N\chi^3)$. We benchmark our method over randomly
generated magic states, as well as in the ground-state of the quantum Ising
chain. Exploiting the extremely favourable scaling, we easily have access to
the non-equilibrium dynamics of the SREs after a quantum quench.
Related papers
- Nonstabilizerness via matrix product states in the Pauli basis [0.0]
We present a novel approach for the evaluation of nonstabilizerness within the framework of matrix product states (MPS)
Our framework provides a powerful tool for efficiently calculating various measures of nonstabilizerness, including stabilizer R'enyi entropies, stabilizer nullity, and Bell magic.
We showcase the efficacy and versatility of our method in the ground states of Ising and XXZ spin chains, as well as in circuits dynamics that has recently been realized in Rydberg atom arrays.
arXiv Detail & Related papers (2024-01-29T19:12:10Z) - Learning the stabilizer group of a Matrix Product State [0.0]
We present a novel classical algorithm designed to learn the stabilizer group of a given Matrix Product State (MPS)
We benchmark our method on $T$-doped states randomly scrambled via Clifford unitary dynamics.
Our method, thanks to a very favourable scaling $mathcalO(chi3)$, represents the first effective approach to obtain a genuine magic monotone for MPS.
arXiv Detail & Related papers (2024-01-29T19:00:13Z) - Finite-Temperature Simulations of Quantum Lattice Models with Stochastic
Matrix Product States [7.376159230492167]
We develop a matrix product state (stoMPS) approach that combines the MPS technique and Monte Carlo samplings.
We benchmark the methods on small system sizes and compare the results to those obtained with minimally entangled typical thermal states.
Our results showcase the accuracy and effectiveness of networks in finite-temperature simulations.
arXiv Detail & Related papers (2023-12-07T16:44:08Z) - Quantum Signal Processing, Phase Extraction, and Proportional Sampling [0.0]
Quantum Signal Processing (QSP) is a technique that can be used to implement a transformation $P(x)$ applied to the eigenvalues of a unitary $U$.
We show that QSP can be used to tackle a new problem, which we call phase extraction, and that this can be used to provide quantum speed-up for proportional sampling.
arXiv Detail & Related papers (2023-03-20T13:05:29Z) - Importance sampling for stochastic quantum simulations [68.8204255655161]
We introduce the qDrift protocol, which builds random product formulas by sampling from the Hamiltonian according to the coefficients.
We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage.
Results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.
arXiv Detail & Related papers (2022-12-12T15:06:32Z) - Quantifying nonstabilizerness of matrix product states [0.0]
We show that nonstabilizerness, as quantified by the recently introduced Stabilizer R'enyi Entropies (SREs), can be computed efficiently for matrix product states (MPSs)
We exploit this observation to revisit the study of ground-state nonstabilizerness in the quantum Ising chain, providing accurate numerical results up to large system sizes.
arXiv Detail & Related papers (2022-07-26T17:50:32Z) - Improved Graph Formalism for Quantum Circuit Simulation [77.34726150561087]
We show how to efficiently simplify stabilizer states to canonical form.
We characterize all linearly dependent triplets, revealing symmetries in the inner products.
Using our novel controlled-Pauli $Z$ algorithm, we improve runtime for inner product computation from $O(n3)$ to $O(nd2)$ where $d$ is the maximum degree of the graph.
arXiv Detail & Related papers (2021-09-20T05:56:25Z) - Non-Markovian Stochastic Schr\"odinger Equation: Matrix Product State
Approach to the Hierarchy of Pure States [65.25197248984445]
We derive a hierarchy of matrix product states (HOMPS) for non-Markovian dynamics in open finite temperature.
The validity and efficiency of HOMPS is demonstrated for the spin-boson model and long chains where each site is coupled to a structured, strongly non-Markovian environment.
arXiv Detail & Related papers (2021-09-14T01:47:30Z) - Sampling Overhead Analysis of Quantum Error Mitigation: Uncoded vs.
Coded Systems [69.33243249411113]
We show that Pauli errors incur the lowest sampling overhead among a large class of realistic quantum channels.
We conceive a scheme amalgamating QEM with quantum channel coding, and analyse its sampling overhead reduction compared to pure QEM.
arXiv Detail & Related papers (2020-12-15T15:51:27Z) - Coherent randomized benchmarking [68.8204255655161]
We show that superpositions of different random sequences rather than independent samples are used.
We show that this leads to a uniform and simple protocol with significant advantages with respect to gates that can be benchmarked.
arXiv Detail & Related papers (2020-10-26T18:00:34Z) - Preparation of excited states for nuclear dynamics on a quantum computer [117.44028458220427]
We study two different methods to prepare excited states on a quantum computer.
We benchmark these techniques on emulated and real quantum devices.
These findings show that quantum techniques designed to achieve good scaling on fault tolerant devices might also provide practical benefits on devices with limited connectivity and gate fidelity.
arXiv Detail & Related papers (2020-09-28T17:21:25Z)
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.