Single Qubit Error Mitigation by Simulating Non-Markovian Dynamics
- URL: http://arxiv.org/abs/2303.03268v1
- Date: Mon, 6 Mar 2023 16:35:44 GMT
- Title: Single Qubit Error Mitigation by Simulating Non-Markovian Dynamics
- Authors: Mirko Rossini, Dominik Maile, Joachim Ankerhold and Brecht I. C Donvil
- Abstract summary: We present a simulation scheme for open qubit dynamics described by a larger class of maps.
We illustrate our scheme on an IBM quantum processor by showing that we can recover the initial state of a Lindblad evolution.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum simulation is a powerful tool to study the properties of quantum
systems. The dynamics of open quantum systems are often described by Completely
Positive (CP) maps, for which several quantum simulation schemes exist. We
present a simulation scheme for open qubit dynamics described by a larger class
of maps: the general dynamical maps which are linear, hermitian preserving and
trace preserving but not necessarily positivity preserving. The latter suggests
an underlying system-reservoir model where both are entangled and thus
non-Markovian qubit dynamics. Such maps also come about as the inverse of CP
maps. We illustrate our simulation scheme on an IBM quantum processor by
showing that we can recover the initial state of a Lindblad evolution. This
paves the way for a novel form of quantum error mitigation. Our scheme only
requires one ancilla qubit as an overhead and a small number of one and two
qubit gates.
Related papers
- Variational simulation of $d$-level systems on qubit-based quantum simulators [0.0]
Many systems in nature are inherently $d$-level, including higher spins, bosons, vibrational modes, and electrons.
To simulate $d$-level systems on qubit-based quantum simulators, an encoding method is required to map the $d$-level system onto a qubit basis.
We develop a systematic method to address the illegitimate states in the Hilbert space.
arXiv Detail & Related papers (2024-05-08T13:41:15Z) - Parallelizing quantum simulation with decision diagrams [2.5999037208435705]
Classical computers face a critical obstacle in simulating quantum algorithms.
Quantum states reside in a Hilbert space whose size grows exponentially to the number of subsystems, i.e., qubits.
This work explores several strategies for parallelizing decision diagram operations, specifically for quantum simulations.
arXiv Detail & Related papers (2023-12-04T02:00:24Z) - Large-scale simulations of Floquet physics on near-term quantum computers [0.3252295747842729]
We introduce the Quantum High-Frequency Floquet Simulation (QHiFFS) algorithm as a method to simulate fast-driven quantum systems on quantum hardware.
Central to QHiFFS is the concept of a kick operator which transforms the system into a basis where the dynamics is governed by a time-independent effective Hamiltonian.
arXiv Detail & Related papers (2023-03-03T20:45:01Z) - Quantum emulation of the transient dynamics in the multistate
Landau-Zener model [50.591267188664666]
We study the transient dynamics in the multistate Landau-Zener model as a function of the Landau-Zener velocity.
Our experiments pave the way for more complex simulations with qubits coupled to an engineered bosonic mode spectrum.
arXiv Detail & Related papers (2022-11-26T15:04:11Z) - Recompilation-enhanced simulation of electron-phonon dynamics on IBM
Quantum computers [62.997667081978825]
We consider the absolute resource cost for gate-based quantum simulation of small electron-phonon systems.
We perform experiments on IBM quantum hardware for both weak and strong electron-phonon coupling.
Despite significant device noise, through the use of approximate circuit recompilation we obtain electron-phonon dynamics on current quantum computers comparable to exact diagonalisation.
arXiv Detail & Related papers (2022-02-16T19:00:00Z) - Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware.
We present an algorithm that compresses the Trotter steps into a single block of quantum gates.
This results in a fixed depth time evolution for certain classes of Hamiltonians.
arXiv Detail & Related papers (2021-08-06T19:38:01Z) - Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
We present a constructive algorithm for generating quantum circuits with time-independent depth.
We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model.
In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
arXiv Detail & Related papers (2021-04-01T19:06:00Z) - Simulating nonnative cubic interactions on noisy quantum machines [65.38483184536494]
We show that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware.
On noisy devices without error correction, we show that simulation results are significantly improved when the quantum program is compiled using modular gates.
arXiv Detail & Related papers (2020-04-15T05:16:24Z) - Roadmap for quantum simulation of the fractional quantum Hall effect [0.0]
A major motivation for building a quantum computer is that it provides a tool to efficiently simulate strongly correlated quantum systems.
In this work, we present a detailed roadmap on how to simulate a two-dimensional electron gas---cooled to absolute zero and pierced by a strong magnetic field---on a quantum computer.
arXiv Detail & Related papers (2020-03-05T10:17:21Z) - 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.