Quantum simulation of Fermi-Hubbard model based on transmon qudit
interaction
- URL: http://arxiv.org/abs/2402.01243v1
- Date: Fri, 2 Feb 2024 09:10:40 GMT
- Title: Quantum simulation of Fermi-Hubbard model based on transmon qudit
interaction
- Authors: Arian Vezvaee, Nathan Earnest-Noble, Khadijeh Najafi
- Abstract summary: We introduce a novel quantum simulation approach utilizing qudits to overcome such complexities.
We first demonstrate a Qudit Fermionic Mapping (QFM) that reduces the encoding cost associated with the qubit-based approach.
We then describe the unitary evolution of the mapped Hamiltonian by interpreting the resulting Majorana operators in terms of physical single- and two-qudit gates.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The Fermi-Hubbard model, a fundamental framework for studying strongly
correlated phenomena could significantly benefit from quantum simulations when
exploring non-trivial settings. However, simulating this problem requires twice
as many qubits as the physical sites, in addition to complicated on-chip
connectivities and swap gates required to simulate the physical interactions.
In this work, we introduce a novel quantum simulation approach utilizing qudits
to overcome such complexities. Leveraging on the symmetries of the
Fermi-Hubbard model and their intrinsic relation to Clifford algebras, we first
demonstrate a Qudit Fermionic Mapping (QFM) that reduces the encoding cost
associated with the qubit-based approach. We then describe the unitary
evolution of the mapped Hamiltonian by interpreting the resulting Majorana
operators in terms of physical single- and two-qudit gates. While the QFM can
be used for any quantum hardware with four accessible energy levels, we
demonstrate the specific reduction in overhead resulting from utilizing the
native Controlled-SUM gate (equivalent to qubit CNOT) for a fixed-frequency
ququart transmon. We further transpile the resulting two transmon-qudit gates
by demonstrating a qudit operator Schmidt decomposition using the
Controlled-SUM gate. Finally, we demonstrate the efficacy of our proposal by
numerical simulation of local observables such as the filling factor and
Green's function for various Trotter steps. The compatibility of our approach
with different qudit platforms paves the path for achieving quantum advantage
in simulating non-trivial quantum many-body systems.
Related papers
- Simulating quantum field theories on gate-based quantum computers [0.0]
We implement a simulation of a quantum field theory in 1+1 space-time dimensions on a gate-based quantum computer.
We show that experimentally relevant quantities like cross-sections for various processes, survival probabilities of various states, etc. can be computed.
arXiv Detail & Related papers (2024-01-09T11:17:08Z) - Quantum Computation and Simulation using Fermion-Pair Registers [0.0]
We propose and analyze an approach to realize quantum computation and simulation using fermionic particles under quantum gas microscopes.
We describe how to engineer the SWAP gate and high-fidelity controlled-phase gates.
We show that 2D quantum Ising Hamiltonians with transverse and longitudinal fields can be efficient simulated by modulating Feshbach interaction strengths.
arXiv Detail & Related papers (2023-06-06T17:59:08Z) - 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) - 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) - Gutzwiller wave function on a quantum computer using a discrete
Hubbard-Stratonovich transformation [0.7734726150561086]
We propose a quantum-classical hybrid scheme for implementing the nonunitary Gutzwiller factor.
The proposed scheme is demonstrated with numerical simulations for the half-filled Fermi-Hubbard model.
arXiv Detail & Related papers (2022-01-27T08:57:04Z) - Simulating the Mott transition on a noisy digital quantum computer via
Cartan-based fast-forwarding circuits [62.73367618671969]
Dynamical mean-field theory (DMFT) maps the local Green's function of the Hubbard model to that of the Anderson impurity model.
Quantum and hybrid quantum-classical algorithms have been proposed to efficiently solve impurity models.
This work presents the first computation of the Mott phase transition using noisy digital quantum hardware.
arXiv Detail & Related papers (2021-12-10T17:32:15Z) - Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems.
By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
arXiv Detail & Related papers (2021-08-03T17:49:09Z) - Towards simulating 2D effects in lattice gauge theories on a quantum
computer [1.327151508840301]
We propose an experimental quantum simulation scheme to study ground state properties in two-dimensional quantum electrodynamics (2D QED) using existing quantum technology.
The proposal builds on a formulation of lattice gauge theories as effective spin models in arXiv:2006.14160.
We present two Variational Quantum Eigensolver (VQE) based protocols for the study of magnetic field effects, and for taking an important first step towards computing the running coupling of QED.
arXiv Detail & Related papers (2020-08-21T01:20:55Z) - 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) - Hartree-Fock on a superconducting qubit quantum computer [30.152226344347064]
Here, we perform a series of quantum simulations of chemistry the largest of which involved a dozen qubits, 78 two-qubit gates, and 114 one-qubit gates.
We model the binding energy of $rm H_6$, $rm H_8$, $rm H_10$ and $rm H_12$ chains as well as the isomerization of diazene.
We also demonstrate error-mitigation strategies based on $N$-representability which dramatically improve the effective fidelity of our experiments.
arXiv Detail & Related papers (2020-04-08T18:00:06Z) - Quantum Statistical Complexity Measure as a Signalling of Correlation
Transitions [55.41644538483948]
We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions.
We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain.
We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
arXiv Detail & Related papers (2020-02-05T00:45:21Z)
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.