Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quantum simulation using arrays of gate-defined quantum dots

U. Mukhopadhyay

Published Oct 7, 2019• 1 citation
Publisher

Abstract

We are entering the era of the second quantum revolution, where we aim to harness the power of quantum mechanics to create new technologies. Quantum technologies have the potential to revolutionize the fields of simulation, computation, communication, sensing, metrology, and many others. Here we discuss analog quantum simulation, which has attracted a lot of attention in the last few years from several platforms. Although arrays of gate-defined quantum dots exhibit significant potential for analog simulation, example experiments have been few and far between. This thesis focuses on simulating the Fermi-Hubbard model using two dimensional (2d) arrays of quantum dots. The first experiment describes the creation and measurement of a 2x2 quantum dot array. Historically, most experiments with quantum dots have been performed with linear arrays due to the relative ease of fabrication. We introduce a bi-layer gate structure, facilitated by the lift-off of sputtered silicon nitride, to create the 2x2 dot array. This gate design enables us to achieve unprecedented tunability of the tunnel coupling between all nearest-neighbor pairs of dots in 2d arrays. We also demonstrate individual control over the chemical potential and the electron occupation of each dot along with accurate measurement of the on-site and inter-site interaction terms. The use of virtual gates significantly aids in the tuning of tunnel coupling and chemical potential. The demonstrated high degree of control of the system along with fast single-shot spin-readout achieved through Pauli spin blockade establish this dot array as a promising simulator of the Fermi-Hubbard model. The 2x2 dot array is used to simulate Nagaoka ferromagnetism in the next experiment. This form of itinerant ferromagnetism arises from the Fermi-Hubbard model, and was first shown analytically in the limit of infinite interaction strengths and infinite lattices by Nagaoka in 1966. Nagaoka ferromagnetism has been a topic of rigorous theoretical studies ever since, but its experimental signature has eluded us for more than five decades. In this experiment, we load the four dot plaquette with three electrons and demonstrate the emergence of spontaneous ferromagnetism by measuring the spin correlation of two out of the three electrons. Changing the topology of the array to an open chain is shown to destroy the ferromagnetic signature, consistent with the Lieb-Mattis theorem. We also show indications that this ferromagnetic ground state can be destroyed by applying a perpendicular magnetic field, unlike most other forms of ferromagnetism. However, this ground state shows striking robustness to the offset in the local potential of any dot. This is the first experimental verification of Nagaoka’s prediction as well as the first simulation of magnetism using quantumdot arrays. The final experiment takes a different approach to simulate the Fermi-Hubbardmodel with a large 2d array of quantum dots. The dot array is created using only three gates in a top-down approach. This allows for only global control over the electron filling and tunnel coupling of the dots, contrary to the previous experiments. The readout is performed with capacitance spectroscopy, which allows us to directly probe the density of states of the two-dimensional electron systems. We measure the disorder levels and optimize both substrates and gating strategies to induce periodic potential, sufficiently stronger than the disorder level, at the 2d electron gas. Although we demonstrate a novel platformfor the realization of artificial lattices of interacting particles, this effort is currently limited by the substrate inhomogeneity.

DOI
10.4233/uuid:e7c4b281-c510-4522-95a6-8a4a5245a4c2

Related papers

Quantum Simulation in Quantum Dot Arrays

Lieven M. K. Vandersypen

Abstract : The authors use electrostatically defined quantum dot arrays to study quantum simulation, examining both large arrays to explore the ground state and excitations of the Fermi-Hubbard model, and to examine very small arrays of 3-4 quantum dots as the basis for simulating superexchange, frustration, magnetism, etc. The large arrays were created by defining a grid-shaped gate on a semiconductor, forcing the electrons to see a periodic potential and be confined in a lattice of sites, where the low temperature reachable by the system in a dilution refrigerator allows examining the phase diagram of the model in a regime where spin correlations have an important influence. Initial plans to perform transport measurement were unsuccessful as the clean room realization of contacts to the two layers of the bilayered heterostructure had very low yield, so the authors performed capacitance spectroscopy measurement instead. This provides direct measurement of density of states, and the lithography process involved allowed grids with 150-200nm periods to be successfully written. The small array examination analyzed how a system of four quantum dots on a square and filled with three electrons allowed the authors to study magnetism of few-body systems, examining whether the Nagaoka theorem could be realizable with quantum dots (conclusion: the ferromagnetic-paramagnetic state is in reach experimentally) and examining the experimental techniques to test the spin-structure of the ground state and induce the transition (finding: application of magnetic field can break the ferromagnetic ground state, in contrast to the usual). The authors also studied a linear array of three dots, resulting in publications in Nature Nanotechnology, Applied Physics Letters, and Annalen Der Physik.

•Dec 16, 2013•0 citations

Ab initio exact diagonalization simulation of the Nagaoka transition in quantum dots

Yao Wang, Juan Pablo Dehollain, Fang Liu +4 more

Recent progress of quantum simulators provides insight into the fundamental problems of strongly correlated systems. To adequately assess the accuracy of these simulators, the precise modeling of the many-body physics, with accurate model parameters, is crucially important. In this paper, we employed an ab initio exact diagonalization framework to compute the correlated physics of a few electrons in artificial potentials. We apply this approach to a quantum-dot system and study the magnetism of the correlated electrons, obtaining good agreement with recent experimental measurements in a plaquette. Through control of dot potentials and separation, including geometric manipulation of tunneling, we examine the Nagaoka transition and determine the robustness of the ferromagnetic state. While the Nagaoka theorem considers only a single-band Hubbard model, in this work we perform extensive ab initio calculations that include realistic multiorbital conditions in which the level splitting is smaller than the interactions. This simulation complements the experiments and provides insight into the formation of ferromagnetism in correlated systems. More generally, our calculation sets the stage for further theoretical analysis of analog quantum simulators at a quantitative level.

arXiv:1907.01658•Physical review. B./Physical review. B•Oct 21, 2019•18 citations

Quantum Simulation of Antiferromagnetic Heisenberg Chain with Gate-Defined Quantum Dots

Cornelis Jacobus van Diepen, Tzu-Kan Hsiao, U. Mukhopadhyay +3 more

Quantum-mechanical correlations of interacting fermions result in the emergence of exotic phases.Magnetic phases naturally arise in the Mott-insulator regime of the Fermi-Hubbard model, where charges are localized and the spin degree of freedom remains.In this regime, the occurrence of phenomena such as resonating valence bonds, frustrated magnetism, and spin liquids is predicted.Quantum systems with engineered Hamiltonians can be used as simulators of such spin physics to provide insights beyond the capabilities of analytical methods and classical computers.To be useful, methods for the preparation of intricate many-body spin states and access to relevant observables are required.Here, we show the quantum simulation of magnetism in the Mott-insulator regime with a linear quantum-dot array.We characterize the energy spectrum for a Heisenberg spin chain, from which we can identify when the conditions for homogeneous exchange couplings are met.Next, we study the multispin coherence with global exchange oscillations in both the singlet and triplet subspace of the Heisenberg Hamiltonian.Last, we adiabatically prepare the low-energy global singlet of the homogeneous spin chain and probe it with two-spin singlettriplet measurements on each nearest-neighbor pair and the correlations therein.The methods and control presented here open new opportunities for the simulation of quantum magnetism benefiting from the flexibility in tuning and layout of gate-defined quantum-dot arrays.

arXiv:2103.08238•Physical Review X•Nov 4, 2021•50 citations

Scalable Control and Measurement of Gate-Defined Quantum Dot Systems

James Colless

There is currently a worldwide effort towards the realisation of large-scale quantum computers that exploit quantum phenomena for information processing. While these computing systems could potentially redefine the technological landscape, harnessing quantum effects is challenging due to their inherently fragile nature and the experimentally demanding environments in which they arise. In order for quantum computation to be viable it is first necessary to demonstrate the operation of two-level quantum systems (qubits) which have long coherence times, can be quickly read out, and can be controlled with high fidelity. Focusing on these key requirements, this thesis presents four experiments towards scalable solid state quantum computing using gate-defined quantum dot devices based on gallium arsenide (GaAs) heterostructures. The first experiment investigates a phonon emission process that limits the charge coherence in GaAs and potentially complicates the microwave control of multi-qubit devices. We show that this microwave analogy to Raman spectroscopy can provide a means of detecting the unique phonon spectral density created by a nanoscale device. Experimental results are compared to a theoretical model based on a non-Markovian master equation and approaches to suppressing electron-phonon coupling are discussed. The second experiment demonstrates a technique involving in-situ gate electrodes coupled to lumped-element resonators to provide high-bandwidth dispersive read-out of the state of a double quantum dot. We characterise the charge sensitivity of this method in the few-electron regime and benchmark its performance against quantum point contact charge sensors. The third experiment implements a low-loss, chip-level frequency multiplexing scheme for the readout of scaled-up spin qubit arrays. Dispersive gate-sensing is realised in combination with charge detection based on two radio frequency quantum point contacts to perform multiplexed readout of a double quantum dot in the few-electron regime. Demonstration of a 10-channel multiplexing device is achieved and limitations in scaling spin qubit readout to large numbers using multiplexed channels discussed. The final experiment ties previously presented results together by realising a micro-architecture for controlling and reading out qubits during the execution of a quantum algorithm. The basic principles of this architecture are demonstrated via the manipulation of a semiconductor qubit using control pulses that are cryogenically routed using a high-electron mobility transistor switching matrix controlled by a field programmable gate array. Finally, several technical results are also presented including the development of printed circuit board solutions to allow the high-frequency measurement of nanoscale devices at cryogenic temperatures and the design of on-chip interconnects used to suppress electromagnetic crosstalk in high-density spin qubit device architectures.

•Oct 10, 2016•0 citations

Emulating Fermi-Hubbard physics with quantum dots

Toivo Hensgens

Interacting electrons on material lattices can build up strong quantum correlations, which in turn can lead to the emergence of a wide range of novel and potentially useful magnetic and electronic material properties. Our understanding of this physics, however, is severely limited by the exponential growth in complexity with system size, which leads all classical methods to fall fundamentally short. In this thesis, I show how artificial lattices of conduction band electrons in semiconductors, so-called quantum dot arrays, can be used to directly emulate and therefore elucidate such Fermi-Hubbard physics. To this end, I focus on two approaches. A top-down approach allows to scale easily, but lacks to ability to control or measure individual sites. A bottom-up approach on the other hand utilizes the small devices employed by the community for qubit experiments, in which the control of individual sites is both a blessing and a curse. We address the issue of control to the point where mapping to relevant models is possible and efficiently calibrating larger devices becomes feasible. These results open up the inherently well-suited and scalable platform of quantum dots to emulate novel quantum states of matter.

•Jan 1, 2018•3 citations

Multi-Dimensional Quantum Capacitance of the Two-Site Hubbard Model: The Role of Tunable Interdot Tunneling

Andrea Secchi, Filippo Troiani

Few-electron states confined in quantum-dot arrays are key objects in quantum computing. The discrimination between these states is essential for the readout of a (multi-)qubit state, and can be achieved through a measurement of the quantum capacitance within the gate-reflectometry approach. For a system controlled by several gates, the dependence of the measured capacitance on the direction of the oscillations in the voltage space is captured by the quantum capacitance matrix. Herein, we apply this tool to study a double quantum dot coupled to three gates, which enable the tuning of both the bias and the tunneling between the two dots. Analytical solutions for the two-electron case are derived within a Hubbard model, showing the overall dependence of the quantum capacitance matrix on the applied gate voltages. In particular, we investigate the role of the tunneling gate and reveal the possibility of exploiting interdot coherences in addition to charge displacements between the dots. Our results can be directly applied to double-dot experimental setups, and pave the way for further applications to larger arrays of quantum dots.

Entropy•Dec 31, 2022•4 citations
We are entering the era of the second quantum revolution, where we aim to harness the power of quantum mechanics to create new technologies. Quantum technologies have the potential to revolutionize the fields of simulation, computation, communication, sensing, metrology, and many others. Here we discuss analog quantum simulation, which has attracted a lot of attention in the last few years from several platforms. Although arrays of gate-defined quantum dots exhibit significant potential for analog simulation, example experiments have been few and far between. This thesis focuses on simulating the Fermi-Hubbard model using two dimensional (2d) arrays of quantum dots. The first experiment describes the creation and measurement of a 2x2 quantum dot array. Historically, most experiments with quantum dots have been performed with linear arrays due to the relative ease of fabrication. We introduce a bi-layer gate structure, facilitated by the lift-off of sputtered silicon nitride, to create the 2x2 dot array. This gate design enables us to achieve unprecedented tunability of the tunnel coupling between all nearest-neighbor pairs of dots in 2d arrays. We also demonstrate individual control over the chemical potential and the electron occupation of each dot along with accurate measurement of the on-site and inter-site interaction terms. The use of virtual gates significantly aids in the tuning of tunnel coupling and chemical potential. The demonstrated high degree of control of the system along with fast single-shot spin-readout achieved through Pauli spin blockade establish this dot array as a promising simulator of the Fermi-Hubbard model. The 2x2 dot array is used to simulate Nagaoka ferromagnetism in the next experiment. This form of itinerant ferromagnetism arises from the Fermi-Hubbard model, and was first shown analytically in the limit of infinite interaction strengths and infinite lattices by Nagaoka in 1966. Nagaoka ferromagnetism has been a topic of rigorous theoretical studies ever since, but its experimental signature has eluded us for more than five decades. In this experiment, we load the four dot plaquette with three electrons and demonstrate the emergence of spontaneous ferromagnetism by measuring the spin correlation of two out of the three electrons. Changing the topology of the array to an open chain is shown to destroy the ferromagnetic signature, consistent with the Lieb-Mattis theorem. We also show indications that this ferromagnetic ground state can be destroyed by applying a perpendicular magnetic field, unlike most other forms of ferromagnetism. However, this ground state shows striking robustness to the offset in the local potential of any dot. This is the first experimental verification of Nagaoka’s prediction as well as the first simulation of magnetism using quantumdot arrays. The final experiment takes a different approach to simulate the Fermi-Hubbardmodel with a large 2d array of quantum dots. The dot array is created using only three gates in a top-down approach. This allows for only global control over the electron filling and tunnel coupling of the dots, contrary to the previous experiments. The readout is performed with capacitance spectroscopy, which allows us to directly probe the density of states of the two-dimensional electron systems. We measure the disorder levels and optimize both substrates and gating strategies to induce periodic potential, sufficiently stronger than the disorder level, at the 2d electron gas. Although we demonstrate a novel platformfor the realization of artificial lattices of interacting particles, this effort is currently limited by the substrate inhomogeneity.
Abstract : The authors use electrostatically defined quantum dot arrays to study quantum simulation, examining both large arrays to explore the ground state and excitations of the Fermi-Hubbard model, and to examine very small arrays of 3-4 quantum dots as the basis for simulating superexchange, frustration, magnetism, etc. The large arrays were created by defining a grid-shaped gate on a semiconductor, forcing the electrons to see a periodic potential and be confined in a lattice of sites, where the low temperature reachable by the system in a dilution refrigerator allows examining the phase diagram of the model in a regime where spin correlations have an important influence. Initial plans to perform transport measurement were unsuccessful as the clean room realization of contacts to the two layers of the bilayered heterostructure had very low yield, so the authors performed capacitance spectroscopy measurement instead. This provides direct measurement of density of states, and the lithography process involved allowed grids with 150-200nm periods to be successfully written. The small array examination analyzed how a system of four quantum dots on a square and filled with three electrons allowed the authors to study magnetism of few-body systems, examining whether the Nagaoka theorem could be realizable with quantum dots (conclusion: the ferromagnetic-paramagnetic state is in reach experimentally) and examining the experimental techniques to test the spin-structure of the ground state and induce the transition (finding: application of magnetic field can break the ferromagnetic ground state, in contrast to the usual). The authors also studied a linear array of three dots, resulting in publications in Nature Nanotechnology, Applied Physics Letters, and Annalen Der Physik.
Recent progress of quantum simulators provides insight into the fundamental problems of strongly correlated systems. To adequately assess the accuracy of these simulators, the precise modeling of the many-body physics, with accurate model parameters, is crucially important. In this paper, we employed an ab initio exact diagonalization framework to compute the correlated physics of a few electrons in artificial potentials. We apply this approach to a quantum-dot system and study the magnetism of the correlated electrons, obtaining good agreement with recent experimental measurements in a plaquette. Through control of dot potentials and separation, including geometric manipulation of tunneling, we examine the Nagaoka transition and determine the robustness of the ferromagnetic state. While the Nagaoka theorem considers only a single-band Hubbard model, in this work we perform extensive ab initio calculations that include realistic multiorbital conditions in which the level splitting is smaller than the interactions. This simulation complements the experiments and provides insight into the formation of ferromagnetism in correlated systems. More generally, our calculation sets the stage for further theoretical analysis of analog quantum simulators at a quantitative level.
Quantum-mechanical correlations of interacting fermions result in the emergence of exotic phases.Magnetic phases naturally arise in the Mott-insulator regime of the Fermi-Hubbard model, where charges are localized and the spin degree of freedom remains.In this regime, the occurrence of phenomena such as resonating valence bonds, frustrated magnetism, and spin liquids is predicted.Quantum systems with engineered Hamiltonians can be used as simulators of such spin physics to provide insights beyond the capabilities of analytical methods and classical computers.To be useful, methods for the preparation of intricate many-body spin states and access to relevant observables are required.Here, we show the quantum simulation of magnetism in the Mott-insulator regime with a linear quantum-dot array.We characterize the energy spectrum for a Heisenberg spin chain, from which we can identify when the conditions for homogeneous exchange couplings are met.Next, we study the multispin coherence with global exchange oscillations in both the singlet and triplet subspace of the Heisenberg Hamiltonian.Last, we adiabatically prepare the low-energy global singlet of the homogeneous spin chain and probe it with two-spin singlettriplet measurements on each nearest-neighbor pair and the correlations therein.The methods and control presented here open new opportunities for the simulation of quantum magnetism benefiting from the flexibility in tuning and layout of gate-defined quantum-dot arrays.
There is currently a worldwide effort towards the realisation of large-scale quantum computers that exploit quantum phenomena for information processing. While these computing systems could potentially redefine the technological landscape, harnessing quantum effects is challenging due to their inherently fragile nature and the experimentally demanding environments in which they arise. In order for quantum computation to be viable it is first necessary to demonstrate the operation of two-level quantum systems (qubits) which have long coherence times, can be quickly read out, and can be controlled with high fidelity. Focusing on these key requirements, this thesis presents four experiments towards scalable solid state quantum computing using gate-defined quantum dot devices based on gallium arsenide (GaAs) heterostructures. The first experiment investigates a phonon emission process that limits the charge coherence in GaAs and potentially complicates the microwave control of multi-qubit devices. We show that this microwave analogy to Raman spectroscopy can provide a means of detecting the unique phonon spectral density created by a nanoscale device. Experimental results are compared to a theoretical model based on a non-Markovian master equation and approaches to suppressing electron-phonon coupling are discussed. The second experiment demonstrates a technique involving in-situ gate electrodes coupled to lumped-element resonators to provide high-bandwidth dispersive read-out of the state of a double quantum dot. We characterise the charge sensitivity of this method in the few-electron regime and benchmark its performance against quantum point contact charge sensors. The third experiment implements a low-loss, chip-level frequency multiplexing scheme for the readout of scaled-up spin qubit arrays. Dispersive gate-sensing is realised in combination with charge detection based on two radio frequency quantum point contacts to perform multiplexed readout of a double quantum dot in the few-electron regime. Demonstration of a 10-channel multiplexing device is achieved and limitations in scaling spin qubit readout to large numbers using multiplexed channels discussed. The final experiment ties previously presented results together by realising a micro-architecture for controlling and reading out qubits during the execution of a quantum algorithm. The basic principles of this architecture are demonstrated via the manipulation of a semiconductor qubit using control pulses that are cryogenically routed using a high-electron mobility transistor switching matrix controlled by a field programmable gate array. Finally, several technical results are also presented including the development of printed circuit board solutions to allow the high-frequency measurement of nanoscale devices at cryogenic temperatures and the design of on-chip interconnects used to suppress electromagnetic crosstalk in high-density spin qubit device architectures.
Interacting electrons on material lattices can build up strong quantum correlations, which in turn can lead to the emergence of a wide range of novel and potentially useful magnetic and electronic material properties. Our understanding of this physics, however, is severely limited by the exponential growth in complexity with system size, which leads all classical methods to fall fundamentally short. In this thesis, I show how artificial lattices of conduction band electrons in semiconductors, so-called quantum dot arrays, can be used to directly emulate and therefore elucidate such Fermi-Hubbard physics. To this end, I focus on two approaches. A top-down approach allows to scale easily, but lacks to ability to control or measure individual sites. A bottom-up approach on the other hand utilizes the small devices employed by the community for qubit experiments, in which the control of individual sites is both a blessing and a curse. We address the issue of control to the point where mapping to relevant models is possible and efficiently calibrating larger devices becomes feasible. These results open up the inherently well-suited and scalable platform of quantum dots to emulate novel quantum states of matter.
Few-electron states confined in quantum-dot arrays are key objects in quantum computing. The discrimination between these states is essential for the readout of a (multi-)qubit state, and can be achieved through a measurement of the quantum capacitance within the gate-reflectometry approach. For a system controlled by several gates, the dependence of the measured capacitance on the direction of the oscillations in the voltage space is captured by the quantum capacitance matrix. Herein, we apply this tool to study a double quantum dot coupled to three gates, which enable the tuning of both the bias and the tunneling between the two dots. Analytical solutions for the two-electron case are derived within a Hubbard model, showing the overall dependence of the quantum capacitance matrix on the applied gate voltages. In particular, we investigate the role of the tunneling gate and reveal the possibility of exploiting interdot coherences in addition to charge displacements between the dots. Our results can be directly applied to double-dot experimental setups, and pave the way for further applications to larger arrays of quantum dots.