Abstract Quantum mechanics often results in extremely complex phenomena, especially when the quantum system under consideration is composed of many interacting particles. The states of these many‐body systems live in a space so large that classical numerical calculations cannot compute them. Quantum simulations can be used to overcome this problem: complex quantum problems can be solved by studying experimentally an artificial quantum system operated to simulate the desired hamiltonian. Quantum dot systems have shown to be widely tunable quantum systems, that can be efficiently controlled electrically. This tunability and the versatility of their design makes them very promising quantum simulators. This paper reviews the progress towards digital quantum simulations with individually controlled quantum dots, as well as the analog quantum simulations that have been performed with these systems. The possibility to use large arrays of quantum dots to simulate the low‐temperature Hubbard model is also discussed. The main issues along that path are presented and new ideas to overcome them are proposed.Abstract Quantum mechanics often results in extremely complex phenomena, especially when the quantum system under consideration is composed of many interacting particles. The states of these many‐body systems live in a space so large that classical numerical calculations cannot compute them. Quantum simulations can be used to overcome this problem: complex quantum problems can be solved by studying experimentally an artificial quantum system operated to simulate the desired hamiltonian. Quantum dot systems have shown to be widely tunable quantum systems, that can be efficiently controlled electrically. This tunability and the versatility of their design makes them very promising quantum simulators. This paper reviews the progress towards digital quantum simulations with individually controlled quantum dots, as well as the analog quantum simulations that have been performed with these systems. The possibility to use large arrays of quantum dots to simulate the low‐temperature Hubbard model is also discussed. The main issues along that path are presented and new ideas to overcome them are proposed.

Annalen der PhysikSep 16, 201397 citations

Prediction of the spin triplet two-electron quantum dots in Si: Towards controlled quantum simulations of magnetic systems

Dmitry Miserev, Oleg P. Sushkov

The ground state of two-electron quantum dots in single-valley materials like GaAs is always a spin singlet regardless of what the potential and interactions are. This statement cannot be generalized to the multivalley materials like $n$ -doped Si. Here we calculate numerically the spectrum of a two-electron Si quantum dot and show that the dot with the lateral size of several nm can have the spin triplet ground state which is impossible in the single-valley materials. Predicted singlet-triplet level crossing in two-electron Si quantum dots can potentially establish the platform for quantum simulation of magnetic many body systems based on quantum dots. We suggest several examples of such systems that open a way to controlled quantum simulations within the condensed matter setting.The ground state of two-electron quantum dots in single-valley materials like GaAs is always a spin singlet regardless of what the potential and interactions are. This statement cannot be generalized to the multivalley materials like $n$-doped Si. Here we calculate numerically the spectrum of a two-electron Si quantum dot and show that the dot with the lateral size of several nm can have the spin triplet ground state which is impossible in the single-valley materials. Predicted singlet-triplet level crossing in two-electron Si quantum dots can potentially establish the platform for quantum simulation of magnetic many body systems based on quantum dots. We suggest several examples of such systems that open a way to controlled quantum simulations within the condensed matter setting.

arXiv:1908.02543Physical review. B./Physical review. BNov 20, 20194 citations

Quantum Computing with Quantum Dots

Taylor & Francis eBooksMar 11, 20080 citations

Quantum Simulation

WORLD SCIENTIFIC (EUROPE) eBooksMay 5, 20260 citations

Long-range electron-electron interactions in quantum dot systems and applications in quantum chemistry

Johannes Knörzer, Cornelis Jacobus van Diepen, Tzu-Kan Hsiao +6 more

Long-range interactions play a key role in several phenomena of quantum physics and chemistry. To study these phenomena, analog quantum simulators provide an appealing alternative to classical numerical methods. Gate-defined quantum dots have been established as a platform for quantum simulation, but for those experiments the effect of long-range interactions between the electrons did not play a crucial role. Here we present a detailed experimental characterization of long-range electron-electron interactions in an array of gate-defined semiconductor quantum dots. We demonstrate significant interaction strength among electrons that are separated by up to four sites, and show that our theoretical prediction of the screening effects matches well the experimental results. Based on these findings, we investigate how long-range interactions in quantum dot arrays may be utilized for analog simulations of artificial quantum matter. We numerically show that about ten quantum dots are sufficient to observe binding for a one-dimensional $\mathrm{H}{}_{2}$ -like molecule. These combined experimental and theoretical results pave the way for future quantum simulations with quantum dot arrays and benchmarks of numerical methods in quantum chemistry.Long-range interactions play a key role in several phenomena of quantum physics and chemistry. To study these phenomena, analog quantum simulators provide an appealing alternative to classical numerical methods. Gate-defined quantum dots have been established as a platform for quantum simulation, but for those experiments the effect of long-range interactions between the electrons did not play a crucial role. Here we present a detailed experimental characterization of long-range electron-electron interactions in an array of gate-defined semiconductor quantum dots. We demonstrate significant interaction strength among electrons that are separated by up to four sites, and show that our theoretical prediction of the screening effects matches well the experimental results. Based on these findings, we investigate how long-range interactions in quantum dot arrays may be utilized for analog simulations of artificial quantum matter. We numerically show that about ten quantum dots are sufficient to observe binding for a one-dimensional $\mathrm{H}{}_{2}$-like molecule. These combined experimental and theoretical results pave the way for future quantum simulations with quantum dot arrays and benchmarks of numerical methods in quantum chemistry.

arXiv:2202.06756Physical Review ResearchJul 15, 202214 citations

n

-doped Si. Here we calculate numerically the spectrum of a two-electron Si quantum dot and show that the dot with the lateral size of several nm can have the spin triplet ground state which is impossible in the single-valley materials. Predicted singlet-triplet level crossing in two-electron Si quantum dots can potentially establish the platform for quantum simulation of magnetic many body systems based on quantum dots. We suggest several examples of such systems that open a way to controlled quantum simulations within the condensed matter setting.

\mathrm{H}{}_{2}

-like molecule. These combined experimental and theoretical results pave the way for future quantum simulations with quantum dot arrays and benchmarks of numerical methods in quantum chemistry.