The germanium quantum information route

Abstract

In the worldwide endeavor for disruptive quantum technologies, germanium is emerging as a versatile material to realize devices capable of encoding, processing, or transmitting quantum information. These devices leverage special properties of the germanium valence-band states, commonly known as holes, such as their inherently strong spin-orbit coupling and the ability to host superconducting pairing correlations. In this Review, we initially introduce the physics of holes in low-dimensional germanium structures with key insights from a theoretical perspective. We then examine the material science progress underpinning germanium-based planar heterostructures and nanowires. We review the most significant experimental results demonstrating key building blocks for quantum technology, such as an electrically driven universal quantum gate set with spin qubits in quantum dots and superconductor-semiconductor devices for hybrid quantum systems. We conclude by identifying the most promising prospects toward scalable quantum information processing.

References in corpus (151)

• Non-Abelian Anyons and Topological Quantum Computation
• Quantum Computation with Quantum Dots
• Unpaired Majorana fermions in quantum wires
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Surface codes: Towards practical large-scale quantum computation
• Spins in few-electron quantum dots
• The Physical Implementation of Quantum Computation
• A generic new platform for topological quantum computation using semiconductor heterostructures
• Coupled quantum dots as quantum gates
• Driven coherent oscillations of a single electron spin in a quantum dot
• Silicon Quantum Electronics
• Majorana fermions in a tunable semiconductor device
• Randomized Benchmarking of Quantum Gates
• Coherent control of a single electron spin with electric fields
• Realizing Majorana zero modes in superconductor-semiconductor heterostructures
• An addressable quantum dot qubit with fault-tolerant control fidelity
• A Two Qubit Logic Gate in Silicon
• A programmable two-qubit quantum processor in silicon
• Electron spin coherence exceeding seconds in high purity silicon
• Storing quantum information for 30 seconds in a nanoelectronic device
• Interfacing spin qubits in quantum dots and donors - hot, dense and coherent
• Spin-flip transitions between Zeeman sublevels in semiconductor quantum dots
• Epitaxy of Semiconductor-Superconductor nanowires
• One-Dimensional Hole Gas in Germanium/Silicon Nanowire Heterostructures
• Phonon-induced decay of the electron spin in quantum dots
• A Coherent Spin-Photon Interface in Silicon
• A Semiconductor Nanowire-Based Superconducting Qubit
• Prospects for Spin-Based Quantum Computing
• Silicon CMOS architecture for a spin-based quantum computer
• Strong spin-photon coupling in silicon
• Electric Dipole Induced Spin Resonance in Quantum Dots
• Double quantum dot with integrated charge sensor based on Ge/Si heterostructure nanowires
• Reduced sensitivity to charge noise in semiconductor spin qubits via symmetric operation
• Spin decoherence of a heavy hole coupled to nuclear spins in a quantum dot
• Ge/Si nanowire mesoscopic Josephson junctions
• Spin relaxation and decoherence of holes in quantum dots
• Fast two-qubit logic with holes in germanium
• A Crossbar Network for Silicon Quantum Dot Qubits
• Rashba spin splitting in two-dimensional electron and hole systems
• Realization of microwave quantum circuits using hybrid superconducting-semiconducting nanowire Josephson elements
• How to realize a robust practical Majorana chain in a quantum dot-superconductor linear array
• Ge hole spin qubit
• Noise suppression using symmetric exchange gates in spin qubits
• Topological quantum computing with a very noisy network and local error rates approaching one percent
• Long-Range Microwave Mediated Interactions Between Electron Spins
• Superconducting Gatemon Qubit based on a Proximitized Two-Dimensional Electron Gas
• Spin Relaxation in Ge/Si Core-Shell Nanowire Qubits
• Observation of extremely slow hole spin relaxation in self-assembled quantum dots
• Strong Spin-Orbit Interaction and Helical Hole States in Ge/Si Nanowires
• A single-hole spin qubit
• Rapid high-fidelity gate-based spin read-out in silicon
• Electric Dipole Spin Resonance for Heavy Holes in Quantum Dots
• Gate-based single-shot readout of spins in silicon
• Spin-Dependent Josephson Current through Double Quantum Dots and Measurement of Entangled Electron States
• Hybrid superconductor-semiconductor devices made from self-assembled SiGe nanocrystals on silicon
• Strong coupling of a spin qubit to a superconducting stripline cavity
• Electrical spin driving by $g$-matrix modulation in spin-orbit qubits
• Quantum Dot Arrays in Silicon and Germanium
• Low disordered, stable, and shallow germanium quantum wells: a playground for spin and hybrid quantum technology
• Gate-reflectometry dispersive readout and coherent control of a spin qubit in silicon
• Cubic Rashba spin-orbit interaction of two-dimensional hole gas in strained-Ge/SiGe quantum well
• Gate-controlled quantum dots and superconductivity in planar germanium
• Quantum information transfer between topological and spin qubit systems
• Direct Rashba spin-orbit interaction in Si and Ge nanowires with different growth directions
• Circuit QED with Hole-Spin Qubits in Ge/Si Nanowire Quantum Dots
• Theory of phonon-induced spin relaxation in laterally coupled quantum dots
• Strong and Tunable Spin-Orbit Coupling of One-Dimensional Holes in Ge/Si Core/Shell Nanowires
• Universal Quantum Computation with Hybrid Spin-Majorana Qubits
• Theory of Hole-Spin Qubits in Strained Germanium Quantum Dots
• Monolithic growth of ultra-thin Ge nanowires on Si(001)
• Spin Splitting in Symmetrical SiGe Quantum Wells
• Hole Spin Coherence in a Ge/Si Heterostructure Nanowire
• Heavy hole states in Germanium hut wires
• Germanium quantum well Josephson field effect transistors and interferometers
• Pauli spin blockade in undoped Si/SiGe two-electron double quantum dots
• Spin-orbit interactions in inversion-asymmetric 2D hole systems: a variational analysis
• Electric field effect on electron spin splitting in SiGe/Si quantum wells
• Majorana Fermions in Ge/Si Hole Nanowires
• Quantum manipulation of two-electron spin states in metastable double quantum dots
• Light effective hole mass in undoped Ge/SiGe quantum wells
• Hybridization and spin decoherence in heavy-hole quantum dots
• Relaxation of hole spins in quantum dots via two-phonon processes
• Spin Orientation of Holes in Quantum Wells
• Electrical manipulation of semiconductor spin qubits within the g-matrix formalism
• Hyperfine-phonon spin relaxation in a single-electron GaAs quantum dot
• On the nature of tunable hole g-factors in quantum dots
• Tunable g factor and phonon-mediated hole spin relaxation in Ge/Si nanowire quantum dots
• Self-controlled growth of highly uniform Ge/Si hut wires for scalable qubit devices
• Electric-field dependent g-factor anisotropy in Ge-Si core-shell nanowire quantum dots
• Antilocalization of Coulomb Blockade in a Ge-Si Nanowire
• Hole-doped semiconductor nanowire on top of an s-wave superconductor: A new and experimentally accessible system for Majorana fermions
• Single-shot readout of hole spins in Ge
• Spin-3/2 physics of semiconductor hole nanowires: Valence-band mixing and tunable interplay between bulk-material and orbital bound-state spin splittings
• Coupling spin qubits via superconductors
• Spin relaxation in (110) and (001) InAs/GaSb superlattices
• Spin relaxation benchmarks and individual qubit addressability for holes in quantum dots
• Magnetic Field Evolution of Spin Blockade in Ge/Si Nanowire Double Quantum Dots
• Anisotropic Pauli spin blockade in hole quantum dots
• Superconducting phase with a chiral $f$-wave pairing symmetry and Majorana fermions induced in a hole-doped semiconductor
• Electron spin coherence of shallow donors in natural and isotopically enriched germanium
• Anomalous spin-resolved point-contact transmission of holes due to cubic Rashba spin-orbit coupling
• Enhanced spin-orbit coupling in core/shell nanowires
• SiGe quantum dots for fast hole spin Rabi oscillations
• Single, double, and triple quantum dots in Ge/Si nanowires
• Ballistic one-dimensional holes with strong g-factor anisotropy in germanium
• Spin-orbit splitting and effective masses in p-type GaAs two-dimensional hole gases
• Strong influence of spin-orbit coupling on magnetotransport in two-dimensional hole systems
• Spin blockade as a probe of Zeeman interactions in hole quantum dots
• Multiple Andreev reflections and Shapiro steps in a Ge-Si nanowire Josephson junction
• Ballistic supercurrent discretization and micrometer-long Josephson coupling in germanium
• Electrical control of the Zeeman spin splitting in two-dimensional hole systems
• Giant g factor tuning of long-lived electron spins in Ge
• Spin-orbit interaction and induced superconductivity in an one-dimensional hole gas
• Using hybrid topological-spin qubit systems for two-qubit-spin gates
• Electric-field Manipulation of the Lande' g Tensor of Holes in In0.5Ga0.5As/GaAs Self-assembled Quantum Dots
• Andreev reflection in Si-engineered Al/InGaAs hybrid junctions
• Spinless composite fermions in an ultra-high quality strained Ge quantum well
• Hard superconducting gap and diffusion-induced superconductors in Ge-Si nanowires
• Josephson effect in a few-hole quantum dot
• Single and Double Hole Quantum Dots in Strained Ge/SiGe Quantum Wells
• Entangling Spins in Double Quantum Dots and Majorana Bound States
• Superconducting grid-bus surface code architecture for hole-spin qubits
• Magnetic field induced valence band mixing in [111] grown semiconductor quantum dots
• Dimensional reduction of the Luttinger Hamiltonian and g-factors of holes in symmetric two-dimensional semiconductor heterostructures
• Acoustic phonons and strain in core/shell nanowires
• Highly tuneable hole quantum dots in Ge-Si core-shell nanowires
• Hole-phonon interactions in quantum dots: Effects of phonon confinement and encapsulation materials on spin-orbit qubits
• Characterization of spin-orbit interactions of GaAs heavy holes using a quantum point contact
• Single-spin manipulation in a double quantum dot in the field of a micromagnet
• Exchange-interaction of two spin qubits mediated by a superconductor
• Self-Organised Fractional Quantisation in a Hole Quantum Wire
• Enhancement-mode buried strained silicon channel quantum dot with tunable lateral geometry
• Detection and control of spin-orbit interactions in a GaAs hole quantum point contact
• Effect of strain on hyperfine-induced hole-spin decoherence in quantum dots
• Dipole coupling of a tunable hole double quantum dot in germanium hut wire to a microwave resonator
• Effective g factor of low-density two-dimensional holes in a Ge quantum well
• Enhancing the dipolar coupling of a $S$-$T_0$ qubit with a transverse sweet spot
• Enhanced Rashba spin-orbit coupling in core-shell nanowires by the interfacial effect
• Orbital effects of a strong in-plane magnetic field on a gate-defined quantum dot
• High Fidelity Singlet-Triplet $S$-$T_{-}$ Qubits in Inhomogeneous Magnetic Fields
• Fast Hole Tunneling Times in Germanium Hut Wires Probed by Single-Shot Reflectometry
• Fractional Quantum Hall States in a Ge Quantum Well
• Ballistic quantum transport through Ge/Si core/shell nanowires
• G-factor of electrons in gate-defined quantum dots in a strong in-plane magnetic field
• Phonon-assisted relaxation and decoherence of singlet-triplet qubits in Si/SiGe quantum dots
• Effective g factor of 2D holes in strained Ge quantum wells
• Density-controlled quantum Hall ferromagnetic transition in a two-dimensional hole system
• Strongly Interacting Holes in Ge/Si Nanowires
• Hole weak anti-localization in a strained-Ge surface quantum well
• Assessing the potential of Ge/SiGe quantum dots as hosts for singlet-triplet qubits
• In-plane magnetic field effect on hole cyclotron mass and $g_z$ factor in high-mobility SiGe/Ge/SiGe structures

Cited by in corpus (166)

• Semiconductor Spin Qubits
• A four-qubit germanium quantum processor
• Semiconductor Qubits In Practice
• Review of performance metrics of spin qubits in gated semiconducting nanostructures
• The 2021 Quantum Materials Roadmap
• A singlet triplet hole spin qubit in planar Ge
• Ultrafast coherent control of a hole spin qubit in a germanium quantum dot
• Direct manipulation of a superconducting spin qubit strongly coupled to a transmon qubit
• Nanomaterials for Quantum Information Science and Engineering
• A single hole spin with enhanced coherence in natural silicon
• Squeezed hole spin qubits in Ge quantum dots with ultrafast gates at low power
• Strong spin-orbit interaction and $g$-factor renormalization of hole spins in Ge/Si nanowire quantum dots
• Operating semiconductor quantum processors with hopping spins
• Simultaneous single-qubit driving of semiconductor spin qubits at the fault-tolerant threshold
• Parity-conserving Cooper-pair transport and ideal superconducting diode in planar Germanium
• Blueprint of a scalable spin qubit shuttle device for coherent mid-range qubit transfer in disordered Si/SiGe/SiO${}_2$
• Recent advances in hole-spin qubits
• Sweet-spot operation of a germanium hole spin qubit with highly anisotropic noise sensitivity
• On-demand electrical control of spin qubits
• Hard superconducting gap in germanium
• Hole spin driving by strain-induced spin-orbit interactions
• Electrical control of the $g$-tensor of a single hole in a silicon MOS quantum dot
• Dielectrics for Two-Dimensional Transition Metal Dichalcogenide Applications
• Coherent spin qubit shuttling through germanium quantum dots
• Enhancement of Proximity Induced Superconductivity in a Planar Ge Hole Gas
• In-situ Tuning of the Electric Dipole Strength of a Double Dot Charge Qubit: Charge Noise Protection and Ultra Strong Coupling
• Fully tunable longitudinal spin-photon interactions in Si and Ge quantum dots
• Germanium wafers for strained quantum wells with low disorder
• Lightly-strained germanium quantum wells with hole mobility exceeding one million
• Universal control of four singlet-triplet qubits
• A 300 mm foundry silicon spin qubit unit cell exceeding 99% fidelity in all operations
• A natural heavy-hole flopping mode qubit in germanium
• Hole Spin Qubits in Ge Nanowire Quantum Dots: Interplay of Orbital Magnetic Field, Strain, and Growth Direction
• Semiconductor materials stacks for quantum dot spin qubits
• Phase Asymmetry of Andreev Spectra From Cooper-Pair Momentum
• A two-dimensional array of single-hole quantum dots
• Variability of electron and hole spin qubits due to interface roughness and charge traps
• Hole spin manipulation in inhomogeneous and non-separable electric fields
• Longitudinal and transverse electric field manipulation of hole spin-orbit qubits in one-dimensional channels
• Strong tunable coupling between two distant superconducting spin qubits
• Probing resonating valence bonds on a programmable germanium quantum simulator
• Gate-Tunable Spin-Orbit Coupling in a Germanium Hole Double Quantum Dot
• Anisotropic g-Factor and Spin-Orbit Field in a Ge Hut Wire Double Quantum Dot
• Electrical control of uniformity in quantum dot devices
• Electrical operation of planar Ge hole spin qubits in an in-plane magnetic field
• A gate tunable transmon qubit in planar Ge
• All-electrical control of hole singlet-triplet spin qubits at low leakage points
• Impact of interface traps on charge noise, mobility and percolation density in Ge/SiGe heterostructures
• Hole spin qubits in thin curved quantum wells
• Planar Josephson junctions in germanium: Effect of cubic spin-orbit interaction
• High-fidelity two-qubit gates of hybrid superconducting-semiconducting singlet-triplet qubits
• Strong hole-photon coupling in planar Ge for probing charge degree and strongly-correlated states
• Charge-noise induced dephasing in silicon hole-spin qubits
• Linear-in-momentum spin orbit interactions in planar Ge/GeSi heterostructures and spin qubits
• Enhanced orbital magnetic field effects in Ge hole nanowires
• Exciton transport in a germanium quantum dot ladder
• High-fidelity spin qubit shuttling via large spin-orbit interaction
• Fermion-parity qubit in a proximitized double quantum dot
• Majorana zero modes in gate-defined germanium hole nanowires
• Geometry of the dephasing sweet spots of spin-orbit qubits
• Phase driving hole spin qubits
• Majorana bound states in germanium Josephson junctions via phase control
• A quantum dot in germanium proximitized by a superconductor
• Light-Hole Gate-Defined Spin-Orbit Qubit
• Cavity-mediated entanglement of parametrically driven spin qubits via sidebands
• Exploiting epitaxial strained germanium for scaling low noise spin qubits at the micron-scale
• Determination of spin-orbit interaction in semiconductor nanostructures via non-linear transport
• Gatemon qubit on a germanium quantum-well heterostructure
• Interacting holes in Si and Ge double quantum dots: from a multiband approach to an effective-spin picture
• Direct microwave spectroscopy of Andreev bound states in planar Ge Josephson junctions
• Electrical operation of hole spin qubits in planar MOS silicon quantum dots
• Strong Charge-Photon Coupling in Planar Germanium Enabled by Granular Aluminium Superinductors
• Quantum heat engines with complex working media, complete Otto cycles and heuristics
• Anisotropic $g$-tensors in hole quantum dots: The role of the transverse confinement direction
• Microscopic analysis of proximity-induced superconductivity and metallization effects in superconductor-germanium hole nanowires
• Coupled vertical double quantum dots at single-hole occupancy
• Nuclear Spin-Depleted, Isotopically Enriched 70Ge/28Si70Ge Quantum Wells
• A two-dimensional 10-qubit array in germanium with robust and localised qubit control
• Valleytronic full configuration-interaction approach: An application to the excitation spectra of Si double-dot qubits
• Modular Autonomous Virtualization System for Two-Dimensional Semiconductor Quantum Dot Arrays
• Industrially fabricated single-electron quantum dots in Si/Si-Ge heterostructures
• Single-step high-fidelity three-qubit gates by anisotropic chiral interactions
• Clock model and parafermions in Rashba nanowires
• Charge-sensing of a Ge/Si core/shell nanowire double quantum dot using a high-impedance superconducting resonator
• Low-energy subband wave-functions and effective $g$-factor of one-dimensional hole gas
• InAs on Insulator: A New Platform for Cryogenic Hybrid Superconducting Electronics
• Germanium-based hybrid semiconductor-superconductor topological quantum computing platforms: Disorder effects
• High quality CVD deposition of Ge layers for Ge/SiGe Quantum Well heterostructures
• Continuous microwave photon counting by semiconductor-superconductor hybrids
• An upper and lower bound to the orientation-dependent linear Rashba spin-orbit coupling of two-dimensional hole gases in semiconductor quantum wells
• Spin-orbit enabled quantum transport channels in a two-hole double quantum dot
• Effective out-of-plane g-factor in strained-Ge/SiGe quantum dots
• Protected Solid-State Qubits
• Reducing disorder in Ge quantum wells by using thick SiGe barriers
• Dephasing of planar Ge hole spin qubits due to 1/$\text{f}$ charge noise
• Significant reduction in semiconductor interface resistance via interfacial atomic mixing
• Acceptor-based qubit in silicon with tunable strain
• Modelling of planar germanium hole qubits in electric and magnetic fields
• Superconductivity in Substitutional Ga-Hyperdoped Ge Epitaxial Thin Films
• Molecular beam epitaxy growth of superconducting tantalum germanide
• Fermi Surface Resonance and Quantum Criticality in Strongly Interacting Fermi Gases
• Atomistic insights into ultrafast SiGe nanoprocessing
• Interband contributions to nonlinear transport in semiconductor nanostructures
• InP/GaSb core-shell nanowires: a novel hole-based platform with strong spin-orbit coupling for full-shell hybrid devices
• Effects of spin-orbit coupling and in-plane Zeeman fields on the critical current in two-dimensional hole gas SNS junctions
• Probing details of spin--orbit coupling through Pauli spin blockade
• Non-equilibrium VLS-grown stable ST12-Ge thin film on Si substrate: A study on strain-induced band-engineering
• Andreev spin relaxation time in a shadow-evaporated InAs weak link
• Low-symmetry nanowire cross-sections for enhanced Dresselhaus spin-orbit interaction
• Toward Axion Signal Extraction in Semiconductor Spin Qubits Via Spectral Engineering
• A spinless spin qubit
• First-Principles Calculation of Alloy Scattering and n-type Mobility in Strained GeSn
• Quantum geometric protocols for fast high-fidelity adiabatic state transfer
• A backgate for enhanced tunability of holes in planar germanium
• Coherence of a field-gradient-driven singlet-triplet qubit coupled to many-electron spin states in 28Si/SiGe
• Quantum estimation and remote charge sensing with a hole-spin qubit in silicon
• Low-energy hole subband dispersions in a cylindrical Ge nanowire: the effects of the nanowire growth direction
• Gate-based spin readout of hole quantum dots with site-dependent $g-$factors
• Josephson Field Effect Transistors with InAs on Insulator and High Permittivity Gate Dielectrics
• Two-band description of the strong `spin'-orbit coupled one-dimensional hole gas in a cylindrical Ge nanowire
• Entangled Photon-Pair Emission in Waveguide Circuit QED from a Cooper Pair Splitter
• Spin susceptibility in interacting two-dimensional semiconductors and bilayer systems at first order: Kohn anomalies and spin density wave ordering
• Investigation of Lasing in Highly Strained Germanium at the Crossover to Direct Band Gap
• Superconducting Proximity Effect in Two-Dimensional Hole Gases
• Electrical manipulation of a hole `spin'-orbit qubit in nanowire quantum dot: the nontrivial magnetic field effects
• All rf-based tuning algorithm for quantum devices using machine learning
• Quantification of the heavy-hole--light-hole mixing in two-dimensional hole gases
• Phase-controlled minimal Kitaev chain in multiterminal Josephson junctions
• Polarimetry With Spins in the Solid State
• A dressed singlet-triplet qubit in germanium
• Theory of superconducting proximity effect in hole-based hybrid semiconductor-superconductor devices
• Efficient adaptive Bayesian estimation of a slowly fluctuating Overhauser field gradient
• Protecting coherence from the environment via Stark many-body localization in a Quantum-Dot Simulator
• Hole subband dispersions in a cylindrical Ge nanowire: exact results based on the axial Luttinger-Kohn Hamiltonian
• Localized Energy States Induced by Atomic-Level Interfacial Broadening in Heterostructures
• Envelope-function theory of inhomogeneous strain in semiconductor nanostructures
• Humble planar defects in SiGe nanopillars
• Spin-photon interaction in a nanowire quantum dot with asymmetrical confining potential
• Hole subband dispersions and strong `spin'-orbit coupling in a cylindrical Ge nanowire
• Rapid optimal work extraction from a quantum-dot information engine
• Singlet-only Always-on Gapless Exchange Qubits with Baseband Control
• Effect of disorder and strain on the operation of planar Ge hole spin qubits
• Hole spin splitting in a Ge quantum dot with finite barriers
• Gate control, g-factors and spin orbit energy of p-type GaSb nanowire quantum dot devices
• Variability of hole spin qubits in planar Germanium
• Unraveling energy flow mechanisms in semiconductors by ultrafast spectroscopy: Germanium as a case study
• Cancelling second order frequency shifts in Ge hole spin qubits via bichromatic control
• Photodriven germanium hole qubit
• Role of anisotropic confining potential and elliptical driving in dynamics of a Ge hole qubit
• Acoustic phonons, spin-phonon coupling and spin relaxation via the lattice reorientation mechanism in hexagonal germanium nanowires
• Electronic structure of Humble defects in Ge and Ge${}_{0.8}$Si${}_{0.2}$
• Supercurrent and multiple Andreev reflections in Ge hut nanowire Josephson Junctions
• Lateral Mn5Ge3 spin-valve in contact with a high-mobility Ge two-dimensional hole gas
• Dressed basis sets for the modeling of exchange interactions in double quantum dots
• Finite Length Effects and Coulomb Interaction in Ge Quantum Well-Based Josephson Junctions Probed with Microwave Spectroscopy
• Giant Rabi frequencies between qubit and excited hole states in silicon quantum dots
• Orbital Hall effect in spin-3/2 hole-doped semiconductors and its implications for orbitronics
• Current cross-correlation spectroscopy of Majorana bound states
• Electrically driven spin resonance with bichromatic driving
• Rashba spin-orbit coupling and artificially engineered topological superconductors
• Optical spin pumping in silicon
• Ge as an orbitronic platform: giant in-plane orbital magneto-electric effect in a 2-dimensional hole gas
• Fully tunable hyperfine interactions of hole spin qubits in Si and Ge quantum dots
• Kramers-protected hardware-efficient error correction with Andreev spin qubits
• Searching strong `spin'-orbit coupled one-dimensional hole gas in strong magnetic fields
• Anomalous zero-field splitting for hole spin qubits in Si and Ge quantum dots