Query: A four-qubit germanium quantum processor

Candidate papers:

abstract: The prospect of building quantum circuits1,2 using advanced semiconductor manufacturing makes quantum dots an attractive platform for quantum information processing3,4. Extensive studies of various materials have led to demonstrations of two qubit logic in gallium arsenide5, silicon6 12 and germanium13. However, interconnecting larger numbers of qubits in semiconductor devices has remained a challenge. Here we demonstrate a four qubit quantum processor based on hole spins in germanium quantum dots. Furthermore, we define the quantum dots in a two by two array and obtain controllable coupling along both directions. Qubit logic is implemented all electrically and the exchange interaction can be pulsed to freely program one qubit, two qubit, three qubit and four qubit operations, resulting in a compact and highly connected circuit. We execute a quantum logic circuit that generates a four qubit Greenberger Horne Zeilinger state and we obtain coherent evolution by incorporating dynamical decoupling. These results are a step towards quantum error correction and quantum simulation using quantum dots.
author_names: Nico W Hendrickx

W I L Lawrie

Maximilian Russ

F van Riggelen

Sander L de Snoo

R N Schouten

Amir Sammak

Giordano Scappucci

Menno Veldhorst
title: A four qubit germanium quantum processor.
venue: Nature
year: 2021

author_names: A J Sigillito

James Loy

D M Zajac

Felix Borjans

Michael J Gullans

Jason R Petta
title: Four qubit quantum processor in isotopically enriched silicon
year: 2019

abstract: Universal quantum information processing requires the execution of single qubit and two qubit logic. Across all qubit realizations 1 spin qubits in quantum dots have great promise to become the central building block for quantum computation 2 Excellent quantum dot control can be achieved in gallium arsenide 3 5 and high fidelity qubit rotations and two qubit logic have been demonstrated in silicon 6 9 but universal quantum logic implemented with local control has yet to be demonstrated. Here we make this step by combining all of these desirable aspects using hole quantum dots in germanium. Good control over tunnel coupling and detuning is obtained by exploiting quantum wells with very low disorder, enabling operation at the charge symmetry point for increased qubit performance. Spin orbit coupling obviates the need for microscopic elements close to each qubit and enables rapid qubit control with driving frequencies exceeding 100 MHz. We demonstrate a fast universal quantum gate set composed of single qubit gates with a fidelity of 99.3 per cent and a gate time of 20 nanoseconds, and two qubit logic operations executed within 75 nanoseconds. Planar germanium has thus matured within a year from a material that can host quantum dots to a platform enabling two qubit logic, positioning itself as an excellent material for use in quantum information applications. Spin qubits based on hole states in strained germanium could offer the most scalable platform for quantum computation.
author_names: Nico W Hendrickx

David P Franke

Amir Sammak

Giordano Scappucci

Menno Veldhorst
title: Fast two qubit logic with holes in germanium
venue: Nature
year: 2020

abstract: Shor's quantum algorithm factorizes integers, and implementing this is a benchmark test in the early development of quantum processors. Researchers now demonstrate this important test in a solid state system: a circuit made up of four superconducting qubits factorizes the number 15.
author_names: Erik Lucero

Rami Barends

Yu Chen

Julian Kelly

Matteo Mariantoni

Anthony Megrant

P J J O'Malley

Daniel Thomas Sank

Amit Vainsencher

J Wenner

T C White

Yi Yin

Andrew N Cleland

John M Martinis
title: Computing prime factors with a Josephson phase qubit quantum processor
year: 2012

abstract: The successful implementation of algorithms on quantum processors relies on the accurate control of quantum bits (qubits) to perform logic gate operations. In this era of noisy intermediate scale quantum (NISQ) computing, systematic miscalibrations, drift, and crosstalk in the control of qubits can lead to a coherent form of error which has no classical analog. Coherent errors severely limit the performance of quantum algorithms in an unpredictable manner, and mitigating their impact is necessary for realizing reliable quantum computations. Moreover, the average error rates measured by randomized benchmarking and related protocols are not sensitive to the full impact of coherent errors, and therefore do not reliably predict the global performance of quantum algorithms, leaving us unprepared to validate the accuracy of future large scale quantum computations. Randomized compiling is a protocol designed to overcome these performance limitations by converting coherent errors into stochastic noise, dramatically reducing unpredictable errors in quantum algorithms and enabling accurate predictions of algorithmic performance from error rates measured via cycle benchmarking. In this work, we demonstrate significant performance gains under randomized compiling for the four qubit quantum Fourier transform algorithm and for random circuits of variable depth on a superconducting quantum processor. Additionally, we accurately predict algorithm performance using experimentally measured error rates. Our results demonstrate that randomized compiling can be utilized to maximally leverage and predict the capabilities of modern day noisy quantum processors, paving the way forward for scalable quantum computing.
author_names: Akel Hashim

R K Naik

A Morvan

J L Ville

Bradley Mitchell

John Mark Kreikebaum

Marc Grau Davis

Ethan Smith

Costin Iancu

Kevin P O'Brien

Ian N Hincks

Joel Wallman

Joseph Emerson

Irfan Siddiqi
title: Randomized compiling for scalable quantum computing on a noisy superconducting quantum processor
year: 2020

abstract: In quantum information processing, spin 3/2 electron or nuclear spin states are known as two qubit states. For SI (S 3/2, I 3/2) spin system, there are 16 four qubit states. In this study, first, four qubit entangled states are obtained by using the matrix representation of Hadamard and CNOT logic gates. By considering 75As@C60 molecule as SI (S 3/2, I 3/2) spin system, four qubit entangled states are also obtained by using the magnetic resonance pulse sequences of Hadamard and CNOT logic gates. Then, it is shown that obtained entangled states can be transformed into each other by the transformation operators.
author_names: A Gun

Selcuk Cakmak

Azmi Gencten
title: Construction of four qubit quantum entanglement for SI (S 3/2, I 3/2) spin system
venue: Quantum Inf. Process.
year: 2013

abstract: Aluminumgermanium nanowires (NWs) thermal activated solid state reaction is a promising system as very sharp and well defined one dimensional contacts can be created between a metal and a semiconductor, that can become a quantum dot if the size becomes sufficiently small. In the search for high performance devices without variability, it is of high interest to allow deterministic fabrication of nanowire quantum dots, avoiding sample variability and obtaining atomic scale precision on the fabricated dot size. In this paper, we present a reliable fabrication process to produce sub10 nm Ge quantum dots (QDs) using a combination of ex situ thermal annealing via rapid thermal annealing (RTA) and in situ Joule heating technique in a transmission electron microscope (TEM) First we present in situ direct joule heating experiments showing how the heating electrode could be damaged due to the formation of Al crystals and voids at the vicinity of the metal/NW contact, likely related with electro migration phenomena. We show that the contact quality can be preserved by including an additional ex situ RTA step prior to the in situ heating. The in situ observations also show in real time how the exchange reaction initiates simultaneously from several locations underneath the Al contact pad, and the Al crystal grows gradually inside the initial Ge NW with the growth interface along a Ge(111) lattice plane. Once the reaction front moves out from underneath the contact metal, two factors jeopardize an atomically accurate control of the Al/Ge reaction interface. We observed a local acceleration of the reaction interface due to the electron beam irradiation in the transmission electron microscope as well as the appearance of large jumps of the interface in unpassivated Ge wires while a smooth advancement of the reaction interface was observed in wires with an Al2O3 protecting shell on the surface. Carefully controlling all aspects of the exchange reaction, we demonstrate a fabrication process combining ex situ and in situ heating techniques to precisely control and produce axial Al/Ge/Al NW heterostructures with an ultra short Ge segment down to 8 nanometers. Practically, the scaling down of Ge segment length is only limited by the microscope resolution.
author_names: M A Luonga

E Robina

N Paucb

P Gentileb

M Sistanic

A Lugsteinc

M Spiesd

B Fernandezd

M I den Hertogd
title: In situ high resolution TEM observation of Aluminum solid state diffusion in Germanium nanowires: fabricating sub 10 nm Ge quantum dots
year: 2020

abstract: A comparative analysis is carried out of the growth peculiarities under molecular beam epitaxy of germanium quantum dots on the silicon surfaces with different crystallographic orientations Si(100) and Si(111) including the case of the presence of tin surfactant on the surface. The free energy change, activation barrier of nucleation, critical thickness of the transition from two dimensional growth to three dimensional one, as well as the surface density and size distribution function of quantum dots in these systems are calculated.
author_names: Andrey P Kokhanenko

Kirill A Lozovoy

Alexander V Voitsekhovskii
title: Comparison of the Growth Processes of Germanium Quantum Dots on the Si(100) and Si(111) Surfaces
year: 2018

abstract: Advancing quantum information processing is predicated on the preparation of ever larger multiqubit states. Photonic realizations of such states may be achieved by increasing the number of photons populating the state or the number of qubits encoded per photon. Typical approaches to the latter strategy utilize distinct degrees of freedom of the photon field. We present here an approach that encodes two qubits per photon in the spatial parity of its transverse spatial profile. Simple linear optical devices transform each parity qubit separately or the two qubits jointly. Furthermore, we demonstrate that entangled photon pairs produced by spontaneous parametric down conversion may be used to prepare arbitrary four qubit states through sculpting the spatial profile of the classical optical pump. Two examples are highlighted the preparation of two photon four qubit Greenberger Horne Zeilinger and W states, whose encoding in a photon pair has thus far eluded other approaches.
author_names: Ayman F Abouraddy

Timothy M Yarnall

Giovanni Di Giuseppe

Malvin Carl Teich

Bahaa E A Saleh
title: Encoding arbitrary four qubit states in the spatial parity of a photon pair
year: 2012

abstract: In this paper theoretical modeling of formation and growth of germanium silicon quantum dots in the method of molecular beam epitaxy (MBE) on different surfaces is carried out. Silicon substrates with crystallographic orientations (100) and (111) are considered. Special attention is paid to the question of growth of quantum dots on the silicon surface covered by tin, since germanium silicon tin system is extremely important for contemporary nano and optoelectronics: for creation of photodetectors, solar cells, light emitting diodes, and fast speed transistors. A theoretical approach for modeling growth processes of such semiconductor compounds during the MBE is presented. Both layer by layer and island nucleation stages in the Stranski Krastanow growth mode are described. A change in free energy during transition of atoms from the wetting layer to an island, activation barrier of the nucleation, critical thickness of 2D to 3D transition, as well as surface density and size distribution function of quantum dots in these systems are calculated with the help of the established model. All the theoretical speculations are carried out keeping in mind possible device applications of these materials. In particular, it is theoretically shown that using of the Si(100) surface covered by tin as a substrate for Ge deposition may be very promising for increasing size homogeneity of quantum dot array for possible applications in low noise selective quantum dot infrared photodetectors.
author_names: Kirill A Lozovoy

Andrey P Kokhanenko

Alexander V Voitsekhovskii
title: Comparative analysis of germanium silicon quantum dots formation on Si(100) Si(111) and Sn/Si(100) surfaces.
venue: Nanotechnology
year: 2018