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Quantum Computing with Semiconductor Spins Lieven M Quantum computing with semiconductor spins Lieven M. K. Vandersypen, and Mark A. Eriksson Citation: Physics Today 72, 8, 38 (2019); doi: 10.1063/PT.3.4270 View online: https://doi.org/10.1063/PT.3.4270 View Table of Contents: https://physicstoday.scitation.org/toc/pto/72/8 Published by the American Institute of Physics ARTICLES YOU MAY BE INTERESTED IN Teleportation for device-scale quantum computing Physics Today 72, 21 (2019); https://doi.org/10.1063/PT.3.4266 Physics in the former Yugoslavia: From socialist dreams to capitalist realities Physics Today 72, 30 (2019); https://doi.org/10.1063/PT.3.4269 The mathematics and physics of electronic structure theory Physics Today 72, 56 (2019); https://doi.org/10.1063/PT.3.4274 The North American eclipse of 1869 Physics Today 72, 46 (2019); https://doi.org/10.1063/PT.3.4271 A systems perspective of quantum computing Physics Today 72, 40 (2019); https://doi.org/10.1063/PT.3.4163 Fifth-generation broadband wireless threatens weather forecasting Physics Today 72, 24 (2019); https://doi.org/10.1063/PT.3.4267 QUANTUM COMPUTING with semiconductor spins Lieven M. K. Vandersypen and Mark A. Eriksson Arrays of electrically and magnetically controllable electron-spin qubits can be lithographically fabricated on silicon wafers. INTEL CORP 38 PHYSICS TODAY | AUGUST 2019 Lieven Vandersypen is an Antoni van Leeuwenhoek Professor in the Kavli Institute of Nanoscience Delft and QuTech, a research center of Delft University of Technology in the Netherlands. Mark Eriksson is a Vilas Distinguished Achievement Professor in the department of physics at the University of Wisconsin–Madison. pen any textbook on quantum mechanics, other. And when the second qubit it- and the two-state system of choice is self starts off in a superposition of states, the two qubits become entan- 1 likely to be a spin- ⁄2 particle, such as an gled with each other. The recent satis- electron. The corresponding states, spin up faction of all those requirements with quantum dots led to the demonstra- and spin down, form the prototypical quantum tion of the first—and at two qubits the bit (qubit), and rotations of the spin state constitute the simplest smallest possible—quantum semi- quantum logic gates. Because of their negative charge, electrons can be conductor processor. That single-electron spins in a manipulated with voltages applied to nanoscale electrodes, or gates. semiconductor chip can act as qubits And the application of appropriate voltages can confine the electrons is remarkable. Unlike atoms or photons to small islands called quantum dots (see the article by Marc Kastner, in a vacuum, an electron in a semi - conductor resides in a noisy, solid-state PHYSICS TODAY, January 1993, page 24). environment. Engineering that envi- ronment so that it doesn’t rapidly de- Twenty years ago Daniel Loss and David DiVincenzo grade or decohere the spin-qubit states has been a key chal- proposed that the spin of a single electron in a semi - lenge for our field. conductor quantum dot could form not just a model but Errors are unavoidable and necessitate quantum error- also a real, physical qubit.1 Their theoretical work pre- correction techniques (see PHYSICS TODAY, February 2005, dated by four years the first experiments to success- page 19). To be effective, the techniques require that initializa- fully trap a single electron in a gate-defined quantum tion, readout, and single- and two-qubit operations have error dot, and it predated by several more years the first co- rates below 1%. Furthermore, quantum error correction involves herent manipulation of a single spin in a semiconduc- an overhead in the number of qubits that can easily reach 1000 tor. Semiconductor spin qubits now come in four dis- physical error-prone qubits to encode one protected error-free tinct flavors, each of which was proposed by theory qubit. Therefore, a future quantum computer capable of solv- that set a target for experiments to pursue. Those exper- ing relevant problems beyond the reach of a supercomputer iments always brought surprises, and the interplay be- will likely contain millions of physical qubits. (See the article tween theory and experiment makes semiconductor spin by David Weiss and Mark Saffman, PHYSICS TODAY, July 2017, qubits a particularly vibrant field of study. page 44.) In this article we describe the experimental develop- Semiconductor quantum dots have a tiny footprint that of- ment and the current state of the art of semiconductor quan- fers the prospect of integrating millions of qubits, akin to clas- tum-dot spin qubits. Functional and scalable qubits must sical integrated circuits. The corresponding electron density in meet well-defined criteria.2 First, reliably initializing each qubit quantum-dot devices, however, is far smaller than in classical into one of its two levels must be possible. Second, the final transistors, with each single electron in a qubit typically spread state of each qubit must be knowable by a projective measure- over a region roughly 20 nm × 20 nm in size. For such a device ment that gives the correct answer with high probability. Third, to work as intended, the materials and nanofabricated struc- qubit manipulation must be implementable using high-quality tures must have very little disorder, to ensure that electrons are single- and two-qubit gates. easy to position and control. Pulling off that achievement en- Imagine the spin state as a vector pointing on a sphere, com- tails uniform patterning of the gate electrodes but also having monly known as the Bloch sphere. Single-qubit gates corre- low densities of trapped charges in the substrate, in the di- spond to rotations of the state vector that are independent of electrics, and at the interfaces. the state of any other qubit in the system. In the case of two- Because of the need for ultrahigh quality, the path to a large- qubit gates, rotation of one qubit depends on the state of the scale quantum computer of any type is a marathon, not a AUGUST 2019 | PHYSICS TODAY 39 SEMICONDUCTOR SPINS x a FIGURE 1. A SCHEMATIC OF TWO TUNNEL-COUPLED QUANTUM DOTS. (a) Two patterned metal layers separated by dielectrics (not shown) define the quantum dots. Voltages applied to the lower-layer gates (orange) delimit the channel, which runs parallel to the x-axis. Voltages applied to the upper-layer gates (blue) shape the potential landscape along the channel as shown in the panel b cross section. (b) An electron is confined in each of two local potential minima, the two quantum dots. Tunnel barriers separate the dots from each other and from electron reservoirs. The reservoirs, whose highest occupied electron E level is at the Fermi energy F, are connected to contacts via implant regions. Upper gate layer b E E Lower gate layer F Implant region x Contact Quantum dots Reservoir sprint. And research today is motivated by a vision that will energy minimum separated from the contact regions by poten- take years to bring to fruition. In the case of semiconductor spin tial barriers. qubits, that vision relies on long coherence times and on recent At low temperature, typically below 4 K, the thermal energy advances in gate fidelity—a common metric to express the is lower than the energy needed to add or remove electrons quality of quantum gates—fueled by a move to silicon-based from the potential well. Thus the well is occupied by a discrete devices. number of electrons. When the electrons are confined tightly Intriguingly, spin qubits in semiconductors could also be enough that orbital motion is frozen out quantum mechani- integrated with classical integrated-circuit technology, includ- cally, the device is known as a quantum dot. ing processing, memory, and the distribution of signals. Inte- Arrays of tunnel-coupled quantum dots can be formed with gration on chip is natural, because quantum-dot qubits use gate additional gate electrodes, as shown in figure 1. The voltages electrodes just as field-effect transistors do. Integration could also on the blue gate electrodes control the depth of the potential occur at the system level, with clusters of chips communicating minima and thereby the number of electrons on each quantum with one another. dot. The voltages on the hatched blue gates control the tunnel barriers between adjacent dots and between the dots and the From transistor to qubit reservoirs. Nowadays, quantum dots are routinely tuned to The field-effect transistor is a good starting point for under- the limit in which just a single electron resides on each dot. standing a quantum dot. In a transistor, the flow of electrons Researchers can verify the tuning by monitoring the current between two contacts (source and drain) is switched on or through an auxiliary nearby quantum dot that acts as an off via the voltage on a metal gate electrode placed above the electrometer. space between the contacts (the channel). A positive gate volt- age attracts electrons to the channel and produces a conducting Spin qubits path from source to drain. A negative gate voltage, by contrast, When one electron resides in each quantum dot in the presence empties the channel such that no source–drain current can of a magnetic field, each electron spin becomes an appealing flow. If one were to replace the gate electrode with three in - qubit. Indeed, that simple configuration, with one electron in dependently biased electrodes, the electronic potential landscape one dot, was proposed by Loss and DiVincenzo in 1998. In sub- between the contacts could be shaped to create a potential- sequent years, alternative spin qubits have made their debut. 40 PHYSICS TODAY | AUGUST 2019 HOW TO INITIALIZE, MANIPULATE, AND READ OUT A SPIN QUBIT Reading out the spin state of an electron on readout, after which an electron with a the rotation axis, and its duration controls a quantum dot involves making a so-called known spin resides in the dot.
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