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Semiconductor Quantum Computation

Xin Zhang, Hai-Ou Li, Gang Cao, Ming Xiao, Guang-Can Guo, Guo-Ping Guo

arXiv:1905.01592v1cond-mat.mes-hallquant-ph

TL;DR

Quantum computing needs qubits and reliable gates to limit accumulated errors and meet fault-tolerance requirements. This review surveys semiconductor qubit control and reports high-fidelity gates and a programmable two-qubit processor, while identifying material and scaling challenges.

  • Problem

    Fault-tolerant quantum computing requires high-fidelity gates because small errors can accumulate, and semiconductor platforms still face material and scalable-design challenges.

    Source: Introduction · p. 3, Material developments · p. 21

  • Method

    The review synthesizes semiconductor single- and two-qubit control progress alongside material developments and challenges.

    Source: Conclusion and outlook · p. 23

  • Results

    Purified-silicon spin control exceeded 99.9% fidelity, two-qubit gate fidelity reached 98%, and a programmable two-qubit quantum processor was demonstrated.

    Source: Spin-1/2 qubit · p. 6, Exchange interaction · pp. 13, 15

  • Takeaways & Limitations

    The review presents semiconductor quantum computation as advancing while identifying readout, materials, and scalable designs as continuing research challenges.

    Source: Conclusion and outlook · p. 23

    For donor spins separated by 16±1 nm, small tunnel coupling prevented measurement of coherent oscillations, indicating that closer spacing is needed for further research.

    Source: Exchange interaction · p. 15

Abstract

from arXiv · show

Semiconductors, a significant type of material in the information era, are becoming more and more powerful in the field of quantum information. In the last decades, semiconductor quantum computation was investigated thoroughly across the world and developed with a dramatically fast speed. The researches vary from initialization, control and readout of qubits, to the architecture of fault tolerant quantum computing. Here, we first introduce the basic ideas for quantum computing, and then discuss the developments of single- and two- qubit gate control in semiconductor. Till now, the qubit initialization, control and readout can be realized with relatively high fidelity and a programmable two-qubit quantum processor was even demonstrated. However, to further improve the qubit quality and scale it up, there are still some challenges to resolve such as the improvement of readout method, material development and scalable designs. We discuss these issues and introduce the forefronts of progress. Finally, considering the positive trend of the research on semiconductor quantum devices and recent theoretical work on the applications of quantum computation, we anticipate that semiconductor quantum computation may develop fast and will have a huge impact on our lives in the near future.

Introduction

Quantum computing uses qubits whose superposition and entanglement support quantum algorithms, while universal circuit computation requires arbitrary single-qubit rotations and two-qubit CNOT gates. Semiconductor devices have demonstrated high-fidelity gates and offer varied qubit platforms, though fault-tolerant computing requires adequate fidelity and scalable arrays.

Introduction

  • Quantum algorithms use superposition and entanglement to address problems including factorization, searching, optimization, and chemical simulation.The review describes these applications as offering nearly exponential speedup over classical computing for a variety of problems.Source: Introduction · p. 2
  • Arbitrary single-qubit rotations plus two-qubit CNOT gates form a universal gate set, and fault tolerance requires controlling errors against the surface-code threshold.The introduction gives a threshold above 99% for single- and two-qubit gate fidelities in a two-dimensional array.Source: Introduction · pp. 2–3
  • Semiconductor qubits include gate-defined quantum-dot electron spins, phosphorus donor spins, and charge qubits in double quantum dots.The review also identifies quantum dots across several material platforms and notes CMOS compatibility for silicon MOS and SOI technologies.Source: Introduction · p. 4
  • Single-qubit gate fidelity above 99.9% and two-qubit gate fidelity of 98% have been reported, while proposals use semiconductor processing tools to scale toward two-dimensional grids.The cited review relates these gate fidelities to approaching the surface-code threshold.Source: Introduction · pp. 3–4

Single qubit gate in semiconductor

Semiconductor single-qubit control spans several encodings, while spin-1/2 qubits use magnetic-resonance techniques and spin-to-charge readout. Reported silicon and donor experiments achieved high control fidelities, whereas hole-spin control remains less established.

Spin-1/2 qubit

  • Spin-1/2 qubits use ESR or NMR magnetic-field bursts, or EDSR electric driving with an effective oscillating magnetic field, to implement universal single-spin control.ESR/NMR bursts drive rotations about the Bloch sphere; EDSR applies microwave bursts to an electrode in a magnetic-field gradient.Source: Spin-1/2 qubit · p. 5
  • Spin-1/2 readout converts spin to charge through spin-selective tunneling or spin blockade, then detects charge with a nearby sensor.Spin blockade distinguishes singlet and triplet states by permitting the S(1,1) to S(0,2) transition while blocking triplet transitions; latching-enhanced readout reached 99.86% fidelity.Source: Spin-1/2 qubit · pp. 5–6
  • Purified silicon spin-1/2 control reached 99.6% fidelity, and EDSR-based silicon control exceeded 99.9%; donor nuclear-spin control exceeded 99.99%.The purified-silicon experiment reported T2* of 120 μs, while donor nuclear-spin dynamical-decoupling measurements found T2 above 30 seconds.Source: Spin-1/2 qubit · p. 6
  • Hole spins offer strong spin-orbit coupling and manipulation rates above 140 MHz, but measured dephasing times were at least tenfold shorter than for electron spins and single-hole control was unproven.The cited rotation time T2π was as short as about 7 ns.Source: Spin-1/2 qubit · pp. 6–7

Singlet-triplet qubit

Singlet-triplet qubits use exchange splitting and a Zeeman-energy difference to control two-spin states by tuning detuning. Work in GaAs and silicon has improved coherence and gate fidelity, while silicon valley states and particular readout arrangements constrain reproducibility and readout choices.

Singlet-triplet qubit

  • A large Zeeman-energy difference combined with real-time Hamiltonian estimation yielded a record single-qubit gate fidelity of about 99% in GaAs.The cited work reports that a large ΔE_z can suppress charge noise; the 99% figure is the reported gate fidelity.Source: Singlet-triplet qubit · p. 8
  • Tuning detuning changes exchange splitting relative to the Zeeman-energy difference, switching singlet-triplet qubit rotation between x and z axes without ESR or EDSR.When exchange splitting vanishes the qubit rotates around x; when it greatly exceeds the Zeeman-energy difference, rotation is around z.Source: Singlet-triplet qubit · p. 8
  • Dynamical nuclear polarization and decoupling improved GaAs coherence, with intrinsic T2 exceeding 200 μs and later reaching 870 μs.Silicon Si/SiGe singlet-triplet qubits reported T2* of about 360 ns, but small valley splitting can lift spin blockade and hinder reproducibility.Source: Singlet-triplet qubit · p. 8
  • Donor singlet-triplet qubits favor energy-selective or tunnel-rate-selective readout, while hybrid donor-dot implementations use latching-enhanced spin blockade.The donor charge-sensor arrangement makes the (1,1) and (0,2) transitions harder to distinguish.Source: Singlet-triplet qubit · p. 8

Exchange-only qubit

The section surveys exchange-only and charge qubits, outlining their encoding, control and readout approaches alongside reported coherence and control results. Both use detuning-dependent dynamics, with charge qubits also supporting direct charge sensing.

Exchange-only qubit

  • Exchange-only qubits encode two states of three spins in a triple quantum dot, with equal left and right exchange splittings in the central (1, 1, 1) configuration.Two additional states may provide leakage channels during control.Source: Exchange-only qubit · pp. 8–9
  • Exchange-only control uses detuning pulses to tune two exchange interactions whose Bloch-sphere axes are 120° apart, enabling universal single-qubit control.Reported approaches include Larmor precession, resonant Rabi oscillations and Landau-Zener-Stückelberg interference.Source: Exchange-only qubit · p. 9

Charge qubit

  • Charge qubits encode states in the excess-electron occupation of a double quantum dot and can be read directly with a charge sensor or transport current.The Hamiltonian combines detuning energy and inter-dot tunneling; pulsing to the anticrossing drives x-axis rotations, while detuning away supports z-axis rotations.Source: Charge qubit · pp. 9–10
  • 86% average qubit fidelity was reported for a resonant Si/SiGe charge qubit; LZS control also achieved rotations as short as ~10 ps and intrinsic dephasing time up to 4 ns.Hybridized silicon valley-orbit states were proposed as a possible route to higher-fidelity control because their energy band is flat over a wider detuning range.Source: Charge qubit · p. 10

Hybrid qubit

The hybrid qubit encodes three-electron spin states in a double quantum dot to combine spin-qubit coherence with charge-qubit manipulation speed. Control can use Larmor precession or Rabi oscillations, and later designs extended the approach beyond silicon valley-orbit states.

Hybrid qubit

  • The hybrid qubit encodes two eigenstates of three electron spins in a double quantum dot, motivated by combining long spin coherence with fast charge manipulation.Its higher state is identified as a primary leakage channel.Source: Hybrid qubit · pp. 11–12
  • Control and readout use distinct energy regimes: Larmor precession or Rabi oscillations drive control, while spin blockade in the charge-like region distinguishes the qubit states.The spin-like region has E_R as the splitting between the two encoded states.Source: Hybrid qubit · p. 12
  • Control fidelity reached 93% for x-axis and 96% for z-axis rotations with Rabi control, after earlier Larmor-control results of 85% and 94%, respectively.Later GaAs and triple-dot variants avoided reliance on silicon valley states; the triple-dot design offered tunable 2–15 GHz operation for frequency multiplexing.Source: Hybrid qubit · p. 12

Two qubit gate in semiconductor

Semiconductor two-qubit gates use several interactions, with exchange coupling enabling gates across multiple qubit types and operating regimes. Reported advances include high-fidelity gates, long-range coupling, and a programmable two-qubit processor.

Exchange interaction

  • The ratio of exchange coupling J to Zeeman energy difference ΔEz determines whether eigenstates are product-like or singlet-triplet-like, and which gates are available.The figure contrasts four regimes and shows detuning-dependent energy shifts when J is much smaller than ΔEz.Source: Exchange interaction · p. 13, Figure 4 · p. 14
  • The √SWAP gate was demonstrated on antiparallel-spin inputs in 180 ps, but the measurement method initially prevented testing parallel-spin inputs.Later single-shot readout enabled a full SWAP truth table across four input states.Source: Exchange interaction · p. 13
  • CZ control with dynamical decoupling supported Deutsch–Jozsa and Grover algorithms; randomized benchmarking measured ~91% gate fidelity.Bell-state tomography gave prepared-state fidelities of 85–89%, with the authors noting SPAM errors in that measurement.Source: Exchange interaction · pp. 13–14
  • 98% fidelity was reported for a CROT gate using constant exchange coupling and two-qubit randomized benchmarking in a purified silicon MOS DQD.A direct CNOT was also demonstrated by controlling inter-dot tunneling, with 78% Bell-state fidelity.Source: Exchange interaction · pp. 14–15
  • Exchange coupling can connect next-nearest-neighbor spins through an empty central dot or a multi-electron dot, and can also couple different qubit types.The review also describes coherent evolution after shuttling an entangled state to a farther dot.Source: Exchange interaction · p. 15
  • Donor-spin exchange requires atomic-scale donor placement; weak tunnel coupling in a device with donors 16±1 nm apart prevented coherent-oscillation measurement.Proposed alternatives relax placement requirements, but the review says these strategies remain to be realized.Source: Exchange interaction · p. 15

Coulomb interaction

Coulomb interaction couples charge configurations across double quantum dots and has been demonstrated for singlet-triplet and charge qubits. Reported results include entangling gates and controlled rotations, with controlled rotations also extended to three qubits.

Coulomb interaction

  • Coulomb-mediated two-qubit gates have been proposed for singlet-triplet, exchange-only, hybrid, and charge qubits; experiments had demonstrated them for singlet-triplet and charge qubits.The figure depicts singlet-triplet and charge-qubit devices and charge-qubit CROT outputs.Source: Coulomb interaction · p. 15, Figure 5 · p. 16
  • A Coulomb-mediated singlet-triplet entangling gate produced a Bell state with 72% fidelity; a later report using a dominating magnetic gradient measured 90% fidelity.The gate is equivalent to a CZ gate up to single-qubit rotations.Source: Coulomb interaction · pp. 15–16
  • Charge-qubit CROT control used the lower-qubit state to shift the upper qubit’s detuning anticrossing, yielding an extracted control fidelity of ~68%.The experiments used electrostatically coupled DQDs and measured the CROT truth table.Source: Coulomb interaction · p. 17
  • Three-qubit controlled rotations were demonstrated with three coupled GaAs DQDs, described as a first attempt beyond the two-qubit limit in semiconductor devices.The review says this result suggests semiconductor qubits are amenable to large-scale manufacture.Source: Coulomb interaction · p. 17

Coupling to the resonator

Resonator coupling provides a route to connect distant semiconductor qubits, but dephasing and photon loss impeded two-qubit gate control. Strong coupling and subsequent photon-mediated coupling demonstrations advanced this approach, while spin-qubit gates remained a future goal.

Coupling to the resonator

  • The Jaynes–Cummings-type Hamiltonian combines resonator photons, the double-quantum-dot transition, and photon–DQD coupling.Detuning and tunneling set the DQD transition frequency and the coupling factor sin θ.Source: Coupling to the resonator · p. 17
  • Changing DQD detuning or tunneling modifies the Hamiltonian and the resonator photons, changing the transmitted or reflected signal’s phase and amplitude.Source: Coupling to the resonator · p. 17
  • Qubit dephasing and photon loss impeded resonator-mediated two-qubit gate control, motivating a strong-coupling regime where g_c exceeds both rates.Source: Coupling to the resonator · pp. 17–18
  • Since 2016, strong resonator–DQD coupling was reported across Si/SiGe, GaAs/AlGaAs, and carbon nanotubes; later work demonstrated tunable photon-mediated charge-qubit coupling and strong spin-photon coupling.Coherent spin-qubit coupling and two-qubit gates were identified as directions for further exploration.Source: Coupling to the resonator · p. 18

Challenges and opportunities

The review presents recent high-fidelity single- and two-qubit control as a developing basis for scalable fault-tolerant computing, while noting unresolved challenges and discussing progress on them.

Challenges and opportunities

  • Despite advances in semiconductor single- and two-qubit control, challenges remain before the field’s next step toward a scalable fault-tolerant fabric.The section introduces these challenges alongside research progress addressing them.Source: Challenges and opportunities · p. 18

Readout of qubits

The review surveys approaches to improve semiconductor-qubit readout, whose speed and fidelity depend on charge-sensor bandwidth and signal-to-noise ratio. Reported methods include rf charge sensing, cryogenic amplification, and resonator-based readout, with a best stated fidelity of 99.7% at 1 kHz bandwidth for rf gate sensors.

Readout of qubits

  • Charge sensitivity combines sensor bandwidth and signal-to-noise ratio; a room-temperature transconductance-amplifier sensor reached 820 μe/√Hz at 30 kHz bandwidth.Source: Readout of qubits · p. 18
  • Rf-SETs and rf-QPCs offered charge sensitivity below 200 μe/√Hz with bandwidth over 1 MHz; an rf-QPC achieved over 90% single-shot fidelity at about 143 kHz.An rf-SET was also used for singlet-triplet readout at 10 MHz bandwidth.Source: Readout of qubits · p. 18
  • At 100 kHz bandwidth, a cryogenic two-stage HEMT achieved SNR 9 and charge sensitivity 300 μe/√Hz, nearly twice as good as the room-temperature-amplifier reference.The adjacent cryogenic circuit also enabled single-shot donor-spin readout with 96% Rabi-oscillation visibility.Source: Readout of qubits · p. 19
  • 99.7% readout fidelity was the best reported for rf-gate-sensor single-shot readout of singlet-triplet qubits, at 1 kHz bandwidth.The reported devices included silicon donors, silicon MOS double dots, and silicon SOI double dots.Source: Readout of qubits · p. 19
  • Distributed superconducting resonators supported qubit readout and frequency multiplexing; a JPA-amplified setup reported 80 μe/√Hz charge sensitivity at 2.6 MHz bandwidth.Resonator readout also enabled dispersive spin-qubit readout and was used in proposals and demonstrations of multiplexed readout.Source: Readout of qubits · p. 19
  • Figure 6 juxtaposes four readout-device approaches with a crossbar-network model and schematic for connecting a two-dimensional quantum-dot array to outside circuitry.Source: Figure 6 · p. 20

Material developments

Scaling semiconductor qubits depends on substrate properties and device design: silicon reduces some spin-noise concerns but brings valley and confinement challenges, while germanium is promising but still requires further validation. Overlapping-gate designs and alternative silicon platforms have demonstrated progress in dot-array fabrication and operation.

Material developments

  • The largest number of qubits controlled in one device was no more than four, while substrate choices trade GaAs mobility and quality against nuclear noise and silicon’s valley and confinement challenges.Purified silicon with less Si29 was among the alternatives pursued to reduce spin noise.Source: Material developments · pp. 20–21
  • Silicon-dot valley splitting complicates qubit control; reported values were 300–800 μeV in MOS, 610–880 μeV in SOI, and 35–270 μeV in Si/SiGe.MOS and SOI splitting could be controlled by electric field, whereas Si/SiGe values varied considerably across samples.Source: Material developments · p. 21
  • Overlapping-gate designs use small electrodes to form dots; Si/SiGe implementations achieved a reproducible nine-dot linear array and shuttled a single charge across it.Silicon MOS dots reached lithographic diameters of 30–40 nm, while Si/SiGe dot-forming electrodes were usually about 80 nm.Source: Material developments · pp. 21–22
  • Silicon MOS devices had no more than four working quantum dots in the cited reports, while poly-Si single-layer gates and SOI offered alternative designs.Source: Material developments · p. 22
  • Germanium can host hole-spin qubits, be isotopically purified, and avoid valley degeneracy, but high-fidelity gates and material homogeneity and reproducibility still need verification.Source: Material developments · p. 22

Scalable design

Scaling semiconductor qubits to tens or hundreds requires architectures that balance wiring feasibility with high-quality performance. Proposed designs remain ahead of experimental demonstrations of two-dimensional dot tuning and charge sensing.

Scalable design

  • Proposed scaling architectures include silicon spin-qubit crossbars, two-dimensional donor lattices, and hybrid donor-dot or flip-flop designs.The review identifies scaling to tens and hundreds of qubits as the next challenge after high-fidelity single- and two-qubit control and readout.Source: Scalable design · p. 22
  • Crossbar designs share control lines, so local operations may cause unwanted effects elsewhere; more direct floating-gate connections trade this risk for greater manufacturing demands.The crossbar also uses layered barrier and plunger lines, shuttling, and global magnetic fields to support loading, control, gates, and readout.Source: Scalable design · p. 22
  • Two-dimensional dot tuning and charge sensing have not yet been demonstrated simultaneously in experiments, leaving a gap between proposed architectures and reproducible devices.The review calls for more experiments to close this gap.Source: Scalable design · pp. 22–23

Conclusion and outlook

The review surveys semiconductor single- and two-qubit control and discusses challenges in readout, materials, and scaling. It anticipates rapid development and significant impact, while noting that near-term NISQ applications could bring research and business opportunities.

Conclusion and outlook

  • The review surveys control of different semiconductor qubits and discusses challenges and opportunities in readout methods, materials, and scalable designs.The authors say space and the writer’s knowledge limit coverage of other emerging or proposed qubit types.Source: Conclusion and outlook · p. 23
  • Several groups aim to improve qubit quality for large-scale integration and scale semiconductor devices to ten or more qubits within the next ten years.The review names groups in the Netherlands and Australia and the French Alternative Energies and Atomic Energy Commission.Source: Conclusion and outlook · p. 23
  • Near-term NISQ applications could bring new opportunities for research and business, even though these devices will not change the world immediately.NISQ is described as 50–100 qubits, capable of surpassing current classical computers, with low circuit depth limited by insufficient control fidelity.Source: Conclusion and outlook · p. 23
  • The authors anticipate that semiconductor quantum devices may develop rapidly and have a major impact on people’s lives.They connect this outlook to further qubit-quality improvements, fault-tolerant computing, and research on new applications.Source: Conclusion and outlook · p. 23
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