Universal logic with encoded spin qubits in silicon.

Quantum computation features known examples of hardware acceleration for certain problems, but is challenging to realize because of its susceptibility to small errors from noise or imperfect control. The principles of fault tolerance may enable computational acceleration with imperfect hardware, but they place strict requirements on the character and correlation of errors1. For many qubit technologies2-21, some challenges to achieving fault tolerance can be traced to correlated errors arising from the need to control qubits by injecting microwave energy matching qubit resonances. Here we demonstrate an alternative approach to quantum computation that uses energy-degenerate encoded qubit states controlled by nearest-neighbour contact interactions that partially swap the spin states of electrons with those of their neighbours. Calibrated sequences of such partial swaps, implemented using only voltage pulses, allow universal quantum control while bypassing microwave-associated correlated error sources1,22-28. We use an array of six 28Si/SiGe quantum dots, built using a platform that is capable of extending in two dimensions following processes used in conventional microelectronics29. We quantify the operational fidelity of universal control of two encoded qubits using interleaved randomized benchmarking30, finding a fidelity of 96.3% ± 0.7% for encoded controlled NOT operations and 99.3% ± 0.5% for encoded SWAP. The quantum coherence offered by enriched silicon5-9,16,18,20,22,27,29,31-37, the all-electrical and low-crosstalk-control of partial swap operations1,22-28 and the configurable insensitivity of our encoding to certain error sources28,33,34,38 all combine to offer a strong pathway towards scalable fault tolerance and computational advantage.

Complete quantum control of a single quantum dot spin using ultrafast optical pulses.

A basic requirement for quantum information processing systems is the ability to completely control the state of a single qubit. For qubits based on electron spin, a universal single-qubit gate is realized by a rotation of the spin by any angle about an arbitrary axis. Driven, coherent Rabi oscillations between two spin states can be used to demonstrate control of the rotation angle. Ramsey interference, produced by two coherent spin rotations separated by a variable time delay, demonstrates control over the axis of rotation. Full quantum control of an electron spin in a quantum dot has previously been demonstrated using resonant radio-frequency pulses that require many spin precession periods. However, optical manipulation of the spin allows quantum control on a picosecond or femtosecond timescale, permitting an arbitrary rotation to be completed within one spin precession period. Recent work in optical single-spin control has demonstrated the initialization of a spin state in a quantum dot, as well as the ultrafast manipulation of coherence in a largely unpolarized single-spin state. Here we demonstrate complete coherent control over an initialized electron spin state in a quantum dot using picosecond optical pulses. First we vary the intensity of a single optical pulse to observe over six Rabi oscillations between the two spin states; then we apply two sequential pulses to observe high-contrast Ramsey interference. Such a two-pulse sequence realizes an arbitrary single-qubit gate completed on a picosecond timescale. Along with the spin initialization and final projective measurement of the spin state, these results demonstrate a complete set of all-optical single-qubit operations.

Entangling single photons from independently tuned semiconductor nanoemitters.

Quantum communication systems based on nanoscale semiconductor devices is challenged by inhomogeneities from device to device. We address this challenge using ZnMgSe/ZnSe quantum-well nanostructures with local laser-based heating to tune the emission of single impurity-bound exciton emitters in two separate devices. The matched emission in combination with photon bunching enables quantum interference from the devices and allows the postselection of polarization-entangled single photons. The ability to entangle single photons emitted from nanometer-sized sources separated by macroscopic distances provides an essential step for a solid-state realization of a large-scale quantum optical network. This paves the way toward measurement-based entanglement generation between remote electron spins localized at macroscopically separated fluorine impurities.

Surface code quantum communication.

Quantum communication typically involves a linear chain of repeater stations, each capable of reliable local quantum computation and connected to their nearest neighbors by unreliable communication links. The communication rate of existing protocols is low as two-way classical communication is used. By using a surface code across the repeater chain and generating Bell pairs between neighboring stations with probability of heralded success greater than 0.65 and fidelity greater than 0.96, we show that two-way communication can be avoided and quantum information can be sent over arbitrary distances with arbitrarily low error at a rate limited only by the local gate speed. This is achieved by using the unreliable Bell pairs to measure nonlocal stabilizers and feeding heralded failure information into post-transmission error correction. Our scheme also applies when the probability of heralded success is arbitrarily low.

Pulsed nuclear pumping and spin diffusion in a single charged quantum dot.

We report the observation of a feedback process between the nuclear spins in a single charged quantum dot under coherently pulsed optical excitation and its trion transition. The optical pulse sequence intersperses resonant narrow-band pumping for spin initialization with off-resonant ultrafast pulses for coherent electron-spin rotation. A hysteretic sawtooth pattern in the free-induction decay of the single electron spin is observed; a mathematical model indicates a competition between optical nuclear pumping and nuclear spin-diffusion. This effect allows dynamic tuning of the electron Larmor frequency to a value determined by the pulse timing, potentially allowing more complex coherent control operations.

Controllable freezing of the nuclear spin bath in a single-atom spin qubit.

The quantum coherence and gate fidelity of electron spin qubits in semiconductors are often limited by nuclear spin fluctuations. Enrichment of spin-zero isotopes in silicon markedly improves the dephasing time [Formula: see text], which, unexpectedly, can extend two orders of magnitude beyond theoretical expectations. Using a single-atom 31P qubit in enriched 28Si, we show that the abnormally long [Formula: see text] is due to the freezing of the dynamics of the residual 29Si nuclei, caused by the electron-nuclear hyperfine interaction. Inserting a waiting period when the electron is controllably removed unfreezes the nuclear dynamics and restores the ergodic [Formula: see text] value. Our conclusions are supported by a nearly parameter-free modeling of the 29Si nuclear spin dynamics, which reveals the degree of backaction provided by the electron spin. This study clarifies the limits of ergodic assumptions in nuclear bath dynamics and provides previously unidentified strategies for maximizing coherence and gate fidelity of spin qubits in semiconductors.

A silicon quantum-dot-coupled nuclear spin qubit.

Single nuclear spins in the solid state are a potential future platform for quantum computing1-3, because they possess long coherence times4-6 and offer excellent controllability7. Measurements can be performed via localized electrons, such as those in single atom dopants8,9 or crystal defects10-12. However, establishing long-range interactions between multiple dopants or defects is challenging13,14. Conversely, in lithographically defined quantum dots, tunable interdot electron tunnelling allows direct coupling of electron spin-based qubits in neighbouring dots15-20. Moreover, the compatibility with semiconductor fabrication techniques21 may allow for scaling to large numbers of qubits in the future. Unfortunately, hyperfine interactions are typically too weak to address single nuclei. Here we show that for electrons in silicon metal-oxide-semiconductor quantum dots the hyperfine interaction is sufficient to initialize, read out and control single 29Si nuclear spins. This approach combines the long coherence times of nuclear spins with the flexibility and scalability of quantum dot systems. We demonstrate high-fidelity projective readout and control of the nuclear spin qubit, as well as entanglement between the nuclear and electron spins. Crucially, we find that both the nuclear spin and electron spin retain their coherence while moving the electron between quantum dots. Hence we envision long-range nuclear-nuclear entanglement via electron shuttling3. Our results establish nuclear spins in quantum dots as a powerful new resource for quantum processing.

Quantifying error and leakage in an encoded Si/SiGe triple-dot qubit.

Quantum computation requires qubits that satisfy often-conflicting criteria, which include long-lasting coherence and scalable control1. One approach to creating a suitable qubit is to operate in an encoded subspace of several physical qubits. Although such encoded qubits may be particularly susceptible to leakage out of their computational subspace, they can be insensitive to certain noise processes2,3 and can also allow logical control with a single type of entangling interaction4 while maintaining favourable features of the underlying physical system. Here we demonstrate high-fidelity operation of an exchange-only qubit encoded in a subsystem of three coupled electron spins5 confined in gated, isotopically enhanced silicon quantum dots6. This encoding requires neither high-frequency electric nor magnetic fields for control, and instead relies exclusively on the exchange interaction4,5, which is highly local and can be modulated with a large on-off ratio using only fast voltage pulses. It is also compatible with very low and gradient-free magnetic field environments, which simplifies integration with superconducting materials. We developed and employed a modified blind randomized benchmarking protocol that determines both computational and leakage errors7,8, and found that unitary operations have an average total error of 0.35%, with half of that, 0.17%, coming from leakage driven by interactions with substrate nuclear spins. The combination of this proven performance with complete control via gate voltages makes the exchange-only qubit especially attractive for use in many-qubit systems.

Quantum computers based on electron spins controlled by ultrafast off-resonant single optical pulses.

We describe a fast quantum computer based on optically controlled electron spins in charged quantum dots that are coupled to microcavities. This scheme uses broadband optical pulses to rotate electron spins and provide the clock signal to the system. Nonlocal two-qubit gates are performed by phase shifts induced by electron spins on laser pulses propagating along a shared waveguide. Numerical simulations of this scheme demonstrate high-fidelity single-qubit and two-qubit gates with operation times comparable to the inverse Zeeman frequency.

Isotopically enhanced triple-quantum-dot qubit.

Like modern microprocessors today, future processors of quantum information may be implemented using all-electrical control of silicon-based devices. A semiconductor spin qubit may be controlled without the use of magnetic fields by using three electrons in three tunnel-coupled quantum dots. Triple dots have previously been implemented in GaAs, but this material suffers from intrinsic nuclear magnetic noise. Reduction of this noise is possible by fabricating devices using isotopically purified silicon. We demonstrate universal coherent control of a triple-quantum-dot qubit implemented in an isotopically enhanced Si/SiGe heterostructure. Composite pulses are used to implement spin-echo type sequences, and differential charge sensing enables single-shot state readout. These experiments demonstrate sufficient control with sufficiently low noise to enable the long pulse sequences required for exchange-only two-qubit logic and randomized benchmarking.

Indistinguishable photons from independent semiconductor nanostructures.

We demonstrate quantum interference between photons generated by the radiative decay processes of excitons that are bound to isolated fluorine donor impurities in ZnSe/ZnMgSe quantum-well nanostructures. The ability to generate single photons from these devices is confirmed by autocorrelation experiments, and the indistinguishability of photons emitted from two independent nanostructures is confirmed via a Hong-Ou-Mandel dip. These results indicate that donor impurities in appropriately engineered semiconductor structures can portray atomlike homogeneity and coherence properties, potentially enabling scalable technologies for future large-scale optical quantum computers and quantum communication networks.

Ultrafast optical spin echo for electron spins in semiconductors.

Spin-based quantum computing and magnetic resonance techniques rely on the ability to measure the coherence time T(2) of a spin system. We report on the experimental implementation of all-optical spin echo to determine the T(2) time of a semiconductor electron-spin system. We use three ultrafast optical pulses to rotate spins an arbitrary angle and measure an echo signal as the time between pulses is lengthened. Unlike previous spin-echo techniques using microwaves, ultrafast optical pulses allow clean T(2) measurements of systems with dephasing times (T_{2};{*}) fast in comparison to the time scale for microwave control. This demonstration provides a step toward ultrafast optical dynamic decoupling of spin-based qubits.