Radio-Frequency-Detected Fast Charge Sensing in Undoped Silicon Quantum Dots

Spin-EPR-pair separation by conveyor-mode single electron shuttling in Si/SiGe

Long-ranged coherent qubit coupling is a missing function block for scaling up spin qubit based quantum computing solutions. Spin-coherent conveyor-mode electron-shuttling could enable spin quantum-chips with scalable and sparse qubit-architecture. Its key feature is the operation by only few easily tuneable input terminals and compatibility with industrial gate-fabrication. Single electron shuttling in conveyor-mode in a 420 nm long quantum bus has been demonstrated previously. Here we investigate the spin coherence during conveyor-mode shuttling by separation and rejoining an Einstein-Podolsky-Rosen (EPR) spin-pair. Compared to previous work we boost the shuttle velocity by a factor of 10000. We observe a rising spin-qubit dephasing time with the longer shuttle distances due to motional narrowing and estimate the spin-shuttle infidelity due to dephasing to be 0.7% for a total shuttle distance of nominal 560 nm. Shuttling several loops up to an accumulated distance of 3.36 μm, spin-entanglement of the EPR pair is still detectable, giving good perspective for our approach of a shuttle-based scalable quantum computing architecture in silicon.

Determination of exciton binding energy using photocurrent spectroscopy of Ge quantum-dot single-hole transistors under CW pumping

We reported exciton binding-energy determination using tunneling-current spectroscopy of Germanium (Ge) quantum dot (QD) single-hole transistors (SHTs) operating in the few-hole regime, under 405-1550 nm wavelength (λ) illumination. When the photon energy is smaller than the bandgap energy (1.46 eV) of a 20 nm Ge QD (for instance, λ = 1310 nm and 1550 nm illuminations), there is no change in the peak voltages of tunneling current spectroscopy even when the irradiation power density reaches as high as 10 µW/µm2. In contrast, a considerable shift in the first hole-tunneling current peak towards positive VG is induced (ΔVG ≈ 0.08 V at 0.33 nW/µm2 and 0.15 V at 1.4 nW/µm2) and even additional photocurrent peaks are created at higher positive VG values (ΔVG ≈ 0.2 V at 10 nW/µm2 irradiation) by illumination at λ = 850 nm (where the photon energy matches the bandgap energy of the 20 nm Ge QD). These experimental observations were further strengthened when Ge-QD SHTs were illuminated by λ = 405 nm lasers at much lower optical-power conditions. The newly-photogenerated current peaks are attributed to the contribution of exciton, biexciton, and positive trion complexes. Furthermore, the exciton binding energy can be determined by analyzing the tunneling current spectra.

Wigner-molecularization-enabled dynamic nuclear polarization

Multielectron semiconductor quantum dots (QDs) provide a novel platform to study the Coulomb interaction-driven, spatially localized electron states of Wigner molecules (WMs). Although Wigner-molecularization has been confirmed by real-space imaging and coherent spectroscopy, the open system dynamics of the strongly correlated states with the environment are not yet well understood. Here, we demonstrate efficient control of spin transfer between an artificial three-electron WM and the nuclear environment in a GaAs double QD. A Landau-Zener sweep-based polarization sequence and low-lying anticrossings of spin multiplet states enabled by Wigner-molecularization are utilized. Combined with coherent control of spin states, we achieve control of magnitude, polarity, and site dependence of the nuclear field. We demonstrate that the same level of control cannot be achieved in the non-interacting regime. Thus, we confirm the spin structure of a WM, paving the way for active control of correlated electron states for application in mesoscopic environment engineering.

A shuttling-based two-qubit logic gate for linking distant silicon quantum processors

Control of entanglement between qubits at distant quantum processors using a two-qubit gate is an essential function of a scalable, modular implementation of quantum computation. Among the many qubit platforms, spin qubits in silicon quantum dots are promising for large-scale integration along with their nanofabrication capability. However, linking distant silicon quantum processors is challenging as two-qubit gates in spin qubits typically utilize short-range exchange coupling, which is only effective between nearest-neighbor quantum dots. Here we demonstrate a two-qubit gate between spin qubits via coherent spin shuttling, a key technology for linking distant silicon quantum processors. Coherent shuttling of a spin qubit enables efficient switching of the exchange coupling with an on/off ratio exceeding 1000, while preserving the spin coherence by 99.6% for the single shuttling between neighboring dots. With this shuttling-mode exchange control, we demonstrate a two-qubit controlled-phase gate with a fidelity of 93%, assessed via randomized benchmarking. Combination of our technique and a phase coherent shuttling of a qubit across a large quantum dot array will provide feasible path toward a quantum link between distant silicon quantum processors, a key requirement for large-scale quantum computation.

A coherent quantum link between distant quantum processors is desirable for scaling up of quantum computation. Noiri et al. demonstrate a strategy to link distant quantum processors in silicon, by implementing a shuttling-based two-qubit gate between spin qubits in a Si/SiGe triple quantum dot.

Universal control of a six-qubit quantum processor in silicon

Future quantum computers capable of solving relevant problems will require a large number of qubits that can be operated reliably1. However, the requirements of having a large qubit count and operating with high fidelity are typically conflicting. Spins in semiconductor quantum dots show long-term promise2,3 but demonstrations so far use between one and four qubits and typically optimize the fidelity of either single- or two-qubit operations, or initialization and readout4-11. Here, we increase the number of qubits and simultaneously achieve respectable fidelities for universal operation, state preparation and measurement. We design, fabricate and operate a six-qubit processor with a focus on careful Hamiltonian engineering, on a high level of abstraction to program the quantum circuits, and on efficient background calibration, all of which are essential to achieve high fidelities on this extended system. State preparation combines initialization by measurement and real-time feedback with quantum-non-demolition measurements. These advances will enable testing of increasingly meaningful quantum protocols and constitute a major stepping stone towards large-scale quantum computers.

Quantum error correction with silicon spin qubits

Future large-scale quantum computers will rely on quantum error correction (QEC) to protect the fragile quantum information during computation1,2. Among the possible candidate platforms for realizing quantum computing devices, the compatibility with mature nanofabrication technologies of silicon-based spin qubits offers promise to overcome the challenges in scaling up device sizes from the prototypes of today to large-scale computers3-5. Recent advances in silicon-based qubits have enabled the implementations of high-quality one-qubit and two-qubit systems6-8. However, the demonstration of QEC, which requires three or more coupled qubits1, and involves a three-qubit gate9-11 or measurement-based feedback, remains an open challenge. Here we demonstrate a three-qubit phase-correcting code in silicon, in which an encoded three-qubit state is protected against any phase-flip error on one of the three qubits. The correction to this encoded state is performed by a three-qubit conditional rotation, which we implement by an efficient single-step resonantly driven iToffoli gate. As expected, the error correction mitigates the errors owing to one-qubit phase-flip, as well as the intrinsic dephasing mainly owing to quasi-static phase noise. These results show successful implementation of QEC and the potential of a silicon-based platform for large-scale quantum computing.

Fast universal quantum gate above the fault-tolerance threshold in silicon

Fault-tolerant quantum computers that can solve hard problems rely on quantum error correction¹. One of the most promising error correction codes is the surface code², which requires universal gate fidelities exceeding an error correction threshold of 99 per cent³. Among the many qubit platforms, only superconducting circuits⁴, trapped ions⁵ and nitrogen-vacancy centres in diamond⁶ have delivered this requirement. Electron spin qubits in silicon^7-15 are particularly promising for a large-scale quantum computer owing to their nanofabrication capability, but the two-qubit gate fidelity has been limited to 98 per cent owing to the slow operation¹⁶. Here we demonstrate a two-qubit gate fidelity of 99.5 per cent, along with single-qubit gate fidelities of 99.8 per cent, in silicon spin qubits by fast electrical control using a micromagnet-induced gradient field and a tunable two-qubit coupling. We identify the qubit rotation speed and coupling strength where we robustly achieve high-fidelity gates. We realize Deutsch-Jozsa and Grover search algorithms with high success rates using our universal gate set. Our results demonstrate universal gate fidelity beyond the fault-tolerance threshold and may enable scalable silicon quantum computers.

4.2 K sensitivity-tunable radio frequency reflectometry of a physically defined p-channel silicon quantum dot

We demonstrate the measurement of p-channel silicon-on-insulator quantum dots at liquid helium temperatures by using a radio frequency (rf) reflectometry circuit comprising of two independently tunable GaAs varactors. This arrangement allows observing Coulomb diamonds at 4.2 K under nearly best matching condition and optimal signal-to-noise ratio. We also discuss the rf leakage induced by the presence of the large top gate in MOS nanostructures and its consequence on the efficiency of rf-reflectometry. These results open the way to fast and sensitive readout in multi-gate architectures, including multi qubit platforms.

Designs for a two-dimensional Si quantum dot array with spin qubit addressability

Electron spins in Si are an attractive platform for quantum computation, backed with their scalability and fast, high-fidelity quantum logic gates. Despite the importance of two-dimensional integration with efficient connectivity between qubits for medium- to large-scale quantum computation, however, a practical device design that guarantees qubit addressability is yet to be seen. Here, we propose a practical 3 × 3 quantum dot device design and a larger-scale design as a longer-term target. The design goal is to realize qubit connectivity to the four nearest neighbors while ensuring addressability. We show that a 3 × 3 quantum dot array can execute four-qubit Grover’s algorithm more efficiently than the one-dimensional counterpart. To scale up the two-dimensional array beyond 3 × 3, we propose a novel structure with ferromagnetic gate electrodes. Our results showcase the possibility of medium-sized quantum processors in Si with fast quantum logic gates and long coherence times.

Electron beam lithography with negative tone resist for highly integrated silicon quantum bits

Process technologies have been developed for electron-beam (EB) lithography aimed at silicon quantum devices and their large-scale integration. It is necessary to understand the proximity effect and construct a method for its correction to perform EB lithography of fine and complicated structures. In this study, we investigate the lithography of Si quantum devices with a point-beam EB system and a maN 2401 negative tone resist, in order to correspond to various types of device structures. We optimize temperatures for specialized pre- and post-exposure bakes for forming ∼20 nm fine patterns with small line-edge roughness. Further, we demonstrated the fabrication of Si-on-insulator device patterns that have some tiny dots connected with many large wires/pads in the layout, with the careful tuning of the dose assignment. In this tuning, we used the EB process simulation to estimate the cumulative dose distribution effectively. In addition, we reproduced the experimentally obtained resist patterns via the EB process simulation after considering the mid-range effect, which is a factors in the proximity effect but is not yet deeply understood. The results of this study are expected to provide useful process technologies for EB lithography, which will help drastically accelerate the research on Si quantum devices with a high degree of freedom.

Quantum tomography of an entangled three-qubit state in silicon

Quantum entanglement is a fundamental property of coherent quantum states and an essential resource for quantum computing¹. In large-scale quantum systems, the error accumulation requires concepts for quantum error correction. A first step toward error correction is the creation of genuinely multipartite entanglement, which has served as a performance benchmark for quantum computing platforms such as superconducting circuits^2,3, trapped ions⁴ and nitrogen-vacancy centres in diamond⁵. Among the candidates for large-scale quantum computing devices, silicon-based spin qubits offer an outstanding nanofabrication capability for scaling-up. Recent studies demonstrated improved coherence times^6-8, high-fidelity all-electrical control^9-13, high-temperature operation^14,15 and quantum entanglement of two spin qubits^9,11,12. Here we generated a three-qubit Greenberger-Horne-Zeilinger state using a low-disorder, fully controllable array of three spin qubits in silicon. We performed quantum state tomography¹⁶ and obtained a state fidelity of 88.0%. The measurements witness a genuine Greenberger-Horne-Zeilinger class quantum entanglement that cannot be separated into any biseparable state. Our results showcase the potential of silicon-based spin qubit platforms for multiqubit quantum algorithms.

Radio-frequency single electron transistors in physically defined silicon quantum dots with a sensitive phase response

Radio-frequency reflectometry techniques are instrumental for spin qubit readout in semiconductor quantum dots. However, a large phase response is difficult to achieve in practice. In this work, we report radio-frequency single electron transistors using physically defined quantum dots in silicon-on-insulator. We study quantum dots which do not have the top gate structure considered to hinder radio frequency reflectometry measurements using physically defined quantum dots. Based on the model which properly takes into account the parasitic components, we precisely determine the gate-dependent device admittance. Clear Coulomb peaks are observed in the amplitude and the phase of the reflection coefficient, with a remarkably large phase signal of ∼45°. Electrical circuit analysis indicates that it can be attributed to a good impedance matching and a detuning from the resonance frequency. We anticipate that our results will be useful in designing and simulating reflectometry circuits to optimize qubit readout sensitivity and speed.

Microwave Photon Detectors Based on Semiconducting Double Quantum Dots

Detectors of microwave photons find applications in different fields ranging from security to cosmology. Due to the intrinsic difficulties related to the detection of vanishingly small energy quanta ℏ ω , significant portions of the microwave electromagnetic spectrum are still uncovered by suitable techniques. No prevailing technology has clearly emerged yet, although different solutions have been tested in different contexts. Here, we focus on semiconductor quantum dots, which feature wide tunability by external gate voltages and scalability for large architectures. We discuss possible pathways for the development of microwave photon detectors based on photon-assisted tunneling in semiconducting double quantum dot circuits. In particular, we consider implementations based on either broadband transmission lines or resonant cavities, and we discuss how developments in charge sensing techniques and hybrid architectures may be beneficial for the development of efficient photon detectors in the microwave range.