Universal control of four singlet-triplet qubits.

The coherent control of interacting spins in semiconductor quantum dots is of strong interest for quantum information processing and for studying quantum magnetism from the bottom up. Here we present a 2 × 4 germanium quantum dot array with full and controllable interactions between nearest-neighbour spins. As a demonstration of the level of control, we define four singlet-triplet qubits in this system and show two-axis single-qubit control of each qubit and SWAP-style two-qubit gates between all neighbouring qubit pairs, yielding average single-qubit gate fidelities of 99.

Single-Electron Occupation in Quantum Dot Arrays at Selectable Plunger Gate Voltage.

The small footprint of semiconductor qubits is favorable for scalable quantum computing. However, their size also makes them sensitive to their local environment and variations in the gate structure. Currently, each device requires tailored gate voltages to confine a single charge per quantum dot, clearly challenging scalability.

Probing the Jaynes-Cummings Ladder with Spin Circuit Quantum Electrodynamics.

We report observations of transitions between excited states in the Jaynes-Cummings ladder of circuit quantum electrodynamics with electron spins (spin circuit QED). We show that unexplained features in recent experimental work correspond to such transitions and present an input-output framework that includes these effects. In new experiments, we first reproduce previous observations and then reveal both excited-state transitions and multiphoton transitions by increasing the probe power and using two-tone spectroscopy.

Reducing charge noise in quantum dots by using thin silicon quantum wells.

Charge noise in the host semiconductor degrades the performance of spin-qubits and poses an obstacle to control large quantum processors. However, it is challenging to engineer the heterogeneous material stack of gate-defined quantum dots to improve charge noise systematically. Here, we address the semiconductor-dielectric interface and the buried quantum well of a Si/SiGe heterostructure and show the connection between charge noise, measured locally in quantum dots, and global disorder in the host semiconductor, measured with macroscopic Hall bars.

Atomic fluctuations lifting the energy degeneracy in Si/SiGe quantum dots.

Electron spins in Si/SiGe quantum wells suffer from nearly degenerate conduction band valleys, which compete with the spin degree of freedom in the formation of qubits. Despite attempts to enhance the valley energy splitting deterministically, by engineering a sharp interface, valley splitting fluctuations remain a serious problem for qubit uniformity, needed to scale up to large quantum processors. Here, we elucidate and statistically predict the valley splitting by the holistic integration of 3D atomic-level properties, theory and transport.

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 reliably. 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 promise 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 readout.

Quantum logic with spin qubits crossing the surface code threshold.

High-fidelity control of quantum bits is paramount for the reliable execution of quantum algorithms and for achieving fault tolerance-the ability to correct errors faster than they occur. The central requirement for fault tolerance is expressed in terms of an error threshold. Whereas the actual threshold depends on many details, a common target is the approximately 1% error threshold of the well-known surface code.

Quantum-coherent nanoscience.

For the past three decades nanoscience has widely affected many areas in physics, chemistry and engineering, and has led to numerous fundamental discoveries, as well as applications and products. Concurrently, quantum science and technology has developed into a cross-disciplinary research endeavour connecting these same areas and holds burgeoning commercial promise. Although quantum physics dictates the behaviour of nanoscale objects, quantum coherence, which is central to quantum information, communication and sensing, has not played an explicit role in much of nanoscience.

CMOS-based cryogenic control of silicon quantum circuits.

The most promising quantum algorithms require quantum processors that host millions of quantum bits when targeting practical applications. A key challenge towards large-scale quantum computation is the interconnect complexity. In current solid-state qubit implementations, an important interconnect bottleneck appears between the quantum chip in a dilution refrigerator and the room-temperature electronics.

Electron cascade for distant spin readout.

The spin of a single electron in a semiconductor quantum dot provides a well-controlled and long-lived qubit implementation. The electron charge in turn allows control of the position of individual electrons in a quantum dot array, and enables charge sensors to probe the charge configuration. Here we show that the Coulomb repulsion allows an initial charge transition to induce subsequent charge transitions, inducing a cascade of electron hops, like toppling dominoes.

Universal quantum logic in hot silicon qubits.

Quantum computation requires many qubits that can be coherently controlled and coupled to each other. Qubits that are defined using lithographic techniques have been suggested to enable the development of scalable quantum systems because they can be implemented using semiconductor fabrication technology. However, leading solid-state approaches function only at temperatures below 100 millikelvin, where cooling power is extremely limited, and this severely affects the prospects of practical quantum computation.

Nagaoka ferromagnetism observed in a quantum dot plaquette.

Engineered, highly controllable quantum systems are promising simulators of emergent physics beyond the simulation capabilities of classical computers. An important problem in many-body physics is itinerant magnetism, which originates purely from long-range interactions of free electrons and whose existence in real systems has been debated for decades. Here we use a quantum simulator consisting of a four-electron-site square plaquette of quantum dots to demonstrate Nagaoka ferromagnetism.

Author Correction: Rapid gate-based spin read-out in silicon using an on-chip resonator.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Tunable Coupling and Isolation of Single Electrons in Silicon Metal-Oxide-Semiconductor Quantum Dots.

Extremely long coherence times, excellent single-qubit gate fidelities, and two-qubit logic have been demonstrated with silicon metal-oxide-semiconductor spin qubits, making it one of the leading platforms for quantum information processing. Despite this, a long-standing challenge in this system has been the demonstration of tunable tunnel coupling between single electrons. Here we overcome this hurdle with gate-defined quantum dots and show couplings that can be tuned on and off for quantum operations.

Rapid gate-based spin read-out in silicon using an on-chip resonator.

Silicon spin qubits are one of the leading platforms for quantum computation. As with any qubit implementation, a crucial requirement is the ability to measure individual quantum states rapidly and with high fidelity. Since the signal from a single electron spin is minute, the different spin states are converted to different charge states.

Spin Lifetime and Charge Noise in Hot Silicon Quantum Dot Qubits.

We investigate the magnetic field and temperature dependence of the single-electron spin lifetime in silicon quantum dots and find a lifetime of 2.8 ms at a temperature of 1.1 K.

A crossbar network for silicon quantum dot qubits.

The spin states of single electrons in gate-defined quantum dots satisfy crucial requirements for a practical quantum computer. These include extremely long coherence times, high-fidelity quantum operation, and the ability to shuttle electrons as a mechanism for on-chip flying qubits. To increase the number of qubits to the thousands or millions of qubits needed for practical quantum information, we present an architecture based on shared control and a scalable number of lines.

Mesoscopic Elastic Distortions in GaAs Quantum Dot Heterostructures.

Quantum devices formed in high-electron-mobility semiconductor heterostructures provide a route through which quantum mechanical effects can be exploited on length scales accessible to lithography and integrated electronics. The electrostatic definition of quantum dots in semiconductor heterostructure devices intrinsically involves the lithographic fabrication of intricate patterns of metallic electrodes. The formation of metal/semiconductor interfaces, growth processes associated with polycrystalline metallic layers, and differential thermal expansion produce elastic distortion in the active areas of quantum devices.

A programmable two-qubit quantum processor in silicon.

Now that it is possible to achieve measurement and control fidelities for individual quantum bits (qubits) above the threshold for fault tolerance, attention is moving towards the difficult task of scaling up the number of physical qubits to the large numbers that are needed for fault-tolerant quantum computing. In this context, quantum-dot-based spin qubits could have substantial advantages over other types of qubit owing to their potential for all-electrical operation and ability to be integrated at high density onto an industrial platform. Initialization, readout and single- and two-qubit gates have been demonstrated in various quantum-dot-based qubit representations.

Strong spin-photon coupling in silicon.

Long coherence times of single spins in silicon quantum dots make these systems highly attractive for quantum computation, but how to scale up spin qubit systems remains an open question. As a first step to address this issue, we demonstrate the strong coupling of a single electron spin and a single microwave photon. The electron spin is trapped in a silicon double quantum dot, and the microwave photon is stored in an on-chip high-impedance superconducting resonator.

Quantum simulation of a Fermi-Hubbard model using a semiconductor quantum dot array.

Interacting fermions on a lattice can develop strong quantum correlations, which are the cause of the classical intractability of many exotic phases of matter. Current efforts are directed towards the control of artificial quantum systems that can be made to emulate the underlying Fermi-Hubbard models. Electrostatically confined conduction-band electrons define interacting quantum coherent spin and charge degrees of freedom that allow all-electrical initialization of low-entropy states and readily adhere to the Fermi-Hubbard Hamiltonian.

Current-Phase Relation of Ballistic Graphene Josephson Junctions.

The current-phase relation (CPR) of a Josephson junction (JJ) determines how the supercurrent evolves with the superconducting phase difference across the junction. Knowledge of the CPR is essential in order to understand the response of a JJ to various external parameters. Despite the rising interest in ultraclean encapsulated graphene JJs, the CPR of such junctions remains unknown.

Side Gate Tunable Josephson Junctions at the LaAlO/SrTiO Interface.

Novel physical phenomena arising at the interface of complex oxide heterostructures offer exciting opportunities for the development of future electronic devices. Using the prototypical LaAlO/SrTiO interface as a model system, we employ a single-step lithographic process to realize gate-tunable Josephson junctions through a combination of lateral confinement and local side gating. The action of the side gates is found to be comparable to that of a local back gate, constituting a robust and efficient way to control the properties of the interface at the nanoscale.

Coherent spin-exchange via a quantum mediator.

Coherent interactions at a distance provide a powerful tool for quantum simulation and computation. The most common approach to realize an effective long-distance coupling 'on-chip' is to use a quantum mediator, as has been demonstrated for superconducting qubits and trapped ions. For quantum dot arrays, which combine a high degree of tunability with extremely long coherence times, the experimental demonstration of the time evolution of coherent spin-spin coupling via an intermediary system remains an important outstanding goal.