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To help develop quantum circuits, much effort has been directed toward achieving the strong-coupling regime by using gate-defined semiconductor quantum dots. Potentially, the magnetic dipole, or spin, of a single electron for use as a qubit has advantages over charge-photon coupling owing to its longer lifetime. Samkharadze et al. hybridized the electron spin with the electron charge in a double silicon quantum dot. This approach yielded strong coupling between the single electron spin and a single microwave photon, providing a route to scalable quantum circuits with spin qubits. Science , this issue p. 1123 Strong coupling is induced between a single electron spin and a single photon. 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. The electric field component of the cavity photon couples directly to the charge dipole of the electron in the double dot, and indirectly to the electron spin, through a strong local magnetic field gradient from a nearby micromagnet. Our results provide a route to realizing large networks of quantum dot–based spin qubit registers.

A two-qubit quantum processor in a silicon device is demonstrated, which can perform the Deutsch–Josza algorithm and the Grover search algorithm. Taken for a spin in silicon The development of platforms for spin-based quantum computing continues apace. The individual components of such a system have been the subject of much investigation, and they have been assembled to implement specific quantum-computational algorithms. Thomas Watson and colleagues have now taken such component integration and control to the next level. Using two single-electron-spin qubits in a silicon-based double quantum dot, they realize a system that can be simply programmed to perform different quantum algorithms on demand. 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 1 , 2 . 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 3 , 4 , 5 . Initialization, readout and single- and two-qubit gates have been demonstrated in various quantum-dot-based qubit representations 6 , 7 , 8 , 9 . However, as seen with small-scale demonstrations of quantum computers using other types of qubit 10 , 11 , 12 , 13 , combining these elements leads to challenges related to qubit crosstalk, state leakage, calibration and control hardware. Here we overcome these challenges by using carefully designed control techniques to demonstrate a programmable two-qubit quantum processor in a silicon device that can perform the Deutsch–Josza algorithm and the Grover search algorithm—canonical examples of quantum algorithms that outperform their classical analogues. We characterize the entanglement in our processor by using quantum-state tomography of Bell states, measuring state fidelities of 85–89 per cent and concurrences of 73–82 per cent. These results pave the way for larger-scale quantum computers that use spins confined to quantum dots.

The electron spin in a silicon-based quantum dot can be controlled electrically for as long as several tens of microseconds, which improves the prospects for quantum information processing based on this type of quantum dot. Nanofabricated quantum bits permit large-scale integration but usually suffer from short coherence times due to interactions with their solid-state environment 1 . The outstanding challenge is to engineer the environment so that it minimally affects the qubit, but still allows qubit control and scalability. Here, we demonstrate a long-lived single-electron spin qubit in a Si/SiGe quantum dot with all-electrical two-axis control. The spin is driven by resonant microwave electric fields in a transverse magnetic field gradient from a local micromagnet 2 , and the spin state is read out in the single-shot mode 3 . Electron spin resonance occurs at two closely spaced frequencies, which we attribute to two valley states. Thanks to the weak hyperfine coupling in silicon, a Ramsey decay timescale of 1 μs is observed, almost two orders of magnitude longer than the intrinsic timescales in GaAs quantum dots 4 , 5 , whereas gate operation times are comparable to those reported in GaAs 6 , 7 , 8 . The spin echo decay time is ∼40 μs, both with one and four echo pulses, possibly limited by intervalley scattering. These advances strongly improve the prospects for quantum information processing based on quantum dots.

Semiconducting quantum dots are considered candidate materials for realizing spin-based quantum computation devices. This Review examines the main results obtained over the past decade concerning the so-called central spin problem, namely the interaction between a single electronic spin or hole with the surrounding nuclear environment. The interaction of an electronic spin with its nuclear environment, an issue known as the central spin problem, has been the subject of considerable attention due to its relevance for spin-based quantum computation using semiconductor quantum dots. Independent control of the nuclear spin bath using nuclear magnetic resonance techniques and dynamic nuclear polarization using the central spin itself offer unique possibilities for manipulating the nuclear bath with significant consequences for the coherence and controlled manipulation of the central spin. Here we review some of the recent optical and transport experiments that have explored this central spin problem using semiconductor quantum dots. We focus on the interaction between 10 4 –10 6 nuclear spins and a spin of a single electron or valence-band hole. We also review the experimental techniques as well as the key theoretical ideas and the implications for quantum information science.

Quantum-mechanical correlations of interacting fermions result in the emergence of exotic phases. Magnetic phases naturally arise in the Mott-insulator regime of the Fermi-Hubbard model, where charges are localized and the spin degree of freedom remains. In this regime, the occurrence of phenomena such as resonating valence bonds, frustrated magnetism, and spin liquids is predicted. Quantum systems with engineered Hamiltonians can be used as simulators of such spin physics to provide insights beyond the capabilities of analytical methods and classical computers. To be useful, methods for the preparation of intricate many-body spin states and access to relevant observables are required. Here, we show the quantum simulation of magnetism in the Mott-insulator regime with a linear quantum-dot array. We characterize the energy spectrum for a Heisenberg spin chain, from which we can identify when the conditions for homogeneous exchange couplings are met. Next, we study the multispin coherence with global exchange oscillations in both the singlet and triplet subspace of the Heisenberg Hamiltonian. Last, we adiabatically prepare the low-energy global singlet of the homogeneous spin chain and probe it with two-spin singlet-triplet measurements on each nearest-neighbor pair and the correlations therein. The methods and control presented here open new opportunities for the simulation of quantum magnetism benefiting from the flexibility in tuning and layout of gate-defined quantum-dot arrays.

We propose a universal, on-chip quantum transducer based on surface acoustic waves in piezoactive materials. Because of the intrinsic piezoelectric (and/or magnetostrictive) properties of the material, our approach provides a universal platform capable of coherently linking a broad array of qubits, including quantum dots, trapped ions, nitrogen-vacancy centers, or superconducting qubits. The quantized modes of surface acoustic waves lie in the gigahertz range and can be strongly confined close to the surface in phononic cavities and guided in acoustic waveguides. We show that this type of surface acoustic excitation can be utilized efficiently as a quantum bus, serving as an on-chip, mechanical cavity-QED equivalent of microwave photons and enabling long-range coupling of a wide range of qubits.

Measurement of coupled quantum systems plays a central role in quantum information processing. We have realized independent single-shot read-out of two electron spins in a double quantum dot. The read-out method is all-electrical, cross-talk between the two measurements is negligible, and read-out fidelities are ∼86% on average. This allows us to directly probe the anticorrelations between two spins prepared in a singlet state and to demonstrate the operation of the two-qubit exchange gate on a complete set of basis states. The results provide a possible route to the realization and efficient characterization of multiqubit quantum circuits based on single quantum dot spins.

The ability to control the quantum state of a single electron spin in a quantum dot is at the heart of recent developments towards a scalable spin-based quantum computer. In combination with the recently demonstrated controlled exchange gate between two neighbouring spins, driven coherent single spin rotations would permit universal quantum operations. Here, we report the experimental realization of single electron spin rotations in a double quantum dot. First, we apply a continuous-wave oscillating magnetic field, generated on-chip, and observe electron spin resonance in spin-dependent transport measurements through the two dots. Next, we coherently control the quantum state of the electron spin by applying short bursts of the oscillating magnetic field and observe about eight oscillations of the spin state (so-called Rabi oscillations) during a microsecond burst. These results demonstrate the feasibility of operating single-electron spins in a quantum dot as quantum bits. Spin qubits ready to roll One of the most promising approaches to realizing a practical quantum bit is to use spin states of single electrons in semiconductor quantum dots. A detailed proposal for such spin qubits was published about ten years ago; since then, all the necessary ingredients to realize it, such as long-lived spin states and the initialization of electron spins, have been reported one by one. Now the last, most difficult step has been accomplished, that of driving coherent spin oscillations for individual electrons, which is necessary to carry out quantum operations. This is achieved by applying oscillating magnetic fields that are resonant with the precession frequencies of the electron spins, generated on-chip near a double quantum dot system. All is now ready to design universal quantum logic gates.

Spin is a fundamental property of all elementary particles. Classically it can be viewed as a tiny magnetic moment, but a measurement of an electron spin along the direction of an external magnetic field can have only two outcomes 1 : parallel or anti-parallel to the field. This discreteness reflects the quantum mechanical nature of spin. Ensembles of many spins have found diverse applications ranging from magnetic resonance imaging 2 to magneto-electronic devices 3 , while individual spins are considered as carriers for quantum information. Read-out of single spin states has been achieved using optical techniques 4 , and is within reach of magnetic resonance force microscopy 5 . However, electrical read-out of single spins 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 has so far remained elusive. Here we demonstrate electrical single-shot measurement of the state of an individual electron spin in a semiconductor quantum dot 14 . We use spin-to-charge conversion of a single electron confined in the dot, and detect the single-electron charge using a quantum point contact; the spin measurement visibility is ∼65%. Furthermore, we observe very long single-spin energy relaxation times (up to ∼0.85 ms at a magnetic field of 8 T), which are encouraging for the use of electron spins as carriers of quantum information.

Heterostructures of graphene and a superconducting metal allow Josephson junctions to be studied in a regime characterized by ballistic transport. Hybrid graphene–superconductor devices have attracted much attention since the early days of graphene research 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 . So far, these studies have been limited to the case of diffusive transport through graphene with poorly defined and modest-quality graphene/superconductor interfaces, usually combined with small critical magnetic fields of the superconducting electrodes. Here, we report graphene-based Josephson junctions with one-dimensional edge contacts 19 of molybdenum rhenium. The contacts exhibit a well-defined, transparent interface to the graphene, have a critical magnetic field of 8 T at 4 K, and the graphene has a high quality due to its encapsulation in hexagonal boron nitride 19 , 20 . This allows us to study and exploit graphene Josephson junctions in a new regime, characterized by ballistic transport. We find that the critical current oscillates with the carrier density due to phase-coherent interference of the electrons and holes that carry the supercurrent caused by the formation of a Fabry–Pérot cavity. Furthermore, relatively large supercurrents are observed over unprecedented long distances of up to 1.5 μm. Finally, in the quantum Hall regime we observe broken symmetry states while the contacts remain superconducting. These achievements open up new avenues to exploit the Dirac nature of graphene in interaction with the superconducting state.