Operation of a silicon quantum processor unit cell above one kelvin.

Quantum computers are expected to outperform conventional computers in several important applications, from molecular simulation to search algorithms, once they can be scaled up to large numbers-typically millions-of quantum bits (qubits)1-3. For most solid-state qubit technologies-for example, those using superconducting circuits or semiconductor spins-scaling poses a considerable challenge because every additional qubit increases the heat generated, whereas the cooling power of dilution refrigerators is severely limited at their operating temperature (less than 100 millikelvin)4-6. Here we demonstrate the operation of a scalable silicon quantum processor unit cell comprising two qubits confined to quantum dots at about 1.5 kelvin. We achieve this by isolating the quantum dots from the electron reservoir, and then initializing and reading the qubits solely via tunnelling of electrons between the two quantum dots7-9. We coherently control the qubits using electrically driven spin resonance10,11 in isotopically enriched silicon12 28Si, attaining single-qubit gate fidelities of 98.6 per cent and a coherence time of 2 microseconds during 'hot' operation, comparable to those of spin qubits in natural silicon at millikelvin temperatures13-16. Furthermore, we show that the unit cell can be operated at magnetic fields as low as 0.1 tesla, corresponding to a qubit control frequency of 3.5 gigahertz, where the qubit energy is well below the thermal energy. The unit cell constitutes the core building block of a full-scale silicon quantum computer and satisfies layout constraints required by error-correction architectures8,17. Our work indicates that a spin-based quantum computer could be operated at increased temperatures in a simple pumped 4He system (which provides cooling power orders of magnitude higher than that of dilution refrigerators), thus potentially enabling the integration of classical control electronics with the qubit array18,19.

Coherent spin control of s-, p-, d- and f-electrons in a silicon quantum dot.

Once the periodic properties of elements were unveiled, chemical behaviour could be understood in terms of the valence of atoms. Ideally, this rationale would extend to quantum dots, and quantum computation could be performed by merely controlling the outer-shell electrons of dot-based qubits. Imperfections in semiconductor materials disrupt this analogy, so real devices seldom display a systematic many-electron arrangement. We demonstrate here an electrostatically confined quantum dot that reveals a well defined shell structure. We observe four shells (31 electrons) with multiplicities given by spin and valley degrees of freedom. Various fillings containing a single valence electron-namely 1, 5, 13 and 25 electrons-are found to be potential qubits. An integrated micromagnet allows us to perform electrically-driven spin resonance (EDSR), leading to faster Rabi rotations and higher fidelity single qubit gates at higher shell states. We investigate the impact of orbital excitations on single qubits as a function of the dot deformation and exploit it for faster qubit control.

Long-range spin transfer in triple quantum dots.

Tunneling in a quantum coherent structure is not restricted to only nearest neighbors. Hopping between distant sites is possible via the virtual occupation of otherwise avoided intermediate states. Here we report the observation of long-range transitions in the transport through three quantum dots coupled in series. A single electron is delocalized between the left and right quantum dots, while the center one remains always empty. Superpositions are formed, and both charge and spin are exchanged between the outermost dots. The delocalized electron acts as a quantum bus transferring the spin state from one end to the other. Spin selection is enabled by spin correlations. The process is detected via the observation of narrow resonances which are insensitive to Pauli spin blockade.

Fast electrical control of single electron spins in quantum dots with vanishing influence from nuclear spins.

We demonstrate fast universal electrical spin manipulation with inhomogeneous magnetic fields. With fast Rabi frequency up to 127 MHz, we leave the conventional regime of strong nuclear-spin influence and observe a spin-flip fidelity >96%, a distinct chevron Rabi pattern in the spectral-time domain, and a spin resonance linewidth limited by the Rabi frequency, not by the dephasing rate. In addition, we establish fast z rotations up to 54 MHz by directly controlling the spin phase. Our findings will significantly facilitate tomography and error correction with electron spins in quantum dots.

Bipolar spin blockade and coherent state superpositions in a triple quantum dot.

Spin qubits based on interacting spins in double quantum dots have been demonstrated successfully. Readout of the qubit state involves a conversion of spin to charge information, which is universally achieved by taking advantage of a spin blockade phenomenon resulting from Pauli's exclusion principle. The archetypal spin blockade transport signature in double quantum dots takes the form of a rectified current. At present, more complex spin qubit circuits including triple quantum dots are being developed. Here we show, both experimentally and theoretically, that in a linear triple quantum dot circuit the spin blockade becomes bipolar with current strongly suppressed in both bias directions and also that a new quantum coherent mechanism becomes relevant. In this mechanism, charge is transferred non-intuitively via coherent states from one end of the linear triple dot circuit to the other, without involving the centre site. Our results have implications for future complex nanospintronic circuits.

Two-qubit gate of combined single-spin rotation and interdot spin exchange in a double quantum dot.

A crucial requirement for quantum-information processing is the realization of multiple-qubit quantum gates. Here, we demonstrate an electron spin-based all-electrical two-qubit gate consisting of single-spin rotations and interdot spin exchange in a double quantum dot. A partially entangled output state is obtained by the application of the two-qubit gate to an initial, uncorrelated state. We find that the degree of entanglement is controllable by the exchange operation time. The approach represents a key step towards the realization of universal multiple-qubit gates.

Electron-spin manipulation and resonator readout in a double-quantum-dot nanoelectromechanical system.

We demonstrate how magnetically coupling a nanomechanical resonator to a double quantum dot confining two electrons can enable the manipulation of a single electron spin and the readout of the resonator's natural frequency. When the Larmor frequency matches the resonator frequency, the electron spin in one of the dots can be selectively and coherently flipped by the magnetized oscillator. By simultaneously measuring the charge state of the two-electron double quantum dots, this transition can be detected thus enabling the natural frequency and displacement of the mechanical oscillator to be determined.

Telegraph noise in coupled quantum dot circuits induced by a quantum point contact.

Charge detection utilizing a highly biased quantum point contact has become the most effective probe for studying few electron quantum dot circuits. Measurements on double and triple quantum dot circuits is performed to clarify a back action role of charge sensing on the confined electrons. The quantum point contact triggers inelastic transitions, which occur quite generally. Under specific device and measurement conditions these transitions manifest themselves as bounded regimes of telegraph noise within a stability diagram. A nonequilibrium transition from artificial atomic to molecular behavior is identified. Consequences for quantum information applications are discussed.

Spin-blockade spectroscopy of a two-level artificial molecule.

Coulomb- and spin-blockade spectroscopy investigations have been performed on an electrostatically defined "artificial molecule" connected to spin polarized leads. The molecule is first effectively reduced to a two-level system by placing both constituent atoms at a specific location of the level spectrum. The spin sensitivity of the conductance enables us to identify the electronic spin states of the two-level molecule. We find in addition that the magnetic field induces variations in the tunnel coupling between the two atoms. The lateral nature of the device is evoked to explain this behavior.

Collapse of the spin-singlet phase in quantum dots.

We present experimental and theoretical results on a new regime in quantum dots in which the filling factor two-singlet state is replaced by new spin polarized phases. We make use of spin blockade spectroscopy to identify the transition to this new regime as a function of the number of electrons. The key experimental observation is a reversal of the phase in the systematic oscillation of the amplitude of Coulomb blockade peaks as the number of electrons is increased above a critical number. It is found theoretically that correlations are crucial to the existence of the new phases.

Spectral weight of the hubbard model through cluster perturbation theory

We calculate the spectral weight of the one- and two-dimensional Hubbard models by performing exact diagonalizations of finite clusters and treating intercluster hopping with perturbation theory. Even with relatively modest clusters (e.g., 12 sites), the spectra thus obtained give an accurate description of the exact results. Spin-charge separation (i.e., an extended spectral weight bounded by singularities dispersing with wave vector) is clearly recognized in the one-dimensional Hubbard model, and so is extended spectral weight in the two-dimensional Hubbard model.