Silicon Qubit Research Articles

A surface code quantum computer in silicon.

The exceptionally long quantum coherence times of phosphorus donor nuclear spin qubits in silicon, coupled with the proven scalability of silicon-based nano-electronics, make them attractive candidates for large-scale quantum computing. However, the high threshold of topological quantum error correction can only be captured in a two-dimensional array of qubits operating synchronously and in parallel-posing formidable fabrication and control challenges. We present an architecture that addresses these problems through a novel shared-control paradigm that is particularly suited to the natural uniformity of the phosphorus donor nuclear spin qubit states and electronic confinement. The architecture comprises a two-dimensional lattice of donor qubits sandwiched between two vertically separated control layers forming a mutually perpendicular crisscross gate array. Shared-control lines facilitate loading/unloading of single electrons to specific donors, thereby activating multiple qubits in parallel across the array on which the required operations for surface code quantum error correction are carried out by global spin control. The complexities of independent qubit control, wave function engineering, and ad hoc quantum interconnects are explicitly avoided. With many of the basic elements of fabrication and control based on demonstrated techniques and with simulated quantum operation below the surface code error threshold, the architecture represents a new pathway for large-scale quantum information processing in silicon and potentially in other qubit systems where uniformity can be exploited.

Multiqubit gates protected by adiabaticity and dynamical decoupling applicable to donor qubits in silicon

We present a strategy for producing multi-qubit gates that promise high fidelity with minimal tuning requirements. Our strategy combines gap protection from the adiabatic theorem with dynamical decoupling in a complementary manner. To avoid degenerate states and maximize the benefit of the gap protection, the scheme is best suited when there are two different kinds of qubits (not mutually resonant). Furthermore, we require a robust operating point in control space where the qubits interact with little sensitivity to noise. This allows us to circumvent a No-Go theorem that prevents block-box dynamically corrected gates [Phys. Rev. A 80, 032314 (2009)]. We show how to apply our strategy to an architecture in Si with P donors where we assume we can shuttle electrons between different donors. Electron spins act as mobile ancillary qubits and P nuclear spins act as long-lived data qubits. This system can have a very robust operating point where the electron spin is bound to a donor in the quadratic Stark shift regime. High fidelity single qubit gates may be performed using well-established global magnetic resonance pulse sequences. Single electron spin preparation and measurement has also been demonstrated. Putting this all together, we present a robust universal gate set for quantum computation.

Strain and electric field control of hyperfine interactions for donor spin qubits in silicon

Control of hyperfine interactions is a fundamental requirement for quantum computing architecture schemes based on shallow donors in silicon. However, at present, there is lacking an atomistic approach including critical effects of central-cell corrections and non-static screening of the donor potential capable of describing the hyperfine interaction in the presence of both strain and electric fields in realistically sized devices. We establish and apply a theoretical framework, based on atomistic tight-binding theory, to quantitatively determine the strain and electric field dependent hyperfine couplings of donors. Our method is scalable to millions of atoms, and yet captures the strain effects with an accuracy level of DFT method. Excellent agreement with the available experimental data sets allow reliable investigation of the design space of multi-qubit architectures, based on both strain-only as well as hybrid (strain+field) control of qubits. The benefits of strain are uncovered by demonstrating that a hybrid control of qubits based on (001) compressive strain and in-plane (100 or 010) fields results in higher gate fidelities and/or faster gate operations, for all of the four donor species considered (P, As, Sb, and Bi). The comparison between different donor species in strained environments further highlights the trends of hyperfine shifts, providing predictions where no experimental data exists. Whilst faster gate operations are realisable with in-plane fields for P, As, and Sb donors, only for the Bi donor, our calculations predict faster gate response in the presence of both in-plane and out-of-plane fields, truly benefiting from the proposed planar field control mechanism of the hyperfine interactions.

Interface-induced heavy-hole/light-hole splitting of acceptors in silicon

The energy spectrum of spin-orbit coupled states of individual sub-surface boron acceptor dopants in silicon have been investigated using scanning tunneling spectroscopy at cryogenic temperatures. The spatially resolved tunnel spectra show two resonances, which we ascribe to the heavy- and light-hole Kramers doublets. This type of broken degeneracy has recently been argued to be advantageous for the lifetime of acceptor-based qubits [R. Ruskov and C. Tahan, Phys. Rev. B 88, 064308 (2013)]. The depth dependent energy splitting between the heavy- and light-hole Kramers doublets is consistent with tight binding calculations, and is in excess of 1 meV for all acceptors within the experimentally accessible depth range (<2 nm from the surface). These results will aid the development of tunable acceptor-based qubits in silicon with long coherence times and the possibility for electrical manipulation.

Quantifying the quantum gate fidelity of single-atom spin qubits in silicon by randomized benchmarking

Building upon the demonstration of coherent control and single-shot readout of the electron and nuclear spins of individual 31P atoms in silicon, we present here a systematic experimental estimate of quantum gate fidelities using randomized benchmarking of 1-qubit gates in the Clifford group. We apply this analysis to the electron and the ionized 31P nucleus of a single P donor in isotopically purified 28Si. We find average gate fidelities of 99.95% for the electron and 99.99% for the nuclear spin. These values are above certain error correction thresholds and demonstrate the potential of donor-based quantum computing in silicon. By studying the influence of the shape and power of the control pulses, we find evidence that the present limitation to the gate fidelity is mostly related to the external hardware and not the intrinsic behaviour of the qubit.

Probing the limits of gate-based charge sensing.

Quantum computation requires a qubit-specific measurement capability to readout the final state of individual qubits. Promising solid-state architectures use external readout electrometers but these can be replaced by a more compact readout element, an in situ gate sensor. Gate-sensing couples the qubit to a resonant circuit via a gate and probes the qubit's radiofrequency polarizability. Here we investigate the ultimate performance of such a resonant readout scheme and the noise sources that limit its operation. We find a charge sensitivity of 37 μe Hz(-1/2), the best value reported for this technique, using the example of a gate sensor strongly coupled to a double quantum dot at the corner states of a silicon nanowire transistor. We discuss the experimental factors limiting gate detection and highlight ways to optimize its sensitivity. In total, resonant gate-based readout has advantages over external electrometers both in terms of reduction of circuit elements as well as absolute charge sensitivity.

Bottom-up superconducting and Josephson junction devices inside a group-IV semiconductor.

Superconducting circuits are exceptionally flexible, enabling many different devices from sensors to quantum computers. Separately, epitaxial semiconductor devices such as spin qubits in silicon offer more limited device variation but extraordinary quantum properties for a solid-state system. It might be possible to merge the two approaches, making single-crystal superconducting devices out of a semiconductor by utilizing the latest atomistic fabrication techniques. Here we propose superconducting devices made from precision hole-doped regions within a silicon (or germanium) single crystal. We analyse the properties of this superconducting semiconductor and show that practical superconducting wires, Josephson tunnel junctions or weak links, superconducting quantum interference devices (SQUIDs) and qubits are feasible. This work motivates the pursuit of 'bottom-up' superconductivity for improved or fundamentally different technology and physics.

Single-shot readout and relaxation of singlet and triplet states in exchange-coupled 31P electron spins in silicon.

We present the experimental observation of a large exchange coupling J ≈ 300 μeV between two (31)P electron spin qubits in silicon. The singlet and triplet states of the coupled spins are monitored in real time by a single-electron transistor, which detects ionization from tunnel-rate-dependent processes in the coupled spin system, yielding single-shot readout fidelities above 95%. The triplet to singlet relaxation time T(1) ≈ 4 ms at zero magnetic field agrees with the theoretical prediction for J-coupled 31P dimers in silicon. The time evolution of the two-electron state populations gives further insight into the valley-orbit eigenstates of the donor dimer, valley selection rules and relaxation rates, and the role of hyperfine interactions. These results pave the way to the realization of two-qubit quantum logic gates with spins in silicon and highlight the necessity to adopt gating schemes compatible with weak J-coupling strengths.

Spinning towards scalable circuits

Silicon devices form the backbone of modern computers. It turns out that they might also be a natural hardware platform for a new era of computing technology that uses the principles of quantum physics. See Letter p.541 Because silicon devices already form the basis for integrated electronic circuits, it would be ideal if future quantum-computing architectures could also be silicon-based, thus making use of the same well-developed fabrication technologies. A promising approach to constructing silicon qubits (quantum bits), first proposed more than a decade ago, is to make use of single dopant atoms in silicon. Jarryd Pla et al. have now made a nanoelectronic silicon device in which they can read out and control the electron spin of a single phosphorous donor atom, and demonstrate exceptionally long spin coherence times (of 200 microseconds). The combination of good qubit performance and practical fabrication approach opens the door to building scalable quantum-computing circuits.

Overcoming dephasing noise with robust optimal control

We address the experimentally relevant problem of robust mitigation of dephasing noise acting on a qubit. We first present an extension of the method of Kuopanportti et al. [Phys. Rev. A 77, 032334 (2008)] for representing $1/{\ensuremath{\omega}}^{\ensuremath{\alpha}}$ noise to the efficient representation of arbitrary Markovian noise. We then add qubit control pulses to enable the design of numerically optimized, two-dimensional, bounded amplitude control functions capable of decoupling the qubit from the dephasing effects of a broad variety of Markovian noise spectral densities during one- and two-qubit quantum operations. We illustrate the method with development of numerically optimized control pulse sequences that minimize decoherence due to a combination of $1/\ensuremath{\omega}$ and constant-offset noise sources. Comparison with the performance of standard dynamical decoupling protocols shows that the numerically optimized pulse sequences are considerably more robust with respect to zero-frequency noise. Application to the mitigation of dephasing noise on spin qubits in silicon indicates that high-fidelity quantum gates may, in principle, be implemented for such qubits with the assistance of current pulse-generation technology.

Electrically detected Rabi oscillations of phosphorus qubits in silicon

Electrically detected magnetic resonance is a sensitive technique for studying electron spins bound to phosphorus atoms in silicon. Using a high magnetic field of 8.6 T increases this sensitivity by accessing a mechanism for spin-to-charge conversion which is different to that in the more commonly used magnetic field of ∼0.33 T. The higher-field regime benefits from a long spin coherence time of over 100 µs because the phosphorus spins that are detected are not coupled to dangling-bonds. Additionally, the high field permits the spin qubits to reach an equilibrium polarization of over 95% at a temperature of 2.8 K. We demonstrate electrically detected Rabi oscillations of these electron spins in the high-field regime. The Rabi frequency is proportional to the square root of the excitation power as expected.

Charge Sensing of Precisely Positioned P Donors in Si

Real-time sensing of (spin-dependent) single-electron tunneling is fundamental to electrical readout of qubit states in spin quantum computing. Here, we demonstrate the feasibility of detecting such single-electron tunneling events using an atomically planar charge sensing layout, which can be readily integrated in scalable quantum computing architectures with phosphorus-donor-based spin qubits in silicon (Si:P). Using scanning tunneling microscopy (STM) lithography on a Si(001) surface, we patterned a single-electron transistor (SET), both tunnel and electrostatically coupled to a coplanar ultrasmall quantum dot, the latter consisting of approximately four P donors. Charge transitions of the quantum dot could be detected both in time-averaged and single-shot current response of the SET. Single electron tunneling between the quantum dot and the SET island on a time-scale (τ ∼ ms) two-orders-of-magnitude faster than the spin-lattice relaxation time of a P donor in Si makes this device geometry suitable for projective readout of Si:P spin qubits. Crucial to scalability is the ability to reproducibly achieve sufficient electron tunnel rates and charge sensitivity of the SET. The inherent atomic-scale control of STM lithography bodes extremely well to precisely optimize both of these parameters.

Engineered valley-orbit splittings in quantum-confined nanostructures in silicon

An important challenge in silicon quantum electronics in the few electron regime is the potentially small energy gap between the ground and excited orbital states in 3D quantum confined nanostructures due to the multiple valley degeneracies of the conduction band present in silicon. Understanding the "valley-orbit" (VO) gap is essential for silicon qubits, as a large VO gap prevents leakage of the qubit states into a higher dimensional Hilbert space. The VO gap varies considerably depending on quantum confinement, and can be engineered by external electric fields. In this work we investigate VO splitting experimentally and theoretically in a range of confinement regimes. We report measurements of the VO splitting in silicon quantum dot and donor devices through excited state transport spectroscopy. These results are underpinned by large-scale atomistic tight-binding calculations involving over 1 million atoms to compute VO splittings as functions of electric fields, donor depths, and surface disorder. The results provide a comprehensive picture of the range of VO splittings that can be achieved through quantum engineering.

Theoretical Calculation of the Magnetic Resonance Frequency of the Electron Spin Embedded Inside a Silicon Host for Solid-State Quantum Computing

The electron-spin magnetic resonance frequency of an electron-spin qubit structure that is proposed for the realization of a quantum computer is rigorously determined by a numerical method. The potential distribution inside the silicon qubit structure is accurately calculated by an electromagnetic simulation method, and the perturbation theory to the second order is formulated to obtain the magnetic resonance frequency of a phosphorus donor electron spin. Our results showed that, for the same qubit structure (Si:P), as originally proposed by Kane for a nuclear-spin qubit quantum computer, a smaller static magnetic field <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> is in favor of producing a wider tunable bandwidth for the magnetic resonance frequency of the electron spin. Our results also reveal that the use of SiGe as an alternative insulation material to the A-gate structure can improve the control efficiency of the A-gate voltage.

Extended interface states enhance valley splitting inSi/SiO2

Interface disorder and its effect on the valley degeneracy of the conduction band edge remains among the greatest theoretical challenges for understanding the operation of spin qubits in silicon. Here, we investigate a counterintuitive effect occurring at Si/SiO2 interfaces. By applying tight binding methods, we show that intrinsic interface states can hybridize with conventional valley states, leading to a large ground state energy gap. The effects of hybridization have not previously been explored in details for valley splitting. We find that valley splitting is enhanced in the presence of disordered chemical bonds, in agreement with recent experiments.

Quantum Hall charge sensor for single-donor nuclear spin detection in silicon

We propose a novel optical and electrical hybrid scheme for the measurement of nuclear spin qubits in silicon. By combining the environmental insensitivity of the integer quantum Hall effect with the optically distinguishable hyperfine states of phosphorus impurities in silicon, our system can offer both nuclear spin measurement and robustness against environmental defects. 31P donor spins in isotopically purified 28Si are often discussed as very promising quantum memory qubits due to their extremely long decoherence times, and our proposed device offers an effective implementation for such a quantum memory system.

Bismuth Qubits in Silicon: The Role of EPR Cancellation Resonances

We investigate electron paramagnetic resonance spectra of bismuth-doped silicon, at intermediate magnetic fields B≃0.1-0.6 T, theoretically and experimentally (with 9.7GHz X-band spectra). We identify a previously unexplored regime of "cancellation resonances," where a component of the hyperfine coupling is resonant with the external field. We show that this regime has experimentally accessible consequences for quantum information applications, such as reduction of decoherence, fast manipulation of the coupled electron-nuclear qubits, and spectral line narrowing.

Device fabrication and transport measurements of FinFETs built with 28Si SOI wafers toward donor qubits in silicon

We report on the fabrication of transistors in a FinFET geometry using isotopically purified silicon-28-on-insulator (28-SOI) substrates. Donor electron spin coherence in natural silicon is limited by spectral diffusion due to the residual 29Si nuclear spin bath, making isotopically enriched nuclear spin-free 28Si substrates a promising candidate for forming spin quantum bit devices. The FinFET architecture is fully compatible with single-ion implant detection for donor-based qubits and the donor spin-state readout through electrical detection of spin resonance. We describe device processing steps and discuss results on electrical transport measurements at 0.3 K.

Multiscale theory of valley splitting in the conduction band of a quantum well

The coupling between $z$ valleys in the conduction band of a Si quantum well arises from phenomena occurring within several atoms from the interface, thus ruling out a theoretical description based on pure effective mass theory. However, the complexity and size of a realistic device precludes an analytical atomistic description. Here, we develop a fully analytical multiscale theory of valley coupling, by combining effective mass and tight binding approaches. The results are of particular interest for silicon qubits and quantum devices, but also provide insight for GaAs quantum wells.

Magnetic-field-assisted manipulation and entanglement of Si spin qubits

Architectures of donor-electron based qubits in silicon near an oxide interface are considered theoretically. We find that the precondition for reliable logic and read-out operations, namely the individual identification of each donor-bound electron near the interface, may be accomplished by fine-tuning electric and magnetic fields, both applied perpendicularly to the interface. We argue that such magnetic fields may also be valuable in controlling two-qubit entanglement via donor electron pairs near the interface.