We develop the theory of single-electron silicon spin qubit relaxation in the presence of a magnetic field gradient. Such field gradients are routinely generated by on-chip micromagnets to allow for electrically controlled quantum gates on spin qubits. We build on a valley-dependent envelope function theory that enables the analysis of the electron wave function in a silicon quantum dot with an arbitrary roughness at the interface. We assume the presence of single-layer atomic steps at a Si/SiGe interface and study how the presence of a gradient field modifies the spin-mixing mechanisms. We show that our theoretical modeling can quantitatively reproduce results of experimental measurements of qubit relaxation in silicon in the presence of a micromagnet. We further study in detail how a field gradient can modify the EDSR Rabi frequency of a silicon spin qubit. While this strongly depends on the details of the interface roughness, interestingly, we find that adding a micromagnet on top of a spin qubit with an ideal interface can even reduce the EDSR frequency within some interval of the external magnetic field strength.
Large-scale quantum computers rely on quantum error correction to protect the fragile quantum information. Among the possible candidates of quantum computing devices, silicon-based spin qubits hold a great promise due to their compatibility to mature nanofabrication technologies for scaling up. Recent advances in silicon-based qubits have enabled the implementations of high quality one and two qubit systems. However, the demonstration of quantum error correction, which requires three or more coupled qubits and often involves a three-qubit gate, remains an open challenge. Here, we demonstrate a…
The three-qubit Toffoli gate plays an important role in quantum error correction and complex quantum algorithms such as Shor's factoring algorithm, motivating the search for efficient implementations of this gate. Here we introduce a Toffoli gate suitable for exchange-coupled electron spin qubits in silicon quantum dot arrays. Our protocol is a natural extension of a previously demonstrated resonantly driven CNOT gate for silicon spin qubits. It is based on a single exchange pulse combined with a resonant microwave drive, with an operation time on the order of 100 ns and fidelity exceeding 99%…
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 qub…
Silicon spin qubits satisfy the necessary criteria for quantum information processing. However, a demonstration of high fidelity state preparation and readout combined with high fidelity single- and two-qubit gates, all of which must be present for quantum error correction, has been lacking. We use a two qubit Si/SiGe quantum processor to demonstrate state preparation and readout with fidelity over 97%, combined with both single- and two-qubit control fidelities exceeding 99%. The operation of the quantum processor is quantitatively characterized using gate set tomography and randomized benchm…
Quantum systems must be prepared, controlled, and measured with high fidelity in order to perform complex quantum algorithms. Control fidelities have greatly improved in silicon spin qubits, but state preparation and readout fidelities have generally been poor. By operating with low electron temperatures and employing high-bandwidth cryogenic amplifiers, we demonstrate single qubit readout visibilities >99%, exceeding the threshold for quantum error correction. In the same device, we achieve average single qubit control fidelities >99.95%. Our results show that silicon spin qubits can be opera…
A fault-tolerant quantum processor may be configured using stationary qubits interacting only with their nearest neighbours, but at the cost of significant overheads in physical qubits per logical qubit. Such overheads could be reduced by coherently transporting qubits across the chip, allowing connectivity beyond immediate neighbours. Here we demonstrate high-fidelity coherent transport of an electron spin qubit between quantum dots in isotopically-enriched silicon. We observe qubit precession in the inter-site tunnelling regime and assess the impact of qubit transport using Ramsey interferom…
Quantum computers have the potential to efficiently solve problems in logistics, drug and material design, finance, and cybersecurity. However, millions of qubits will be necessary for correcting inevitable errors in quantum operations. In this scenario, electron spins in gate-defined silicon quantum dots are strong contenders for encoding qubits, leveraging the microelectronics industry know-how for fabricating densely populated chips with nanoscale electrodes. The sophisticated material combinations used in commercially manufactured transistors, however, will have a very different impact on …
Universal quantum computation will require qubit technology based on a scalable platform, together with quantum error correction protocols that place strict limits on the maximum infidelities for one- and two-qubit gate operations. While a variety of qubit systems have shown high fidelities at the one-qubit level, superconductor technologies have been the only solid-state qubits manufactured via standard lithographic techniques which have demonstrated two-qubit fidelities near the fault-tolerant threshold. Silicon-based quantum dot qubits are also amenable to large-scale manufacture and can ac…
Using micromagnets to enable electron spin manipulation in silicon qubits has emerged as a very popular method, enabling single-qubit gate fidelities larger than 99:9%. However, these micromagnets also apply stray magnetic field gradients onto the qubits, making the spin states susceptible to electric field noise and limiting their coherence times. We describe here a magnet design that minimizes qubit dephasing, while allowing for fast qubit control and addressability. Specifically, we design and optimize magnet dimensions and position relative to the quantum dots, minimizing dephasing from ma…
The flip-flop qubit, encoded in the states with antiparallel donor-bound electron and donor nuclear spins in silicon, showcases long coherence times, good controllability, and, in contrast to other donor-spin-based schemes, long-distance coupling. Electron spin control near the interface, however, is likely to shorten the relaxation time by many orders of magnitude, reducing the overall qubit quality factor. Here, we theoretically study the multilevel system that is formed by the interacting electron and nuclear spins and derive analytical effective two-level Hamiltonians with and without peri…
Quantum computation requires high-fidelity single-qubit and two-qubit gates on a scalable platform. Silicon spin qubits are a promising platform toward realization of this goal. In this paper we show how to perform single-qubit and CZ gates in a linear chain of three spin qubits with always-on exchange coupling, which is relevant for certain dot- and donor-based silicon devices. We also show how to make the CZ gate robust against both charge noise and pulse length error using a two-tone pulse shaping method. The robust pulse maintains a fidelity of 99.99% at 3.5% fluctuations in exchange or pu…
A high degree of controllability and long coherence time make the nuclear spin of a phosphorus donor in isotopically purified silicon a promising candidate for a quantum bit. However, long-distance two-qubit coupling and fast, robust gates remain outstanding challenges for these systems. Here, following recent proposals for long-distance coupling via dipole-dipole interactions, we present a simple method to implement fast, high-fidelity arbitrary single- and two-qubit gates in the absence of charge noise. Moreover, we provide a method to make the single-qubit gates robust to moderate levels of…
Spin-orbit effects, inherent to electrons confined in quantum dots at a silicon heterointerface, provide a means to control electron spin qubits without the added complexity of on-chip, nanofabricated micromagnets or nearby coplanar striplines. Here, we demonstrate a novel singlet-triplet qubit operating mode that can drive qubit evolution at frequencies in excess of 200 MHz. This approach offers a means to electrically turn on and off fast control, while providing high logic gate orthogonality and long qubit dephasing times. We utilize this operational mode for dynamical decoupling experiment…
Quantum entanglement is a fundamental property of coherent quantum states and an essential resource for quantum computing. While two-qubit entanglement has been demonstrated for spins in silicon, creation of multipartite entanglement, a first step toward implementing quantum error correction, has remained challenging due to the difficulties in controlling a multi-qubit array, such as device disorder, magnetic and electrical noises and exacting exchange controls. Here, we show operation of a fully functional three-qubit array in silicon and generation of a three-qubit Greenberger-Horne-Zeilinge…
Fault-tolerant quantum computers which can solve hard problems rely on quantum error correction. One of the most promising error correction codes is the surface code, which requires universal gate fidelities exceeding the error correction threshold of 99 per cent. Among many qubit platforms, only superconducting circuits, trapped ions, and nitrogen-vacancy centers in diamond have delivered those requirements. Electron spin qubits in silicon are particularly promising for a large-scale quantum computer due to their nanofabrication capability, but the two-qubit gate fidelity has been limited to …
A two-qubit controlled-NOT (CNOT) gate, realized by a controlled-phase (C-phase) gate combined with single-qubit gates, has been experimentally implemented recently for quantum-dot spin qubits in isotopically enriched silicon, a promising solid-state system for practical quantum computation. In the experiments, the single-qubit gates have been demonstrated with fault-tolerant control-fidelity, but the infidelity of the two-qubit C-phase gate is, primarily due to the electrical noise, still higher than the required error threshold for fault-tolerant quantum computation (FTQC). Here, by taking t…
The performance requirements for fault-tolerant quantum computing are very stringent. Qubits must be manipulated, coupled, and measured with error rates well below 1%. For semiconductor implementations, silicon quantum dot spin qubits have demonstrated average single-qubit Clifford gate error rates that approach this threshold, notably with error rates of 0.14% in isotopically enriched $^{28}$Si/SiGe devices. This gate performance, together with high-fidelity two-qubit gates and measurements, is only known to meet the threshold for fault-tolerant quantum computing in some architectures when as…
Spin-orbit coupling is relatively weak for electrons in bulk silicon, but enhanced interactions are reported in nanostructures such as the quantum dots used for spin qubits. These interactions have been attributed to various dissimilar interface effects, including disorder or broken crystal symmetries. In this Letter, we use a double-quantum-dot qubit to probe these interactions by comparing the spins of separated singlet-triplet electron pairs. We observe both intravalley and intervalley mechanisms, each dominant for [110] and [100] magnetic field orientations, respectively, that are consiste…
Silicon nanoelectronic devices can host single-qubit quantum logic operations with fidelity better than 99.9%. For the spins of an electron bound to a single donor atom, introduced in the silicon by ion implantation, the quantum information can be stored for nearly 1 second. However, manufacturing a scalable quantum processor with this method is considered challenging, because of the exponential sensitivity of the exchange interaction that mediates the coupling between the qubits. Here we demonstrate the conditional, coherent control of an electron spin qubit in an exchange-coupled pair of $^{…
The nuclear spin of a phosphorus atom in silicon has been used as a quantum bit in various quantum-information experiments. It has been proposed that this nuclear-spin qubit can be efficiently controlled by an ac electric field, when embedded in a two electron dot-donor setup subject to intrinsic or artificial spin-orbit interaction. Exposing the qubit to control electric fields in that setup exposes it to electric noise as well. In this work, we describe the effect of electric noise mechanisms, such as phonons and $1/f$ charge noise, and estimate the corresponding decoherence time scales of t…
We study theoretically the phonon-induced relaxation and decoherence processes in the hybrid qubit in silicon. Hybrid qubit behaves as a charge qubit when the detuning is close to zero and as spin qubit for large detuning values. It is realized starting from an electrostatically defined double quantum dot where three electrons are confined and manipulated through only electrical tuning. By employing a three-level effective model for the qubit and describing the environment bath as a series of harmonic oscillators in the thermal equilibrium states, we extract the relaxation and decoherence time…
Single spin qubits based on phosphorus donors in silicon are a promising candidate for a large-scale quantum computer. Despite long coherence times, achieving uniform magnetic control remains a hurdle for scale-up due to challenges in high-frequency magnetic field control at the nanometre-scale. Here, we present a proposal for a flopping-mode electric dipole spin resonance qubit based on the combined electron and nuclear spin states of a double phosphorus donor quantum dot. The key advantage of utilising a donor-based system is that we can engineer the number of donor nuclei in each quantum do…
Solid state quantum processors based on spins in silicon quantum dots are emerging as a powerful platform for quantum information processing. High fidelity single- and two-qubit gates have recently been demonstrated and large extendable qubit arrays are now routinely fabricated. However, two-qubit gates are mediated through nearest-neighbor exchange interactions, which require direct wavefunction overlap. This limits the overall connectivity of these devices and is a major hurdle to realizing error correction, quantum random access memory, and multi-qubit quantum algorithms. To extend the conn…
The fidelity of two-qubit gates using silicon spin qubits is limited by charge noise. When attempting to dynamically compensate for charge noise using local echo pulses, crosstalk can cause complications. We present a method of using a deep neural network to optimize the components of an analytically designed composite pulse sequence, resulting in a two-qubit gate robust against charge noise errors while also taking crosstalk into account. We analyze two experimentally motivated scenarios. For a scenario with strong EDSR driving and negligible crosstalk, the composite pulse sequence yields up …
With qubit measurement and control fidelities above the threshold of fault-tolerance, much attention is moving towards the daunting task of scaling up the number of physical qubits to the large numbers needed for fault tolerant quantum computing. Here, quantum dot based spin qubits may offer significant advantages due to their potential for high densities, all-electrical operation, and integration onto an industrial platform. In this system, the initialisation, readout, single- and two-qubit gates have been demonstrated in various qubit representations. However, as seen with other small scale …
The presence of valley states is a significant obstacle to realizing quantum information technologies in Silicon quantum dots, as leakage into alternate valley states can introduce errors into the computation. We use a perturbative analytical approach to study the dynamics of exchange-coupled quantum dots with valley degrees of freedom. We show that if the valley splitting is large and electrons are not properly initialized to valley eigenstates, then time evolution of the system will lead to spin-valley entanglement. Spin-valley entanglement will also occur if the valley splitting is small an…
Spin-$\frac{1}{2}$ $^{119}$Sn nuclei in a silicon semiconductor could make excellent qubits. Nuclear spins in silicon are known to have long coherence times. Tin is isoelectronic with silicon, so we expect electrons can easily shuttle from one Sn atom to another to propagate quantum information via a hyperfine interaction that we predict, from all-electron linearized augmented plane wave density functional theory calculations, to be roughly ten times larger than intrinsic $^{29}$Si. A hyperfine-induced electro-nuclear controlled-phase (e-n-CPhase) gate operation, generated (up to local rotatio…
Significant advances have been made towards fault-tolerant operation of silicon spin qubits, with single qubit fidelities exceeding 99.9%, several demonstrations of two-qubit gates based on exchange coupling, and the achievement of coherent single spin-photon coupling. Coupling arbitrary pairs of spatially separated qubits in a quantum register poses a significant challenge as most qubit systems are constrained to two dimensions (2D) with nearest neighbor connectivity. For spins in silicon, new methods for quantum state transfer should be developed to achieve connectivity beyond nearest-neighb…
Scaling of silicon spin qubits under correlated noise
RIKEN（理化学研究所）；Slovak Academy of Sciences, Institute of Physics（斯洛伐克科学院物理研究所）；QuTech and Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学量子技术与纳米科学卡弗里研究所）；University of Basel（巴塞尔大学）
Quantum computation requires many qubits that can be coherently controlled and coupled to each other. Qubits that are defined using lithographic techniques are often argued to be promising platforms for scalability, since they can be implemented using semiconductor fabrication technology. However, leading solid-state approaches function only at temperatures below 100 mK, where cooling power is extremely limited, and this severely impacts the perspective for practical quantum computation. Recent works on spins in silicon have shown steps towards a platform that can be operated at higher tempera…
Quantum computers are expected to outperform conventional computers for a range of important problems, from molecular simulation to search algorithms, once they can be scaled up to large numbers of quantum bits (qubits), typically millions. For most solid-state qubit technologies, e.g. those using superconducting circuits or semiconductor spins, scaling poses a significant challenge as every additional qubit increases the heat generated, while the cooling power of dilution refrigerators is severely limited at their operating temperature below 100 mK. Here we demonstrate operation of a scalable…
