Dynamics of two coupled semiconductor spin qubits in a noisy environment
S. Das Sarma, Robert E. Throckmorton, Yang-Le Wu
备注：
11.5 pages, 18 figures. Added new figures to emphasize the effects of charge noise. Expanded the introduction and conclusion to discuss how to experimentally verify our results and to connect it with previous work on larger spin systems. Published in Phys. Rev. B; this is the published version
We theoretically consider the temporal dynamics of two coupled spin qubits (e.g., semiconductor quantum dots) driven by the inter-qubit spin-spin coupling. The presence of environmental noise (e.g., charge traps, nuclear spins, random magnetic impurities) is accounted for by including random magnetic field and random inter-qubit coupling terms in the Hamiltonian. Both Heisenberg coupling and Ising coupling between the spin qubits are considered, corresponding respectively to exchange and capacitive gates as appropriate for single spin and singlet-triplet semiconductor qubit systems, respectively. Both exchange (Heisenberg) and capacitive (Ising) coupling situations can be solved numerically exactly even in the presence of noise, leading to the key findings that (i) the steady-state return probability to the initial state remains close to unity in the presence of strong noise for many, but not all, starting spin configurations, and (ii) the return probability as a function of time is oscillatory with a characteristic noise-controlled decay toward the steady-state value. We also provide results for the magnetization dynamics of the coupled two-qubit system. Our predicted dynamics can be directly tested in the already existing semiconductor spin qubit setups providing insight into their coherent interaction dynamics. Retention of the initial state spin memory even in the presence of strong environmental noise has important implications for quantum computation using spin qubits.
The interface between superconducting Josephson junction and semiconductor position-based qubit implemented in coupled semiconductor q-dots is described such that it can be the base for electrostatic interface between superconducting and semiconductor quantum computer. Modification of Andreev Bound State in Josephson junction by the presence of semiconductor qubit in its proximity and electrostatic interaction with superconducting qubit is spotted by the minimalist tight-binding model. The obtained analytical results allow in creating interface between semiconductor quantum computer and superc…
We present efficient methods to reliably characterize and tune gate-defined semiconductor spin qubits. Our methods are designed to target the tuning procedures of semiconductor double quantum dot in GaAs heterostructures, but can easily be adapted to other quantum-dot-like qubit systems. These tuning procedures include the characterization of the inter-dot tunnel coupling, the tunnel coupling to the surrounding leads and the identification of the various fast initialization points for the operation of the qubit. Since semiconductor-based spin qubits are compatible with standard semiconductor p…
Detection of moving charge in free space is presented in the framework of single electron CMOS devices. It opens the perspective for construction of new type detectors for beam diagnostic in accelerators or for the detection of solar wind. General phenomenological model of noise acting on position based qubit implemented in semiconductor quantum dots is given in the framework of simplistic tight-binding model. Furthermore the effect of accelerator beam on the system of 2 electrostatically coupled qubits is formulated by tight-binding equations. The position based qubits of various topologies a…
We develop a new spectroscopic method to quickly and intuitively characterize the coupling of two microwave-photon-coupled semiconductor qubits via a high-impedance resonator. Highly distinctive and unique geometric patterns are revealed as we tune the qubit tunnel couplings relative to the frequency of the mediating photons. These patterns are in excellent agreement with a simulation using the Tavis-Cummings model, and allow us to readily identify different parameter regimes for both qubits in the detuning space. This method could potentially be an important component in the overall spectrosc…
We report the use of dispersive gate sensing (DGS) as a means of probing the charge environment of heterostructure-based qubit devices. The DGS technique, which detects small shifts in the quantum capacitance associated with single-electron tunnel events, is shown to be sensitive to pockets of charge in the potential-landscape likely under, and surrounding, the surface gates that define qubits and their readout sensors. Configuring a quantum point contact (QPC) as a localized emitter, we show how these charge pockets are activated by the relaxation of electrons tunneling through a barrier. The…
Charge noise remains the primary obstacle to the development of quantum information technologies with semiconductor spin qubits. We use an exact analytical calculation to determine the effects of quasistatic charge noise on a ring of three equally spaced exchange-coupled quantum dots. We calculate the disorder-averaged return probability from a specific initial state, and use it to determine the coherence time T2* and show that it depends only on the disorder strength and not the mean interaction strength. We also use a perturbative approach to investigate other arrangements of three or four q…
In this theoretical manuscript I propose a scheme for entangling a single electron semiconductor spin qubit with a single electron semiconductor charge qubit in a triangular triple quantum dot configuration. Two out of three quantum dots are used to define a single electron semiconductor charge qubit. Furthermore, the spin qubit is embedded in the Zeeman sub-levels of the third quantum dot. Combining single qubit gates with entangling CNOT gates allows one to construct a SWAP gate, and therefore to use the semiconductor spin qubit as a long-lived memory for the semiconductor charge qubit.
While spin qubits based on gate-defined quantum dots have demonstrated very favorable properties for quantum computing, one remaining hurdle is the need to tune each of them into a good operating regime by adjusting the voltages applied to electrostatic gates. The automation of these tuning procedures is a necessary requirement for the operation of a quantum processor based on gate-defined quantum dots, which is yet to be fully addressed. We present an algorithm for the automated fine-tuning of quantum dots, and demonstrate its performance on a semiconductor singlet-triplet qubit in GaAs. The …
Distributing entanglement between distant semiconductor qubit registers using a shared-control shuttling link
QuTech and Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学量子纳米科学卡弗里研究所和QuTech）；QuTech and Netherlands Organisation for Applied Scientific Research (TNO)（QuTech和荷兰应用科学研究组织（TNO））
Justification of tight-binding model from Schroedinger formalism for various topologies of position-based semiconductor qubits is presented in this work. Simplistic tight-binding model allows for description of single-electron devices at large integration scale. However it is due to the fact that tight-binding model omits the integro-differential equations that arise from electron-electron interaction in Schroedinger model. Two approaches are given in derivation of tight-binding model from Schroedinger equation. First approach is conducted by usage of Green functions obtained from Schroedinger…
The Coulomb interactions between electrons play important roles in coupling multiple qubits in various quantum systems. Here we demonstrate controlled quantum operations of three electron charge qubits based on three capacitively coupled semiconductor double quantum dots. The strong interactions between one double dot and other two double dots enable us to control the coherent rotations of one target qubit by the states of two control qubits.
We study the exchange interaction between two hole-spin qubits in a double quantum dot setup in a silicon nanowire in the presence of magnetic and electric fields. Based on symmetry arguments we show that there exists an effective spin that is conserved even in highly anisotropic semiconductors, provided that the system has a twofold symmetry with respect to the direction of the applied magnetic field. This finding facilitates the definition of qubit basis states and simplifies the form of exchange interaction for two-qubit gates in coupled quantum dots. If the magnetic field is applied along …
In recent years semiconducting qubits have undergone a remarkable evolution, making great strides in overcoming decoherence as well as in prospects for scalability, and have become one of the leading contenders for the development of large-scale quantum circuits. In this Review we describe the current state of the art in semiconductor charge and spin qubits based on gate-controlled semiconductor quantum dots, shallow dopants, and color centers in wide band gap materials. We frame the relative strengths of the different semiconductor qubit implementations in the context of quantum simulations, …
The development of novel quantum bits is key to extend the scope of solid-state quantum information science and technology. Using first-principles calculations, we propose that large metal ion - vacancy complexes are promising qubit candidates in two binary crystals: 4H-SiC and w-AlN. In particular, we found that the formation of neutral Hf- and Zr-vacancy complexes is energetically favorable in both solids; these defects have spin-triplet ground states, with electronic structures similar to those of the diamond NV center and the SiC di-vacancy. Interestingly, they exhibit different spin-strai…
Measurement-based quantum computing (MBQC) promises natural compatibility with quantum error correcting codes at the cost of a polynomial increase in physical qubits. MBQC proposals have largely focused on photonic systems, where 2-qubit gates are difficult. Semiconductor spin qubits in quantum dots, on the other hand, offer fast 2-qubit gates via the exchange interaction. In exchange-based quantum computing, as with other solid-state qubits, leakage to higher states is a serious problem that must be mitigated. Here, two hybrid measurement-exchange schemes are proposed which quantify the benef…
Since the 1998 proposal to build a quantum computer using dopants in semiconductors as qubits, much progress has been achieved on semiconductors nano fabrication and control of charge and spins in single dopants. However, an important problem remains, which is the control at the atomic scale of the dopants positioning. We propose to circumvent this problem by using 2 dimensional materials as hosts. Since the first isolation of graphene in 2004, the number of new 2D materials with favorable properties for electronics has been growing. Dopants in 2 dimensional systems are more tightly bound and …
We present a numerically-optimized multipulse framework for the quantum control of a single-electron charge qubit. Our framework defines a set of pulse sequences, necessary for the manipulation of the ideal qubit basis, that avoids errors associated with excitations outside the computational subspace. A novel control scheme manipulates the qubit adiabatically, while also retaining high speed and ability to perform a general single-qubit rotation. This basis generates spatially localized logical qubit states, making readout straightforward. We consider experimentally realistic semiconductor qub…
In this perspective piece, I benchmark gallium arsenide, silicon, and germanium as material platforms for gate-defined quantum dot spin qubits. I focus on materials stacks, quantum dot architectures, bandstructure properties and qualifiers for disorder from electrical transport. This brief note is far from being exhaustive and should be considered a first introduction to the materials challenges and opportunities towards a larger spin qubit quantum processor.
Determination of qubit initialisation and measurement fidelity is important for the overall performance of a quantum computer. However, the method by which it is calculated in semiconductor qubits varies between experiments. In this paper we present a full theoretical analysis of electronic single-shot readout and describe critical parameters to achieve high fidelity readout. In particular, we derive a model for energy selective state readout based on a charge detector response and examine how to optimise the fidelity by choosing correct experimental parameters. Although we focus on single ele…
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. We use charge sensing to discriminate between the (2,0) and (1,1) charge states of a double …
A crucial requirement for scalable quantum-information processing is the realization of multiple-qubit quantum gates. Universal multiple-qubit gates can be implemented by a set of universal single qubit gates and any one kind of two-qubit gate, such as a controlled-NOT (CNOT) gate. Semiconductor quantum dot qubits are a leading approach for the physical implementation of quantum computation, due to their potential for large-scale integration. Two-qubit gate operations have been so far only demonstrated in individual electron spin-based quantum dot systems. Due to the relatively short de-cohere…
The fault-tolerant operation of logical qubits is an important requirement for realizing a universal quantum computer. Spin qubits based on quantum dots have great potential to be scaled to large numbers because of their compatibility with standard semiconductor manufacturing. Here, we show that a quantum error correction code can be implemented using a four-qubit array in germanium. We demonstrate a resonant SWAP gate and by combining controlled-Z and controlled-$\text{S}^{-1}$ gates we construct a Toffoli-like three-qubit gate. We execute a two-qubit phase flip code and find that we can pres…
Coherence of superconducting qubits can be improved by implementing designs that protect the parity of Cooper pairs on superconducting islands. Here, we introduce a parity-protected qubit based on voltage-controlled semiconductor nanowire Josephson junctions, taking advantage of the higher harmonic content in the energy-phase relation of few-channel junctions. A symmetric interferometer formed by two such junctions, gate-tuned into balance and frustrated by a half-quantum of applied flux, yields a cos(2ϕ) Josephson element, reflecting coherent transport of pairs of Cooper pairs. We demonstrate…
We analyze the coupling of two qubits via an epitaxial semiconducting junction. In particular, we consider three configurations that include pairs of transmons or gatemons as well as gatemon-like two qubits formed by an epitaxial four-terminal junction. These three configurations provide an electrical control of the interaction between the qubits by applying voltage to a metallic gate near the semiconductor junction and can be utilized to naturally realize a controlled-Z gate (CZ). We calculate the fidelity and timing for such CZ gate. We demonstrate that in the absence of decoherence, the CZ …
Semiconductor qubits rely on the control of charge and spin degrees of freedom of electrons or holes confined in quantum dots (QDs). They constitute a promising approach to quantum information processing [1, 2], complementary to superconducting qubits [3]. Typically, semiconductor qubit-qubit coupling is short range [1, 2, 4, 5], effectively limiting qubit distance to the spatial extent of the wavefunction of the confined particle, which represents a significant constraint towards scaling to reach dense 1D or 2D arrays of QD qubits. Following the success of circuit quantum eletrodynamics [6], …
School of Electrical Engineering and Telecommunications, UNSW（新南威尔士大学电气与电信工程学院）；DIRAQ（Diraq公司）；IMEC（比利时微电子研究中心）；KU Leuven（荷语鲁汶大学）；Edward S. Rogers Sr. Dept. of Electrical and Computer Engineering, University of Toronto（多伦多大学爱德华·S·罗杰斯Sr.电气与计算机工程系）；ARC Centre of Excellence for Engineered Quantum Systems, School of Physics, The University of Sydney（悉尼大学物理学院工程量子系统卓越中心）；Microsoft Quantum Sydney, The University of Sydney（悉尼大学微软量子悉尼实验室）
