We propose an implementation scheme for holonomic, i.e., geometrical, quantum information processing based on semiconductor nanostructures. Our quantum hardware consists of coupled semiconductor macroatoms addressed/controlled by ultrafast multicolor laser-pulse sequences. More specifically, logical qubits are encoded in excitonic states with different spin polarizations and manipulated by adiabatic time-control of the laser amplitudes . The two-qubit gate is realized in a geometric fashion by exploiting dipole-dipole coupling between excitons in neighboring quantum dots.
Based on electron spins in semiconductor quantum dots as qubits, a new quantum controlled-NOT(CNOT) gate is constructed in solid nanostructure without resorting to spin-spin interactions. Single electron tunneling technology and coherent quantum-dot cellular automata architecture are used to generate an ancillary charge entangled state. Using the ancillary charge entangled state as an intermediate state, we obtain a spin entangled state and design a CNOT gate by using only single spin rotations.
Nonlocal two-qubit gates are geometrically represented by tetrahedron known as Weyl chamber within which perfect entanglers form a polyhedron. We identify that all edges of the Weyl chamber and polyhedron are formed by single parametric gates. Nonlocal attributes of these edges are characterized using entangling power and local invariants. In particular, SWAP (power)alpha family of gates constitutes one edge of the Weyl chamber with SWAP-1/2 being the only perfect entangler. Finally, optimal constructions of controlled-NOT using SWAP-1/2 gate and gates belong to three edges of the polyhedron a…
In this paper we study the implementation of non-adiabatic geometrical quantum gates with in semiconductor quantum dots. Different quantum information enconding/manipulation schemes exploiting excitonic degrees of freedom are discussed. By means of the Aharanov-Anandan geometrical phase one can avoid the limitations of adiabatic schemes relying on adiabatic Berry phase; fast geometrical quantum gates can be in principle implemented
Nonlocal two-qubit quantum gates are represented by canonical decomposition or equivalently by operator-Schmidt decomposition. The former decomposition results in geometrical representation such that all the two-qubit gates form tetrahedron within which perfect entanglers form a polyhedron. On the other hand, it is known from the later decomposition that Schmidt number of nonlocal gates can be either 2 or 4. In this work, some aspects of later decomposition are investigated. It is shown that two gates differing by local operations possess same set of Schmidt coefficients. Employing geometrical…
The dependence of the g-factors of semiconductor donors on applied electric and magnetic fields is of immense importance in spin based quantum computation and in semiconductor spintronics. The donor g-factor Stark shift is sensitive to the orientation of the electric and magnetic fields and strongly influenced by the band-structure and spin-orbit interactions of the host. Using a multimillion atom tight-binding framework the spin-orbit Stark parameters are computed for donors in multi-valley semiconductors, silicon and germanium. Comparison with limited experimental data shows good agreement f…
A semiconductor-based charge qubit, confined in double quantum dots, can be a platform to implement quantum computing. However, it suffers severely from charge noises. Here, we provide a theoretical framework to implement universal geometric quantum gates in this system. We find that, while the detuning noise can be suppressed by operating near its corresponding sweet spot, the tunneling noise, on the other hand, is amplified and becomes the dominant source of error for single-qubit gates, a fact previously insufficiently appreciated. We demonstrate, through numerical simulation, that the geom…
It is shown that entangling two-qubit phase gates for quantum computation with atoms inside a resonant optical cavity can be generated via common laser addressing, essentially, within one step. The obtained dynamical or geometrical phases are produced by an evolution that is robust against dissipation in form of spontaneous emission from the atoms and the cavity and demonstrates resilience against fluctuations of control parameters. This is achieved by using the setup introduced by Pachos and Walther [Phys. Rev. Lett. 89, 187903 (2002)] and employing entangling Raman- or STIRAP-like transition…
The ability to perform gates in multiqubit systems that are robust to noise is of crucial importance for the advancement of quantum information technologies. However, finding control pulses that cancel noise while performing a gate is made difficult by the intractability of the time-dependent Schrodinger equation, especially in multiqubit systems. Here, we show that this issue can be sidestepped by using a formalism in which the cumulative error during a gate is represented geometrically as a curve in a multi-dimensional Euclidean space. Cancellation of noise errors to leading order correspond…
We propose an implementation of holonomic (geometrical) quantum gates by means of semiconductor nanostructures. Our quantum hardware consists of semiconductor macroatoms driven by sequences of ultrafast laser pulses ({\it all optical control}). Our logical bits are Coulomb-correlated electron-hole pairs (excitons) in a four-level scheme selectively addressed by laser pulses with different polarization. A universal set of single and two-qubit gates is generated by adiabatic change of the Rabi frequencies of the lasers and by exploiting the dipole coupling between excitons.
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 …
We propose an on-demand single photon source for quantum cryptography using a metal-insulator-semiconductor quantum dot capacitor structure. The main component in the semiconductor is a p-doped quantum well, and the cylindrical gate under consideration is only nanometers in diameter. As in conventional metal-insulator-semiconductor capacitors, our system can also be biased into the inversion regime. However, due to the small gate area, at the onset of inversion there are only a few electrons residing in a quantum dot. In addition, because of the strong size quantization and large Coulomb energ…
A potential scheme is proposed for realizing a two-qubit quantum gate in semiconductor quantum dots. Information is encoded in the spin degrees of freedom of one excess conduction electron of each quantum dot. We propose to use two lasers, radiation two neighboring QDs, and tuned to blue detuning with respect to the resonant frequencies of individual excitons. The two-qubit phase gate can be achieved by means of both Pauli-blocking effect and dipole-dipole coupling between intermediate excitonic states.
We present a solid-state implementation of ultrafast conditional quantum gates. Our proposal for a quantum-computing device is based on the spin degrees of freedom of electrons confined in semiconductor quantum dots, thus benefiting from relatively long decoherence times. More specifically, combining Pauli blocking effects with properly tailored ultrafast laser pulses, we are able to obtain sub-picosecond spin-dependent switching of the Coulomb interaction, which is the essence of our conditional phase-gate proposal. This allows us to realize {\it a fast two qubit gate which does not translate…
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…
We propose a scheme for a two-qubit conditional phase gate by quantum Zeno effect with semiconductor quantum dots. The system consists of two charged dots and one ancillary dot that can perform Rabi oscillations under a resonant laser pulse. The quantum Zeno effect is induced by phonon-assisted exciton relaxation between the ancillary dot and the charged dots, which is equivalent to a continuous measurement. We solve analytically the master equation and simulate the dynamics of the system using a realistic set of parameters. In contrast to standard schemes, larger phonon relaxation rates incre…
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.
Implementations for quantum computing require fast single- and multi-qubit quantum gate operations. In the case of optically controlled quantum dot qubits theoretical designs for long-range two- or multi-qubit operations satisfying all the requirements in quantum computing are not yet available. We have developed a design for a fast, long-range two-qubit gate mediated by a photonic microcavity mode using excited states of the quantum dot-cavity system that addresses these needs. This design does not require identical qubits, it is compatible with available optically induced single qubit operat…
The universal quantum computation is obtained when there exists asymmetric anisotropic exchange between electron spins in coupled semiconductor quantum dots. The asymmetric Heisenberg model can be transformed into the isotropic model through the control of two local unitary rotations for the realization of essential quantum gates. The rotations on each qubit are symmetrical and depend on the strength and orientation of asymmetric exchange. The implementation of the axially symmetric local magnetic fields can assist the construction of quantum logic gates in anisotropic coupled quantum dots. Th…
In a large-scale quantum computer, the cost of communications will dominate the performance and resource requirements, place many severe demands on the technology, and constrain the architecture. Unfortunately, fault-tolerant computers based entirely on photons with probabilistic gates, though equipped with "built-in" communication, have very large resource overheads; likewise, computers with reliable probabilistic gates between photons or quantum memories may lack sufficient communication resources in the presence of realistic optical losses. Here, we consider a compromise architecture, in wh…
We present a realization of two-qubit controlled-phase gate, based on the linear and nonlinear properties of the probe and signal optical pulses in an asymmetric GaAs/AlGaAs double quantum wells. It is shown that, in the presence of cross-phase modulation, a giant cross-Kerr nonlinearity and mutually matched group velocities of the probe and signal optical pulses can be achieved while realizing the suppression of linear and self-Kerr optical absorption synchronously. These characteristics serve to exhibit an all-optical two-qubit controlled-phase gate within efficiently controllable photon-pho…
We show that the g-factor and the spin-flip time T_{1} of a heterojunction quantum dot is very sensitive to the band-bending interface electric field even in the absence of wave function penetration into the barrier. When this electric field is of the order of 10^{5} V/cm, g and T_{1} show high sensitivity to dot radius and magnetic field arising from the interplay between Rashba and Dresselhaus spin-orbit interactions. This result opens new possibilities for the design of a quantum dot spin quantum computer where g-factor and T_{1} can be engineered by manipulating the spin-orbit coupling thr…
We demonstrate a 12 quantum dot device fabricated on an undoped Si/SiGe heterostructure as a proof-of-concept for a scalable, linear gate architecture for semiconductor quantum dots. The device consists of 9 quantum dots in a linear array and 3 single quantum dot charge sensors. We show reproducible single quantum dot charging and orbital energies, with standard deviations less than 20% relative to the mean across the 9 dot array. The single quantum dot charge sensors have a charge sensitivity of 8.2 x 10^{-4} e/root(Hz) and allow the investigation of real-time charge dynamics. As a demonstrat…
Universal quantum computation (UQC) using Majorana fermions on a 2D topological superconducting (TS) medium remains an outstanding open problem. This is because the quantum gate set that can be generated by braiding of the Majorana fermions does not include \emph{any} two-qubit gate and also the single-qubit $π/8$ phase gate. In principle, it is possible to create these crucial extra gates using quantum interference of Majorana fermion currents. However, it is not clear if the motion of the various order parameter defects (vortices, domain walls, \emph{etc.}), to which the Majorana fermions ar…
We construct a quantum gate entangler based on selective phase rotation transform. In particular, we established a relation between quantum integral transform and quantum gates entangler in terms of universal controlled gates for multi-qubit states. Our construction is also related to the geometrical structure of multipartite quantum systems.
Scalable fault-tolerant quantum computer architectures require quantum gates that operate within a small fraction of the qubit decoherence time and with high accuracy over a bandwidth set by the decoherence rate. Electron spin quantum bits in Si are promising because of long decoherence times (~0.5 ms), but electrical gating schemes still seem problematic. Oxide-semiconductor heterostructures have the potential for precise electrical control of gate operations in the semiconductor, using optical rectification in the ferroelectric oxide. Accurate (~80 dB), local (~10 nm), dynamic (>THz) and pro…
In this Letter, we present a physical scheme for implementing the discrete quantum Fourier transform in a coupled semiconductor double quantum dot system. The main controlled-R gate operation can be decomposed into many simple and feasible unitary transformations. The current scheme would be a useful step towards the realization of complex quantum algorithms in the quantum dot system.
We consider two new quantum gate mechanisms based on nuclear spins in hyperpolarized solid $^{129}Xe$ and HCl mixtures and inorganic semiconductors. We propose two schemes for implementing a controlled NOT (CNOT) gate based on nuclear magnetic resonance (NMR) spectroscopy and magnetic resonance imaging (MRI) from hyperpolarized solid $^{129}Xe$ and HCl mixtures and optically pumped NMR in semiconductors. Such gates might be built up with particular spins addressable based on MRI techniques and optical pumping and optical detection techniques. The schemes could be useful for implementing actual…
We design and analyze a logical qubit composed of a linear array of electron spins in semiconductor quantum dots. To avoid the difficulty of fully controlling a two-dimensional array of dots, we adapt spin control and error correction to a one-dimensional line of silicon quantum dots. Control speed and efficiency are maintained via a scheme in which electron spin states are controlled globally using broadband microwave pulses for magnetic resonance while two-qubit gates are provided by local electrical control of the exchange interaction between neighboring dots. Error correction with two-, th…
We show that all geometric quantum gates (GQG's in short), which are quantum gates only with geometric phases, are robust against control field strength errors. As examples of this observation, we show (1) how robust composite rf-pulses in NMR are geometrically constructed and (2) a composite rf-pulse based on Trotter-Suzuki Formulas is a GQG.
In addition to magnetic field and electric charge noise adversely affecting spin qubit operations, performing single-qubit gates on one of multiple coupled singlet-triplet qubits presents a new challenge---crosstalk, which is inevitable (and must be minimized) in any multiqubit quantum computing architecture. We develop a set of dynamically-corrected pulse sequences that are designed to cancel the effects of both types of noise (i.e., field and charge) as well as crosstalk to leading order, and provide parameters for these corrected sequences for all 24 of the single-qubit Clifford gates. We t…
We introduce a hybrid qubit based on a semiconductor nanowire with an epitaxially grown superconductor layer. Josephson energy of the transmon-like device ("gatemon") is controlled by an electrostatic gate that depletes carriers in a semiconducting weak link region. Strong coupling to an on-chip microwave cavity and coherent qubit control via gate voltage pulses is demonstrated, yielding reasonably long relaxation times (0.8 μs) and dephasing times (1 μs), exceeding gate operation times by two orders of magnitude, in these first-generation devices. Because qubit control relies on voltages rath…
In this paper, we present a machine learning framework to design high-fidelity multi-qubit gates for quantum processors based on quantum dots in silicon, with qubits encoded in the spin of single electrons. In this hardware architecture, the control landscape is vast and complex, so we use the deep reinforcement learning method to design optimal control pulses to achieve high fidelity multi-qubit gates. In our learning model, a simulator models the physical system of quantum dots and performs the time evolution of the system, and a deep neural network serves as the function approximator to lea…
We present a theoretical study of single-qubit operations by oscillatory fields on various semiconductor platforms. We explicitly show how to perform faster gate operations by going beyond the universally-used rotating wave approximation (RWA) regime, while using only two sinusoidal pulses. No complicated pulse shaping or optimal control sequences are required. We first show for specific published experiments how much error is currently incurred by implementing pulses designed using standard RWA. We then show that an even modest increase in gate speed would cause problems in using RWA for gate…
A GaAs/AlGaAs based two-qubit quantum device that allows the controlled generation and straightforward detection of entanglement by measuring a stationary current-voltage characteristic is proposed. We have developed a two-particle Green's function method of open systems and calculate the properties of three-dimensional interacting entangled systems non-perturbatively. We present concrete device designs and detailed, charge self-consistent predictions. One of the qubits is an all-electric Mach-Zehnder interferometer that consists of two electrostatically defined quantum wires with coupling win…
Dynamically correcting for unwanted interactions between a quantum system and its environment is vital to achieving the high-fidelity quantum control necessary for a broad range of quantum information technologies. In recent work, we uncovered the complete solution space of all possible driving fields that suppress transverse quasistatic noise errors while performing single-qubit operations. This solution space lives within a simple geometrical framework that makes it possible to obtain globally optimal pulses subject to a set of experimental constraints by solving certain geometrical optimiza…
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…
As with any quantum computing platform, semiconductor quantum dot devices require sophisticated hardware and controls for operation. The increasing complexity of quantum dot devices necessitates the advancement of automated control software and image recognition techniques for rapidly evaluating charge stability diagrams. We use an image analysis toolbox developed in Python to automate the calibration of virtual gates, a process that previously involved a large amount of user intervention. Moreover, we show that straightforward feedback protocols can be used to simultaneously tune multiple tun…
Limitations of the $g$-tensor formalism of semiconductor spin qubits
ELTE Eötvös Loránd University（厄特沃什·罗兰大学）；Institute of Physics, Budapest University of Technology and Economics（布达佩斯技术与经济大学物理研究所）；HUN-REN-BME-BCE Quantum Technology Research Group（匈牙利研究网络-布达佩斯技术与经济大学-布达佩斯经济与商业学院量子技术研究组）
We study quantum coherence in a semiconductor charge qubit formed from a GaAs double quantum dot containing a single electron. Voltage pulses are applied to depletion gates to drive qubit rotations and non-invasive state readout is achieved using a quantum point contact charge detector. We measure a maximum coherence time of ~7 ns at the charge degeneracy point, where the qubit level splitting is first-order-insensitive to gate voltage fluctuations. We compare measurements of the coherence time as a function of detuning with predictions from a 1/f noise model.
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…
Recent experiments have demonstrated superconducting transmon qubits with semiconductor nanowire Josephson junctions. These hybrid gatemon qubits utilize field effect tunability characteristic for semiconductors to allow complete qubit control using gate voltages, potentially a technological advantage over conventional flux-controlled transmons. Here, we present experiments with a two-qubit gatemon circuit. We characterize qubit coherence and stability and use randomized benchmarking to demonstrate single-qubit gate errors below 0.7% for all gates, including voltage-controlled $Z$ rotations. W…
Capacitively coupled semiconductor spin qubits hold promise as the building blocks of a scalable quantum computing architecture with long-range coupling between distant qubits. However, the two-qubit gate fidelities achieved in experiments to date have been severely limited by decoherence originating from charge noise and hyperfine interactions with nuclear spins, and are currently unacceptably low for any conceivable multi-qubit gate operations. Here, we present control protocols that implement two-qubit entangling gates while substantially suppressing errors due to both types of noise. These…
High-fidelity control of quantum bits is paramount for the reliable execution of quantum algorithms and for achieving fault-tolerance, the ability to correct errors faster than they occur. The central requirement for fault-tolerance is expressed in terms of an error threshold. Whereas the actual threshold depends on many details, a common target is the ~1% error threshold of the well-known surface code. Reaching two-qubit gate fidelities above 99% has been a long-standing major goal for semiconductor spin qubits. These qubits are well positioned for scaling as they can leverage advanced semico…
We theoretically show that spontaneously interlayer-coherent bilayer quantum Hall droplets should allow robust and fault-tolerant pseudospin quantum computation in semiconductor nanostructures with voltage-tuned external gates providing qubit control and a quantum Ising Hamiltonian providing qubit entanglement. Using a spin-boson model we estimate decoherence to be small $(\sim 10^{-5})$.
The realization of quantum computers and quantum Internet requires not only quantum gates and quantum memories, but also transistors at single-photon levels to control the flow of information encoded on single photons. Single-photon transistor (SPT) is an optical transistor in the quantum limit, which uses a single photon to open or block a photonic channel. In sharp contrast to all previous SPT proposals which are based on single-photon nonlinearities, here I present a novel design for a high-gain and high-speed (up to THz) SPT based on a linear optical effect - giant circular birefringence (…
Generalized electrostatic quantum swap gate implemented in the chain of 2 double coupled quantum dots using single electron in semiconductor is presented in tight-binding simplistic model specifying both analytic and numerical results. The anticorrelation principle coming from Coulomb electrostatic repulsion is exploited in single electron devices. The formation of quantum entanglement is specified and supported by analytical results. The difference between classical and quantum picture is given. The correlations between geometry of quantum structures and entanglement dynamics are shown in ana…
Recent achievements in the field of gate defined semiconductor quantum dots reinforce the concept of a spin-based quantum computer consisting of nodes of locally connected qubits which communicate with each other via superconducting circuit resonator photons. In this work we theoretically demonstrate a versatile set of quantum gates between adjacent spin qubits defined in semiconductor quantum dots situated within the same node of such a spin-based quantum computer. The electric dipole acquired by the spin of an electron that moves across a double quantum dot potential in a magnetic field grad…
