Entangled qubits transported through space is a key element in many prospective quantum information systems, from long-distance quantum communication to large modular quantum processors. The moving qubits are decohered by time- and space-dependent noises with finite extent of correlations. Since the qubit paths are interrelated, the phase fluctuations experienced by the qubits exhibit peculiar correlations, which are difficult to analyze with the conventional theory of random processes. We propose an approach to this problem based on the concept of trajectories on random sheets. We establish its efficacy with a specific example of the electron spins shuttled in semiconductor structures, and derive explicit solutions, revealing the role of unusual noise correlations. We also demonstrate how the analysis of noise correlations can enhance the shuttling fidelity, by studying transport of two entangled spins encoding a logical qubit. The proposed approach enabled us to specify the favorable conditions for this encoding, and find a particularly beneficial shuttling regime. We also describe application of this approach to other shuttling scenarios, and explain its utility for analysis of other types of systems, such as atomic qubits and photons in quantum networks.
Entangled qubits transported through space is a key element in many prospective quantum information systems, from long-distance quantum communication to large modular quantum processors. The moving qubits are decohered by time- and space-dependent noises with finite extent of correlations. Since the qubit paths are interrelated, the phase fluctuations experienced by the qubits exhibit peculiar correlations, which are difficult to analyze with the conventional theory of random processes. We propose an approach to this problem based on the concept of trajectories on random sheets. We establish its efficacy with a specific example of the electron spins shuttled in semiconductor structures, and derive explicit solutions, revealing the role of unusual noise correlations. We also demonstrate how the analysis of noise correlations can enhance the shuttling fidelity, by studying transport of two entangled spins encoding a logical qubit. The proposed approach enabled us to specify the favorable conditions for this encoding, and find a particularly beneficial shuttling regime. We also describe application of this approach to other shuttling scenarios, and explain its utility for analysis of other types of systems, such as atomic qubits and photons in quantum networks.
Shuttling of spin qubits between different locations is a key element in many prospective semiconductor systems for quantum information processing, but the shuttled qubits should be protected from decoherence caused by by time- and space-dependent noise. Since the paths of different spin qubits are interrelated, the noise acting on the shuttled spins exhibits complex and unusual correlations. We appraise the role of these correlations using the concept of trajectories on random sheets, and demonstrate that they can drastically affect the efficiency of coherence protection. These correlations can be exploited to enhance the shuttling fidelity, and we show that by encoding a logical qubit in a state of two sequentially shuttled entangled spins, high fidelity can be achieved even for very slow shuttling. We identify the conditions favoring this encoding, and quantify improvement in the shuttling fidelity in comparison with single-spin shuttling.
Reliable long-range qubit shuttling is a powerful tool for scalable quantum computing architectures. We investigate strategies to improve the coherence of moving spin qubits by performing continuous dynamical decoupling by modulating their confinement potential. Specifically, we introduce temporal and spatial breathing shuttling protocols that leverage spin-orbit interactions in hole-spin systems to electrically drive the qubit while moving. This enables efficient dressed-state shuttling, where the spin is continuously rotated during transport, suppressing the effect of low-frequency noise. Using the filter function formalism, we identify driving regimes that efficiently mitigate both global and local magnetic and electric noise sources. We find that confinement-modulated shuttling can significantly enhance coherence during transport, while revealing distinct limitations depending on the correlation length of the noise. Applying our framework to germanium hole-spin qubits, we show that these protocols provide a practical route toward noise-resilient long-range coherent quantum links.
The efficiency of the future devices for quantum information processing will be limited mostly by the finite decoherence rates of the qubits. Recently, substantial progress was achieved in enhancing the time within which a solid-state qubit demonstrates coherent dynamics. This progress is based mostly on a successful isolation of the qubits from external decoherence sources. Under these conditions, the material-inherent sources of noise start to play a crucial role. In most cases, the noise that the quantum device demonstrates has a 1/ f spectrum. This suggests that the environment that destroys the phase coherence of the qubit can be thought of as a system of two-state fluctuators, which experience random hops between their states. In this short review, the current state of the theory of the decoherence due to the qubit interaction with the fluctuators is discussed. The effect of such an environment on two different protocols of the qubit manipulations, free induction and echo signal, is described. It turns out that in many important cases the noise produced by the fluctuators is non-Gaussian. Consequently, the results of the interaction of the qubit with the fluctuators are not determined by the pair correlation function alone. We describe the effect of the fluctuators using the so-called spin-fluctuator model. Being quite realistic, this model allows one to exactly evaluate the qubit dynamics in the presence of one fluctuator. This solution is found, and its features, including non-Gaussian effects, are analyzed in detail. We extend this consideration to systems of large numbers of fluctuators, which interact with the qubit and lead to the 1/ f noise. We discuss existing experiments on the Josephson qubit manipulation and try to identify non-Gaussian behavior.
It is generally assumed that environmental noise arising from thermal fluctuations are detrimental to preserving coherence and entanglement in a quantum system. In the simplest sense, dephasing and decoherence are tied to energy fluctuations driven by coupling between the system and the normal modes of the bath. Here, we explore the role of noise correlation in an open-loop model quantum communication system whereby the ‘sender’ and the ‘receiver’ are subject to local environments with various degrees of correlation or anti-correlation. We introduce correlation within the spectral density by solving multidimensional stochastic differential equations and introduce these into the Redfield equations of motion for the system density matrix. We find that correlation can enhance both the fidelity and purity of a maximally entangled (Bell) state. Moreover, by comparing the evolution of different initial Bell states, we show that one can effectively probe the correlation between two local environments. These observations may be useful in the design of high-fidelity quantum gates and communication protocols.
Single spin quantum dot qubits in silicon are a promising candidate for a scalable quantum processor due to their long coherence times, compact size, and ease of integration into existing fabrication technologies. Realizing a large quantum processor composed of thousands or more logical qubits requires the integration of conventional transistor circuitry \nand wiring interconnects to control each individual dot in the processor. The high density of control wiring required for these processors presents many engineering challenges. In this thesis, we propose a surface code quantum processor for silicon quantum dot qubits based on a node/network architecture. Local nodes consisting of just seven quantum dots are \nspatially separated on the order of microns to facilitate space for the necessary high density wiring. Entanglement is distributed between individual nodes via shuttling of entangled electron pairs throughout the network. X or Z stabilizer operations, necessary for operating the surface code, are realized by distributing three electron spin singlet pairs across four local nodes followed by local gate operations and ancilla measurements. Simulations of electron shuttling indicate that adiabatic transport is possible on timescales that do not bottleneck the processor speed. Phase rotation of the shuttled spin, induced by the Stark shift, can lower the overall shuttling fi delity; however, the error can be mitigated by proper electrostatic tuning of the stationary electron's g-factor. Using realistic noise models, we estimate error thresholds with respect to single and two-qubit gate fidelities as well as \nsinglet dephasing errors during shuttling. Electron shuttling is a key resource of the proposed network architecture. We continue the shuttling simulations by presenting an algorithm for finding constant-adiabatic shuttling control pulses, which enables a more rigorous study of how different conditions impact the shuttling speed and fidelity. These constant adiabatic pulses are used to optimize the physical device geometry to maximize charge shuttling speeds up to 300 nm/ns in the single-valley case. We then switch to an effective Hamiltonian representation where spin and valley degrees of freedom are accounted for during shuttling. Using realistic device and material parameters, shuttle speeds in the range 10-100 nm/ns with high spin entanglement \n fidelities are obtained when the tunneling energy exceeds the Zeeman energy. High fidelity shuttling also requires the inter-dot valley phase difference to be below a threshold determined by the ratio of tunneling and Zeeman energies, so that spin-valley-orbit mixing is weak. In this regime, we find that the primary source of infi delity is a coherent spin rotation that is correctable, in principle, using single spin rotations. Two-qubit gates in the network architecture are mediated by the exchange interaction, \nan interaction that stems from the Coulomb interaction but manifests as a rotation between the |0,1> and |1,0> two qubit states. Realizing fault tolerant two-qubit gates has proven difficult in silicon quantum dots due to charge noise which perturbs the electron orbitals states, causing decoherence. Quantitatively accurate modelling of exchange in general quantum dot networks is important towards realizing fault tolerant gates. Traditional modelling methods, such as a full con figuration interaction approach, are cumbersome due to significant computational overhead required when accounting for the electron-electron interactions in the calculation. We present a modi ed linear combination of harmonic orbitals con figuration interaction (LCHO-CI) approach which signifi cantly reduces the computational time for obtaining quantitatively accurate estimations of exchange. The method works by approximating the single electron orbitals of the quantum dot network using an orthogonal basis of harmonic orbitals. This choice of orthogonal basis allows a precalculated library of matrix elements to be used in evaluating the Coulomb interactions, which speeds up the LCHO-CI calculation. The modi ed LCHO-CI approach is then used to study how the physical device geometry impacts the charge noise sensitivity of a double quantum dot system. We fi nd that, in general, geometries which increase the dot charging energy and decrease the gate lever arms improve the system's sensitivity to charge noise. We conclude this thesis by pivoting away from theoretical studies of silicon quantum dots and towards experimental studies of electron transport in dopant-free GaAs heterostructures. In modulation doped GaAs heterostructures, a doping layer is used to induce a two-dimensional electron gas (2DEG) at the heterojunction. Dopant-free GaAs lack the doping layer which makes fabrication more difficult as local electron reservoirs must be used to bring carriers and induce a 2DEG. The lack of the doping layer offers several advantages over modulation doped heterostructures, such as gate-ability of the 2DEG and ability to make ambipolar devices (both n- and p-type ohmic contacts). Realizing n- and p-type ohmic contacts requires etching a recess pit and depositing the ohmic material at an angle in order to preventing screening of the top gate when inducing a 2DEG or two-dimensional hole gas (2DHG). Magnetotransport experiments are used to characterize an induced 2DEG and 2DHG in a Hall bar fabricated on a 310 nm deep single heterojunction. The carrier mobility and density can be tuned using the top gate, and we achieve peak mobility values of 4.5E6 cm2/Vs and 0.65E6 cm2/Vs for the 2DEG and 2DHG respectively. We then move to a one-dimensional system and study electron transport through a quantum point contact. Conductance quantization is observed, and subband spectroscopy \nmeasurements indicate a 1D subband spacing of 4.5 meV. Finally, we study dynamically driven electron transport in a zero-dimensional system using a tunable-barrier quantum dot acting as a single electron pump. Single electron pumping is observed up to T = 5 K, and fi ts to the electron cascade model suggests pumping errors of 1.87 ppm when operated at a driving frequency of f = 500 MHz.
Maintaining quantum coherence and entanglement in the presence of environmental noise, particularly within non-Markovian contexts, represents a significant challenge for the progression of quantum information science and technology. This study offers a substantial advancement by investigating the dynamics of a two-qubit system subjected to diverse noise conditions, encompassing relaxation, dephasing, and their cumulative effects. By employing quantum-state-diffusion equations specifically crafted for non-Markovian environments, we introduce an innovative strategy to counteract the detrimental influences of environmental noise on quantum teleportation fidelity and entanglement concurrence. Our results underscore the potential for external interventions to markedly improve the resilience of quantum information processing tasks over prolonged durations, especially in settings where dephasing noise prevails. A key revelation is the intricate relationship between dephasing noise and the initial state of entanglement, which profoundly impacts the occurrence of entanglement sudden death. This research not only deepens our comprehension of quantum system dynamics under noisy circumstances but also furnishes practical directives for engineering robust quantum systems, a necessity for the development of scalable quantum technologies.