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Journal of Physics Condensed Matter

Electron dynamics in quantum gate operation

Andrew Kerridge, Anthony Henry Harker, Arthur Marshall Stoneham

Published Jun 19, 2007• 10 citations
Publisher

Abstract

We model the evolving time-dependent electronic structure of a solid-state quantum gate as it performs basic quantum operations. Our time-dependent configuration-interaction method follows the evolution of two donor electron spin qubits interacting with a third, optically excited, control spin in an applied magnetic field, a possible realization of the basic component of a proposed quantum information processor. We identify unitary operations which approximately disentangle the control spin, and use them to construct high-accuracy two-electron operations that are locally equivalent to CNOT, SWAP and operations. From our evaluation of the accuracy of a set of candidate gates we estimate the residual entanglement of the control electron and overall gate operation times. These results attest to the feasibility of the silicon-based quantum gates proposed by Stoneham, Fisher and Greenland.

DOI
10.1088/0953-8984/19/28/282201

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•Jan 1, 2024•0 citations
We model the evolving time-dependent electronic structure of a solid-state quantum gate as it performs basic quantum operations. Our time-dependent configuration-interaction method follows the evolution of two donor electron spin qubits interacting with a third, optically excited, control spin in an applied magnetic field, a possible realization of the basic component of a proposed quantum information processor. We identify unitary operations which approximately disentangle the control spin, and use them to construct high-accuracy two-electron operations that are locally equivalent to CNOT, SWAP and operations. From our evaluation of the accuracy of a set of candidate gates we estimate the residual entanglement of the control electron and overall gate operation times. These results attest to the feasibility of the silicon-based quantum gates proposed by Stoneham, Fisher and Greenland.
Abstract We studied the dynamics of a pair of single-electron double quantum dots (DQDs) under longitudinal and transverse static magnetic fields and time-dependent harmonic modulation of their interaction couplings. We propose to modulate the tunnel coupling between the QDs to produce one-qubit gates and the exchange coupling between DQDs to generate entangling gates, the set of operations required for quantum computing. We developed analytical approximations to set the conditions to control the qubits and applied them to numerical calculations to test the accuracy and robustness of the analytical model. The results shows that the unitary evolution of the two-electron state performs the designed operations even under conditions shifted from the ideal ones.
The construction of a solid-state quantum computer remains a coveted, yet elusive goal. Among the most promising scalable candidates are the spin-based approaches, where qubits are represented by electron spins in quantum dots, or by donor-atom nuclear or electron spins, or by combinations thereof. It has been widely assumed that one-qubit gates in these systems, which are based on single-spin addressing, suffer from severe technical difficulties, including slow speed of operation, heating, and device and materials complexity, such as g-factor engineering. For this reason a variety of approaches have been suggested to circumvent one-qubit gates, including encoding the state of a qubit into two or more spins. These approaches inevitably introduce substantial overhead. Here we show that one-qubit gates can in fact be generated using only modest and presently feasible technological requirements. Our solution uses only global magnetic fields and controllable Heisenberg exchange interactions, thus circumventing the need for single-spin addressing. We explicitly show how to build up one-qubit gates from these components using simple pulse sequences. This should substantially simplify the implemention of spin-based solid state quantum computers.
A solid-state two-qubit quantum gate was recently proposed that might be made in a silicon fabrication plant in the near future. In this class of device, entanglement between two quantum bits is controlled by a change from a largely unentangled ground electronic state to an excited state in which useful entanglement can be produced. Such gates have potential advantages, both because they exploit known solid-state behaviour and they separate the storage and manipulation of quantum information. It is important that the excitation step does not create decoherence. We analyse a type of gate proposed before, in which the excitation involves a control electron that interacts with the qubit spins in the excited state. The dynamics of an idealized (but fairly general) gate of this type show that it can be operated to produce a standard two-qubit entangling state.
Scalable quantum processors require high-fidelity universal quantum logic operations in a manufacturable physical platform. Donors in silicon provide atomic size, excellent quantum coherence and compatibility with standard semiconductor processing, but no entanglement between donor-bound electron spins has been demonstrated to date. Here we present the experimental demonstration and tomography of universal one- and two-qubit gates in a system of two weakly exchange-coupled electrons, bound to single phosphorus donors introduced in silicon by ion implantation. We observe that the exchange interaction has no effect on the qubit coherence. We quantify the fidelity of the quantum operations using gate set tomography (GST), and we use the universal gate set to create entangled Bell states of the electrons spins, with fidelity 91.3 ± 3.0%, and concurrence 0.87 ± 0.05. These results form the necessary basis for scaling up donor-based quantum computers. Donors spins in silicon are coherent, high-performance qubits, but scale-up has been challenging. Here the authors present the first experimental demonstration of exchange-based, entangling two qubit gates between electrons bound to 31P donors in Si.
The growing interest in quantum computers has triggered various approaches for the realization of a large-scale quantum processor that can eventually outperform classical high-performance computers. Quantum computers are attracting increasing attention for their potential to enormously accelerate the simulation of quantum systems and the solution of optimization problems, promising an immense impact, particularly in fields such as chemistry, medicine, and cybersecurity. Although it is still a long way to a practical quantum device, the progress over the last decades has shown encouraging results for a so far limited number of quantum bits, or qubits for short, which represent the computational units of the processor. One promising platform for the implementation of qubits is the spin of charge carriers in semiconductor quantum dots. Especially the use of purified silicon as a host material has significantly improved the performance of quantum operations. Advanced fabrication techniques from the established semiconductor industry in principle allow for the manufacturing of a large number of qubits on a small chip, making them specifically competitive from the perspective of scalability. In this thesis, we investigate challenges for electron spin qubits, particularly in the context of scaling to large qubit arrays for quantum computation. We evaluate the performance of quantum gates, present error mitigation strategies, and propose new quantum operations for two particular spin qubit implementations. In a dense array of Loss-DiVincenzo spin qubits on a chip, quantum information can be electrically controlled by microwave pulses. For neighboring qubits, capacitive couplings of nearby electrodes lead to crosstalk that affects the quantum computation. The first examination in this thesis addresses the effect of crosstalk on idling and operating spin qubits due to an interfering microwave drive. After the analysis and characterization of the performance, we suggest mitigation protocols for different constellations of important quantum gates, which can be easily implemented experimentally. We further show how to reduce crosstalk in a two-qubit gate using an asymmetric driving scheme, resulting in an enormous improvement of the gate performance, and may be used to generally overcome the obstacle of crosstalk. An additional source of errors in spin qubit registers originates from the finite residual exchange interaction between neighboring qubits. It arises due to a finite overlap of the electron wave functions and is caused by the limited speed at which the applied voltages can be controlled. We evaluate the fidelity of doing quantum operations under these circumstances with a varying number of neighboring qubits and present robust mitigation schemes with a decent performance also in the presence of noise. Besides crosstalk, another crucial observation in experiments using microwaves is the heating caused by the delivery of high-power radio frequency pulses to the quantum chip and results in a change of the qubit properties. We therefore investigate the impact of phonons on the energy levels in spin qubits to identify a temperature-dependent correction to the qubit state splitting. As microwave pulses are associated with potential errors, exchange-only qubits represent a promising alternative to achieve universal quantum computation only using baseband control. Therefore, we shift our focus towards exchange-only qubits and outline the main error sources in these systems, including residual exchange interactions between spins, charge noise from the applied voltages, and magnetic fluctuations in the material. A consequential complication of this implementation is that the quantum information can leak out of the qubit states. This effect, however, can be reduced in the presence of a finite magnetic field, as we will demonstrate in this thesis. The gate construction for exchange-only qubits usually requires more pulse steps than in the previous qubit type. Nevertheless, if exchange interactions are switched on simultaneously, this can result in faster quantum gates, as we demonstrate in this thesis. Especially the discovery of a quantum operation that introduces relative phases between computational and leakage states can be of interest for the construction of two-qubit gates and will be discussed in an example for a special operation space.