Running a Six-Qubit Quantum Circuit on a Silicon Spin-Qubit Array
I. Fernández de Fuentes, Eline Raymenants, Brennan Undseth, Oriol Pietx-Casas, Stephan G. J. Philips, Mateusz Tomasz Mądzik, Sander L. de Snoo, Sergey V. Amitonov, Larysa Tryputen, A.T. Schmitz, A. Y. Matsuura, Giordano Scappucci, Lieven M. K. Vandersypen
The simplicity of encoding a qubit in the state of a single electron spin and the potential for their integration into industry-standard microchips continue to drive the field of semiconductor-based quantum computing. After a series of key first-principles demonstrations validating universal gate operations, initialization and readout, three-qubit algorithms have already been realized with silicon-based quantum dots in past years. Devices containing more qubits have become available since then but experiments have not gone beyond meeting the DiVincenzo criteria. In this work, we fully exploit the capacity of a spin-qubit array and implement a six-qubit quantum circuit, the largest utilizing semiconductor quantum technology. By programming the quantum processor, we execute quantum circuits across all permutations of three, four, five, and six neighboring qubits, demonstrating successful programmable multi-qubit operation throughout the array. Using an error model that incorporates quasi-static noise allows us to qualitatively explain some key trends in our experimental results and highlight the necessity to minimize idling times through simultaneous operations, extending dephasing times, and consistently improving state preparation and measurement fidelities.
The simplicity of encoding a qubit in the state of a single electron spin and the potential for their integration into industry-standard microchips continue to drive the field of semiconductor-based quantum computing. After a series of key first-principles demonstrations validating universal gate operations, initialization and readout, three-qubit algorithms have already been realized with silicon-based quantum dots in past years. Devices containing more qubits have become available since then but experiments have not gone beyond meeting the DiVincenzo criteria. In this work, we fully exploit the capacity of a spin-qubit array and implement a six-qubit quantum circuit, the largest utilizing semiconductor quantum technology. By programming the quantum processor, we execute quantum circuits across all permutations of three, four, five, and six neighboring qubits, demonstrating successful programmable multi-qubit operation throughout the array. Using an error model that incorporates quasi-static noise allows us to qualitatively explain some key trends in our experimental results and highlight the necessity to minimize idling times through simultaneous operations, extending dephasing times, and consistently improving state preparation and measurement fidelities.
Abstract Future quantum computers capable of solving relevant problems will require a large number of qubits that can be operated reliably 1 . However, the requirements of having a large qubit count and operating with high fidelity are typically conflicting. Spins in semiconductor quantum dots show long-term promise 2,3 but demonstrations so far use between one and four qubits and typically optimize the fidelity of either single- or two-qubit operations, or initialization and readout 4–11 . Here, we increase the number of qubits and simultaneously achieve respectable fidelities for universal operation, state preparation and measurement. We design, fabricate and operate a six-qubit processor with a focus on careful Hamiltonian engineering, on a high level of abstraction to program the quantum circuits, and on efficient background calibration, all of which are essential to achieve high fidelities on this extended system. State preparation combines initialization by measurement and real-time feedback with quantum-non-demolition measurements. These advances will enable testing of increasingly meaningful quantum protocols and constitute a major stepping stone towards large-scale quantum computers.
Silicon-based spin qubits have emerged as a promising platform for scalable quantum computation due to their compatibility with advanced semiconductor fabrication and integration with classical CMOS electronics. As fabrication capabilities advance toward larger, higher-yield devices, the field is transitioning from academic prototypes toward processors ultimately requiring millions of qubits. This shift places increasing emphasis on developing operating techniques that scale with qubit number. In this thesis, a four qubit SiMOS processor is used to investigate three key aspects of multi-qubit operation for spin-based quantum computing. First, tuning and operation techniques for parallel double-quantum-dot unit cells are developed. Electron loading strategies enable four-qubit operation in an isolated charge configuration, and universal single- and two-qubit control is demonstrated. The native gate set is characterised using gate set tomography. The processor is operated as two unit cells that can be initialised and read out in parallel, providing two independent parity measurements per shot, without increasing operation time or degrading state preparation and measurement fidelity. Second, control techniques for generating multi-qubit entangled states and executing general quantum circuits are established. Three-qubit maximally entangled states, including cluster and Greenberger–Horne–Zeilinger states, are generated and measured with a maximum fidelity of 82.5%. A Mermin value of 3.14 is achieved, certifying genuine tripartite entanglement. A fully symmetric dynamically decoupled gate sequence is developed, extending the entanglement lifetime beyond T2* to a limit set by T2-Hahn. A workflow for compiling, executing, and analysing arbitrary circuits from OpenQASM is also demonstrated. Finally, the first mid-circuit measurements in a silicon spin-qubit system are presented. This capability is extended to feedforward control, including a novel “in-layer” method that performs conditional phase operations without routing information to the classical control layer. This approach leverages measurement-induced backaction as a control mechanism. Both in-layer and FPGA-enabled feedforward strategies are benchmarked, and their dominant error channels are identified.
We computationally investigate the programmability of quantum circuits that are manipulated with electron spins in semiconductor devices based on the silicon/silicon-germanium heterostructure. Using our multi-scale modeling approach whose workloads are fairly accelerated with a parallel computing, we design an electrically defined quantum dot structure that confines up to 5 electron spins with bias controls, and calculate the sets of electrical biases that serve as the standard operation modes that can initialize the system with weakly or strongly correlated spins. With the secured operation modes, we discuss how essential universal gates can be implemented, and demonstrate end-to-end operations of two different 5-qubit algorithm circuits. This work not only reveals the fundamental guidelines for designs of silicon quantum processors that may not be easy to be procured directly from existing commercial softwares or experiments, but presents the details of a practical method for a computational analysis of quantum information processing in silicon devices that would be hard to be conducted withab-initiosimulations.
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.
Abstract Quantum computation (QC) is one of the most challenging quantum technologies that promise to revolutionize data computation in the long-term by outperforming the classical supercomputers in specific applications. Errors will hamper this quantum revolution if not sufficiently limited and corrected by quantum error correction codes thus avoiding quantum algorithm failures. In particular millions of highly-coherent qubits arranged in a two-dimensional array are required to implement the surface code, one of the most promising codes for quantum error correction. One of the most attractive technologies to fabricate such large number of almost identical high-quality devices is the well known metal-oxide-semiconductor technology. Silicon quantum processor manufacturing can leverage the technological developments achieved in the last 50 years in the semiconductor industry. Here, we review modeling, fabrication aspects and experimental figures of merit of qubits defined in the spin degree of freedom of charge carriers confined in quantum dots and donors in silicon devices along with classical electronics innovations for qubit control and readout. Furthermore, we discuss potential applications of the technology and finally we review the role of start-ups and companies in the silicon-based QC era.
The understanding of quantum mechanics enabled the development of technology such as transistors and has been the foundation of today’s information age. Actively using quantum mechanics to build quantum technology may cause a second revolution in handling information. However, to execute meaningful algorithms, largescale quantum computers have to be built. Such systems are constructed from many qubits, the quantum version of the classical bit. While exciting progress is being made across a range of different qubit platforms, achieving the radical scalability that is necessary to build a largescale processor could be a roadblock. Huge challenges are put on reproducibility, inand output connectivity and material quality. Qubits based on the spins of electrons and holes confined in semiconductor quantum dots may have an important advantage in constructing quantum processors. This platform can profit from the advanced semiconductor industry that was responsible for the first computing revolution. Group IV semiconductors such as silicon and germanium have a high compatibility with industrial semiconductor manufacturing and contain stable isotopes with zero nuclear spin. The materials can be isotopically purified and serve as excellent hosts for spins with long quantum coherence. In Chapter 3 we present quantum dot arrays in silicon metaloxidesemiconductor (SiMOS), strained silicon (Si/SiGe) and strained germanium (Ge/SiGe). A nearly identical integration scheme based on an overlapping gate structure can be used to define quantum dots in each platform. Each platform has its own opportunities, which are carefully assessed. By employing charge sensing we confirm that all quantum dots can be depleted to the singleelectron regime. We compare capacitive crosstalk and find it to be the smallest in SiMOS, relevant for the tuning of quantum dot arrays. Using this crossplatform integration, we can study qubits in each platform with minimal overhead. Long coherence times, excellent singlequbit gate fidelities and twoqubit logic have been demonstrated with SiMOS spin qubits, making it one of the leading platforms for quantum information processing. However, due to the high disorder at the Si/SiO2 interface compared to Ge/SiGe and Si/SiGe interface, quantum dots defined in SiMOS are small and achieving sufficient control over single electrons has been a long standing challenge. In Chapter 5 we show experiments on a double quantum dot that can be isolated from its reservoir. We demonstrate a tunable tunnel coupling between single electrons up to 13 GHz and tunable tunnel rates down to below 1 Hz. These results mark an important step towards the required degree of control over the location of and coupling between quantum dots, necessary for the operation of a large array.