Building a large-scale quantum computer requires the co-optimization of both the quantum bits (qubits) and their control electronics. By operating the CMOS control circuits at cryogenic temperatures (cryo-CMOS), and hence in close proximity to the cryogenic solid-state qubits, a compact quantum-computing system can be achieved, thus promising scalability to the large number of qubits required in a practical application. This work presents a cryo-CMOS microwave signal generator for frequency-multiplexed control of $4\times 32$ qubits (32 qubits per RF output). A digitally intensive architecture offering full programmability of phase, amplitude, and frequency of the output microwave pulses and a wideband RF front end operating from 2 to 20 GHz allow targeting both spin qubits and transmons. The controller comprises a qubit-phase-tracking direct digital synthesis (DDS) back end for coherent qubit control and a single-sideband (SSB) RF front end optimized for minimum leakage between the qubit channels. Fabricated in Intel 22-nm FinFET technology, it achieves a 48-dB SNR and 45-dB spurious-free dynamic range (SFDR) in a 1-GHz data bandwidth when operating at 3 K, thus enabling high-fidelity qubit control. By exploiting the on-chip 4096-instruction memory, the capability to translate quantum algorithms to microwave signals has been demonstrated by coherently controlling a spin qubit at both 14 and 18 GHz.

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A Scalable Cryo-CMOS Controller for the Wideband Frequency-Multiplexed Control of Spin Qubits and Transmons

This paper discloses a mixed-signal control unit of a fully integrated semiconductor quantum processor SoC realized in a 22nm FD-SOI technology. Independent high-resolution DACs that set the amplitude and pulse-width of the control signals were integrated for each qubit, enabling both a programmable semiconductor qubit operation and a per-qubit individual calibration that compensates for the process variability. The lower deco-herence time of the semiconductor charge-qubits as compared to their spin-qubit counterparts was mitigated by using a high frequency of control unit operation. This is facilitated by the co-integration on the same die of the semiconductor quantum structures together with their corresponding classic control circuitry. The main challenge of achieving deep cryogenic operation for the mixed-signal classic control circuit was surpassed by using programmable local heating DACs that slightly boost the local temperature of the control blocks above the average temperature of the die, which needs to be maintained around 4 K to enable a reliable quantum operation. A staged multi-phase operation was adopted for the digital core in order to minimize the quantum decoherence originated in digital noise injection. The high-frequency clock tree and divider allows the generation of sub-20 ps fast edge control pulses with programmable widths down to 166 ps. This offers a wide quantum computation window when compared with the 1µs decoherence time of the charge-qubit structures.

A Mixed-Signal Control Core for a Fully Integrated Semiconductor Quantum Computer System-on-Chip

Quantum information processing systems rely on a broad range of microwave technologies and have spurred development of microwave devices and methods in new operating regimes. Here we review the use of microwave signals and systems in quantum computing, with specific reference to three leading quantum computing platforms: trapped atomic ion qubits, spin qubits in semiconductors, and superconducting qubits. We highlight some key results and progress in quantum computing achieved through the use of microwave systems, and discuss how quantum computing applications have pushed the frontiers of microwave technology in some areas. We also describe open microwave engineering challenges for the construction of large-scale, fault-tolerant quantum computers.

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Microwaves in Quantum Computing

Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is now being studied in diverse fields ranging from condensed matter to quantum gravity. However, measuring entanglement remains a challenge. This is especially so in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Making use of our single-site-resolved control of ultracold bosonic atoms in optical lattices, we prepare two identical copies of a many-body state and interfere them. This enables us to directly measure quantum purity, Rényi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly correlated many-body systems.

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Measuring entanglement entropy in a quantum many-body system

Considering the enormous advances in nanometer-scale CMOS technology that now allows one to reliably fabricate billions of switching devices on a single silicon die, electrostatically controlled quantum dots (implemented as quantum wells) appear to be promising candidates for a massive implementation of quantum bits (qubits) and quantum logic circuits in order to facilitate high-volume production of quantum computers. In this paper, the case of finite two-well and multiple-well potentials arising from semiconductor charged-coupled structures are treated in a rigorous way by Schrodinger formalism. The modeling methodologies presented to allow one to describe the dynamics of quantum states in non-ideal geometries, account for some mechanisms of qubit decoherence and model electrostatic interaction between electrons that lead to entanglement. The presented methodology can be scaled up to circuits of greater complexity.

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Modeling of Semiconductor Electrostatic Qubits Realized Through Coupled Quantum Dots

In this study, a formal definition, robustness analysis and discussion on the control of a position-based semiconductor charge qubit are presented. Such a qubit can be realized in a chain of coupled quantum dots, forming a register of charge-coupled transistor-like devices, and is intended for CMOS implementation in scalable quantum computers. We discuss the construction and operation of this qubit, its Bloch sphere, and relation with maximally localized Wannier functions which define its position-based nature. We then demonstrate how to build a tight-binding model of single and multiple interacting qubits from first principles of the Schrodinger formalism. We provide all required formulae to calculate the maximally localized functions and the entries of the Hamiltonian matrix in the presence of interaction between qubits. We use three illustrative examples to demonstrate the electrostatic interaction of electrons and discuss how to build a model for many-electron (qubit) system. To conclude this study, we show that charge qubits can be entangled through electrostatic interaction.

CMOS Position-Based Charge Qubits: Theoretical Analysis of Control and Entanglement

Properties of two types of position-dependent electrostatic qubits: eigenenergy-based and Wannier-based, are treated with Schrodinger formalism. Their operating principles are given. The corresponding quantum universal gates for selected qubit types are described and their possible implementation is suggested. The modeling methodology of setting and reading semiconductor qubit is suggested. The interface between superconducting and semiconductor quantum computer is proposed and its implementation and operating principles are described.

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From two types of electrostatic position-dependent semiconductor qubits to quantum universal gates and hybrid semiconductor-superconducting quantum computer

This letter presents a single-electron injection device for position-based charge qubit structures implemented in 22-nm fully depleted silicon-on-insulator CMOS. Quantum dots are implemented in local well areas separated by tunnel barriers controlled by gate terminals overlapping with a thin 5-nm undoped silicon film. Interface of the quantum structure with classical electronic circuitry is provided with single-electron transistors that feature doped wells on the classic side. A small $0.7\times 0.4\,\,\mu \text{m}^{2}$ elementary quantum core is co-located with control circuitry inside the quantum operation cell which is operating at 3.5 K and a 2-GHz clock frequency. With this apparatus, we demonstrate a single-electron injection into a quantum dot.

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Panagiotis Giounanlis

Papers

A Mixed-Signal Control Core for a Fully Integrated Semiconductor Quantum Computer System-on-Chip

Modeling of Semiconductor Electrostatic Qubits Realized Through Coupled Quantum Dots

CMOS Position-Based Charge Qubits: Theoretical Analysis of Control and Entanglement

From two types of electrostatic position-dependent semiconductor qubits to quantum universal gates and hybrid semiconductor-superconducting quantum computer

A Single-Electron Injection Device for CMOS Charge Qubits Implemented in 22-nm FD-SOI