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Global optimal control for quantum gates and Hamiltonian synthesis

ELIA IANNIELLO

Published Sep 16, 2026• 0 citations
OpenAlex

Abstract

Globally controlled superconducting qubit systems are regaining popularity due to their potential to solve one of the problems that most threatens the scalability of these platforms: the wiring problem. In fact, current quantum computers based on this technology rely on a local approach to qubit control, which, as the number of qubits increases, results in a cable density that interferes with the processor’s proper functioning. Adopting a global control approach makes it possible to reduce the number of cables and thus improve scalability. Since globally controlled architectures capable of universal quantum computation have already been proposed, the natural next step in the study of these platforms is the application of optimal control techniques. Indeed, given the global nature of the controls, optimization takes place across the entire system simultaneously, offering possibilities that would otherwise be unattainable with local control. The main objective of this work is to investigate these possible applications, focusing primarily on three aspects: digital quantum computation, quantum simulation, and the scalability of optimized pulses.

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Globally controlled superconducting qubit systems are regaining popularity due to their potential to solve one of the problems that most threatens the scalability of these platforms: the wiring problem. In fact, current quantum computers based on this technology rely on a local approach to qubit control, which, as the number of qubits increases, results in a cable density that interferes with the processor’s proper functioning. Adopting a global control approach makes it possible to reduce the number of cables and thus improve scalability. Since globally controlled architectures capable of universal quantum computation have already been proposed, the natural next step in the study of these platforms is the application of optimal control techniques. Indeed, given the global nature of the controls, optimization takes place across the entire system simultaneously, offering possibilities that would otherwise be unattainable with local control. The main objective of this work is to investigate these possible applications, focusing primarily on three aspects: digital quantum computation, quantum simulation, and the scalability of optimized pulses.
We propose a platform to implement a scalable universal quantum computer based on a 2D array of superconducting qubits. Notably, calculations in our scheme are enabled by a set of only three global driving signals, irrespective of the number of qubits, ensuring full scalability of the computation. In stark contrast with the existing literature, global control in our scheme is achieved by leveraging the longitudinal ZZ coupling between neighboring qubits. We show how this enables information flow, one-and two-qubit gates through a series of three global pulses that act together on different subsets of the physical qubits in our system. These findings provide an alternative route to the realization of scalable and fault-tolerant superconducting quantum computers with reduced wiring, bringing them one step closer to solving practical problems in our daily lives.
The thesis investigates three challenges in superconducting quantum computing: efficient quantum gate compilation, scalable microwave interfacing of quantum processors (QPUs), and electrical annealing of Josephson junctions.The first part addresses an inefficiency in contemporary two-qubit gate compilation. Universal quantum computation requires only a single entangling two-qubit gate alongside single-qubit rotations, but this minimal gate set requires up to three additional two-qubit gates for every unsupported gate. I show how access to multiple inequivalent two-qubit gate classes overcomes this inefficiency. I experimentally realised an unsupported SWAP operation using one parametric CZ and one parametric iSWAP gate on a circuit-QED architecture. A Kraus-Cirac analysis shows that this combination belongs to the SWAP equivalency class, the fundamental reason for the reduction in two-qubit gates. The experiment demonstrates a rare case of simultaneous CZ and iSWAP support in the same quantum circuit, illustrating how access to multiple inequivalent gate classes can reduce compilation overhead on real hardware.The second part explores direct digital synthesis of microwave signals for interfacing with quantum processors. Conventional control uses heterodyne upconversion with IQ mixers, requiring compensation of LO leakage and IQ skew. I investigated a mixerless architecture based on high-speed DAC/ADC systems to generate and analyse the required microwave signals. CZ and iSWAP gate experiments subsequently verify that the platform is equivalent to conventional QPU setups.The third part investigates post-fabrication electrical tuning of Josephson junctions, in which voltage pulses modify junction resistance to correct fabrication-induced transmon-frequency variations. The speed of resistance change was found to depend exponentially on pulse amplitude. A novel stepwise protocol achieved a 270% resistance increase in an 11-month-old 11.5 kΩ junction, corresponding to a ~2 GHz reduction in transmon frequency, the largest reported selective resistance modification to date. Simulations show that resistance, charging-energy, and superconducting-gap uncertainties contribute equally to the uncertainty in the final qubit frequency. The results support a picture where electrical manipulation modifies the energy landscape, accelerating natural junction ageing.The thesis demonstrates that investigating gate-level compilation strategies, fully digital QPU control, and post-fabrication tuning, helps advance the understanding of how to approach scalable superconducting quantum processors.
The advancement of scalable quantum information processing relies on the accurate and parallel manipulation of a vast number of qubits, potentially reaching into the millions. Superconducting qubits, traditionally controlled through individual circuitry, currently face a formidable scalability challenge due to the excessive use of wires. This challenge is nearing a critical point where it might soon surpass the capacities of on-chip routing, I/O packaging, testing platforms, and economically feasible solutions. Here we introduce a multiplexed control scheme that efficiently utilizes shared control lines for operating multiple qubits and couplers. By integrating quantum hardware-software co-design, our approach utilizes advanced techniques like frequency multiplexing and individual tuning. This enables simultaneous and independent execution of single- and two-qubit gates with significantly simplified wiring. This scheme has the potential to diminish the number of control lines by one to two orders of magnitude in the near future, thereby substantially enhancing the scalability of superconducting quantum processors.
Simple, precise, and robust control is demanded for qubit operations on large quantum information processors. However, existing routes to high-fidelity quantum control heavily rely on arbitrary waveform generators that are difficult to scale up. Here, we show that the arbitrary control of a quantum system can be achieved by simply turning the control fields on and off in a proper sequence. The switching instances can be designed using conventional quantum optimal control algorithms, while the required computational resources for matrix exponentials can be substantially reduced. We demonstrate the flexibility and robustness of the resulting control protocol, and illustrate it in the context of superconducting quantum circuits. We expect this proposal to be achievable with current semiconductor and superconductor technologies, which offers a significant step towards scalable quantum computing.
This thesis describes our work on optimizing quantum control and scaling up quantum computers. We demonstrate the application of automatic differentiation in quantum optimal control, which allows us to specify advanced optimization criteria and incorporate them in the optimization process of quantum control with ease. These criteria enable more intricate control on the evolution path, suppression of departures from the truncated model subspace, as well as minimization of the physical time needed to perform high-fidelity state preparation and unitary gates. We subsequently present our experimental efforts in efficiently scaling up a quantum computer. The innovation of quantum random access memory (qRAM) architecture with multimode circuit QED establishes a promising path towards expanding the information processing power of a quantum device, without introducing control-resources overhead. Using a single Josephson junction transmon circuit serving as the central processor, we demonstrate universal operations on a nine-qubit random access memory. We further present our experimental results in establishing bidirectional and deterministic photonic communication between two remote superconducting multimode processors, connected through a one-meter long coaxial cable. This device demonstrates a prototype of setting up a scalable and distributed quantum computing cluster that could solve a harder computational problem.
Optimization of constrained quantum control problems powers quantum technologies. This task becomes very difficult when these control problems are nonconvex and plagued with dense local extrema. For such problems, current optimization methods must be repeated many times to find good solutions, each time requiring many simulations of the system. Here, we present (QCPOP), a method that eliminates this problem by directly finding globally optimal solutions. The resulting increase in speed, which can be a thousandfold or more, makes it possible to solve problems that were previously intractable. This remarkable advance is due to global optimization methods recently developed for polynomial functions. We demonstrate the power of this method by showing that it obtains an optimal solution in a single run for a problem in which local extrema are so dense that gradient methods require thousands of runs to reach a similar fidelity. Since QCPOP is able to find the global optimum for quantum control, we expect that it will not only enhance the utility of quantum control by making it much easier to find the necessary protocols, but also provide a key tool for understanding the precise limits of quantum technologies. Finally, we note that the ability to cast quantum control as polynomial optimization resolves an open question regarding the computability of exact solutions to quantum control problems.