Alternative computing paradigms open the door to exploiting recent innovations in computational hardware to probe the fundamental thermodynamic limits of information processing. One such paradigm employs superconducting quantum interference devices (SQUIDs) to execute classical computations. This, though, requires constructing sufficiently complex superconducting circuits that support a suite of useful information processing tasks and storage operations, as well as understanding these circuits' energetics. First-principles circuit design leads to prohibitive algebraic complications when deriving the effective equations of motion—complications that to date have precluded achieving these goals, let alone doing so efficiently. We circumvent these complications by (i) specializing our class of circuits and physical operating regimes, (ii) synthesizing existing derivation techniques to suit these specializations, and (iii) implementing solution-finding optimizations which facilitate physically interpreting circuit degrees of freedom that respect physically grounded constraints. This leads to efficient and practical circuit prototyping, as well as accessing scalable circuit architectures. The analytical efficiency is demonstrated by reproducing the potential energy landscape generated by a SQUID. We then show how inductively coupling two SQUIDs produces a device that is capable of executing two-bit computations via its composite potential energy landscape. More generally, the synthesized methods detailed here provide a basis for constructing universal logic gates and investigating their thermodynamic performance.
Alternative computing paradigms open the door to exploiting recent innovations in computational hardware to probe the fundamental thermodynamic limits of information processing. One such paradigm employs superconducting quantum interference devices (SQUIDs) to execute classical computations. This, though, requires constructing sufficiently complex superconducting circuits that support a suite of useful information processing tasks and storage operations, as well as understanding these circuits' energetics. First-principles circuit design leads to prohibitive algebraic complications when deriving the effective equations of motion—complications that to date have precluded achieving these goals, let alone doing so efficiently. We circumvent these complications by (i) specializing our class of circuits and physical operating regimes, (ii) synthesizing existing derivation techniques to suit these specializations, and (iii) implementing solution-finding optimizations which facilitate physically interpreting circuit degrees of freedom that respect physically grounded constraints. This leads to efficient and practical circuit prototyping, as well as accessing scalable circuit architectures. The analytical efficiency is demonstrated by reproducing the potential energy landscape generated by a SQUID. We then show how inductively coupling two SQUIDs produces a device that is capable of executing two-bit computations via its composite potential energy landscape. More generally, the synthesized methods detailed here provide a basis for constructing universal logic gates and investigating their thermodynamic performance.
Reducing the energy inefficiency of conventional CMOS-based computing devices-which rely on logically irreversible gates to process information-remains both a fundamental engineering challenge and a practical social challenge of increasing importance. We extend an alternative computing paradigm that manipulates microstate distributions to store information in the metastable minima determined by an effective potential energy landscape. These minima serve as mesoscopic memories that are manipulated by a dynamic landscape to perform information processing. Central to our results is the control erase protocol, which controls the landscape's metastable minima to determine whether information is preserved or erased. Importantly, successive protocol executions can implement a NAND gate-a logically irreversible universal logic gate. We show how to practically implement CEs in a device created by two inductively coupled superconducting quantum interference devices (SQUIDs). We identify circuit parameter ranges that give rise to effective CEs and establish the device's robustness against thermally induced errors. These SQUID-based logical devices are capable of operating above GHz frequencies and at the kBT energy scale. Due to this, optimized devices and associated protocols provide a universal-computation substrate that is both computationally fast and energy efficient.
The physical nature of computation imposes fundamental limits on the energy efficiency of information processing, as formalized by Landauer's principle, which establishes a minimum thermodynamic cost for information erasure. This dissertation investigates near-Landauer-limit computation using superconducting Quantum Flux Parametrons (QFPs). We first establish the theoretical foundations of physical computation, including logical and thermodynamic reversibility, stochastic thermodynamics, and the relationship between information, entropy, and energy dissipation. Building upon these principles, we develop and analyze computational protocols based on QFPs and Coupled QFPs (CQFPs). Numerical simulations demonstrate thermodynamically efficient bit erasure, bit-flip operations, and a superconducting realization of the Szilard Engine. We further demonstrate universal combinational logic through a NAND gate, as well as signal fan-out through a copier gate and memory through a D-latch, providing the essential primitives required for scalable digital computation. A central result of this work is the demonstration that momentum, conventionally regarded as a source of error in superconducting logic, can instead be exploited as a computational resource. By operating QFP circuits in the underdamped regime, momentum-assisted protocols achieve simultaneous improvements in speed, fidelity, and energy efficiency. These results establish QFP-based superconducting circuits as a promising platform for near-Landauer-limit computation and provide a foundation for future momentum-assisted superconducting dynamical computing architectures.
This review aims to provide researchers, experimentalists, and quantum engineers with an updated and technically grounded perspective on the implementation of quantum gates in superconducting NISQ devices. The goal is to establish a comprehensive bridge between theoretical quantum circuit synthesis and its practical, experimental implementation, focusing on superconducting quantum technologies. We systematically examine the diverse landscape of superconducting qubits and processor architectures, ranging from conventional transmons to alternative and unconventional designs, evaluating their unique design trade-offs, connectivity constraints, device physics, and materials impact. Moving from theory to actual implementation, we detail how single- and two-qubit operations are synthesized via microwave-driven and flux-activated pulses. We here present our pulse engineering, wave shaping, calibration workflows, demonstrating how to bridge the gap between abstract gate models and real-world hardware limitations in the direction of a hardware-software co-design framework. To validate these operations, we choose benchmarking methodologies with the purpose to get the more efficient metric for the specific evaluation aspect, including truth tables and quantum process tomography. Therefore, we both discuss the theoretical concepts behind the gate synthesis and show experimental implementation of most fundamental gates by proposing a practical workflow.
Prior to early this century, the semiconductor microprocessor can be scaled according to the Moore's law, basically doubling its performance in every 18 months. Only recently, the energy efficiency of semiconductor integrated circuits has become a concern than their computational capabilities since their power dissipation scales nonlinear with clock frequency. The specific energy dissipation per logic operation for a modern semiconductor computer is still over 6 orders of magnitude above the thermodynamic threshold kBTln2. It has been known for a long time that this thermodynamic limit on the energy dissipation per logic operation can be overcome by physically and logically reversible circuits. Reversible circuits based on nSQUIDs (negative SQUIDs) or dc SQUIDs (superconducting quantum interference device) with negative mutual inductance between the arms of the SQUID loop, are introduced and investigated in this thesis. First test reversible circuit contains one 8-stage shift register, cells that transfer the input data to the outputs. Dynamic of this circuit illustrates unique properties which agree well with theoretical analysis. Based on the knowledge from the study of shift register, a new timing belt clocking scheme built upon the moving vortices along long Josephson junction (LJJ) is introduced and analyzed. The test circuits for this new scheme contain two 8-stage shift registers, one with direct and the other with inverted outputs. The energy dissipation per nSQUID gate per bit measured for these test circuits at 4 K temperature is already below the thermodynamic threshold. A family of logical gates based on the new timing belt and nSQUIDs shift register are continued to be developed and these gates are capable of fundamentally low energy dissipation and the ability to operate in both irreversible and reversible modes. Moreover, the extremely low energy dissipation in these circuits makes them a natural candidate to support circuitry working in quantum mode with unique advantages.
As quantum computing progresses into the new Quantum Utility era—marked by the ca- pability to execute increasingly complex computations with improved fault tolerance—systems exceeding 1,000 qubits have already been demonstrated by Atom Computing and IBM. While the majority of academic and industrial efforts remain focused on qubit-based archi- tectures, built on decades of work in two-state computational logic and algorithms, growing attention is now turning to the untapped potential of qudits—quantum units that ex- tend beyond the binary nature of qubits. Research into qudits is gaining momentum, as increasing the number of computational states per unit can significantly enhance compu- tational power and reduce circuit complexity. This paradigm shift opens the door to more efficient quantum algorithms and hardware architectures. Moreover, hybrid systems that integrate qubits and qudits may provide a powerful bridge between existing technologies and next-generation performance—making qudit research a critical frontier in unlocking the full potential of quantum computing.This dissertation presents a comprehensive framework for implementing a hybrid quan- tum architecture using fluxonium-based qudits. Fluxonium circuits, constructed from a superconducting loop interrupted by a Josephson junction and a large inductance, exhibit strong anharmonicity and non-fixed selection rules. These features enable multiple direct transitions between quantum states, which can be precisely tuned through a set of circuit parameters known as fluxonium characteristic values. A detailed study of these parameters was conducted to identify optimal qudit systems within a ten-dimensional Hilbert space (D = 10), with estimated coherence times comparable to those of conventional qubit sys- tems. Theoretical and numerical tools were developed to extend the approach to higher dimensions. A set of universal qudit logic gates was designed for arbitrary dimensions D = 2^n, as well as some gates and gate combinations in high dimension Hilbert space. The study demonstrates a significant reduction in gate complexity—particularly in the number of driving pulses required for multiply-controlled gates. Additionally, hybrid logic circuits using D = 8 and D = 4 qudits were analyzed, revealing reduced circuit complexity com- pared to qubit-only implementations. In summary, this work shows that fluxonium superconducting circuits are well-suited systems extending the traditional two-level qubit into multi-level qudit operation, where accessing higher energy levels can enhance computational capacity, reduce gate overhead, and enable more efficient quantum algorithms compared to standard qubit architectures.
Abstract We implement a Szilard engine using a 2-bit logical unit consisting of inductively coupled quantum flux parametrons—Josephson-junction superconducting circuits with applications in both the classical and quantum information processing regimes. Detailed simulations show that it is highly thermodynamically efficient while functioning as a Maxwell demon—converting heat to work. The physically-calibrated design is targeted to direct experimental exploration. However, in realizing experiments variations in Josephson junction fabrication introduce asymmetries that result in energy inefficiency and low operational fidelity. We provide a design solution that mitigates these practical challenges. The resulting platform is ideally suited to probe the thermodynamic foundations of information processing devices far from equilibrium.