Scalable quantum computation in realistic devices requires that precise control can be implemented efficiently in the presence of decoherence and operational errors. We propose a general constructive procedure for designing robust unitary gates on an open quantum system without encoding or measurement overhead. Our results allow for a low-level error correction strategy solely based on Hamiltonian engineering using realistic bounded-strength controls and may substantially reduce implementation requirements for fault-tolerant quantum computing architectures.
Scalable quantum computation in realistic devices requires that precise control can be implemented efficiently in the presence of decoherence and operational errors. We propose a general constructive procedure for designing robust unitary gates on an open quantum system without encoding or measurement overhead. Our results allow for a low-level error correction strategy solely based on Hamiltonian engineering using realistic bounded-strength controls and may substantially reduce implementation requirements for fault-tolerant quantum computing architectures.
Quantum computers promise to solve computational problems that are inaccessible to classical machines. The reliable execution of large-scale quantum algorithms requires robust operations in the presence of noise. Quantum error correction addresses this challenge by encoding quantum information redundantly across several physical qubits, such that errors can be detected and corrected during a computation. However, no single error-correcting code intrinsically supports an inherently robust, fault-tolerant implementation of all gates needed for universal quantum computing. Moreover, most modern approaches to both quantum error correction and the implementation of universal logical operations on encoded qubits rely on mid-circuit measurements and feed-forward control. These types of operations are technologically demanding, often slow, and prone to high error rates, and they limit the overall success probability of quantum algorithms. In this thesis, we develop fault-tolerant protocols and circuits for quantum error correction and universal logical computation, with an emphasis on implementations compatible with current hardware systems. We first focus on fault-tolerant quantum error correction on small codes. By comparing different protocols, we identify trade-offs between compact circuit constructions and their robustness to noise. We then assess their practical performance by comparing numerical simulations of noisy circuits with experimental data. Beyond the preservation of encoded information, we study how universal logic can be implemented in a fault-tolerant manner on encoded qubits. A central approach considered in this thesis is code switching, in which logical information is transferred between two distinct error-correcting codes that support complementary sets of inherently fault-tolerant logical gates. In combination, these codes give access to a complete universal fault-tolerant logical gate set. In this thesis, we determine conditions that allow us to construct fault-tolerant protocols for code switching. We adapt these protocols to the capabilities of current hardware, thereby enabling the first experimental realization of universal fault-tolerant logic by means of code switching. However, the overall performance of these schemes is limited by slow and noisy mid-circuit measurements. To address this bottleneck, we construct a suite of measurement-free fault-tolerant universal operations that do not require any measurements during the execution of an algorithm. In this framework, error correction and logical operations are implemented coherently as part of the quantum circuit, without mid-circuit measurements or in-sequence classical control. We introduce measurement-free code-switching schemes that can be scaled to arbitrary code distances through concatenation, and which thereby provide, in principle, arbitrarily strong error suppression. We further tailor our approach to the capabilities of current trapped-ion quantum processors. New circuit constructions support the first experimental implementation of a logical quantum algorithm without mid-circuit measurements, demonstrated through Grover's search on three encoded qubits. Together, the results of this thesis expand the toolbox for early fault-tolerant quantum computation. They show how protocols for quantum error correction and universal logical gates can be designed without mid-circuit measurements with realistic hardware constraints in mind, opening new pathways towards universal quantum logic.
The key for realizing fault-tolerant quantum computation lies in maintaining the coherence of all qubits so that high-fidelity and robust quantum manipulations on them can be achieved. One of the promising approaches is to use geometric phases in the construction of universal quantum gates, due to their intrinsic robustness against certain types of local noise. However, due to limitations in previous implementations, the noise-resilience feature of nonadiabatic holonomic quantum computation (NHQC) still needs to be improved. Here, in combination with the dynamical-correction technique, we propose a general protocol of universal NHQC with simplified control, which can greatly suppress the effect of the accompanied X errors, retaining the main merit of geometric quantum operations. Numerical simulation shows that the performance of our gate can be much better than that of previous protocols. Remarkably, when incorporating a decoherence-free subspace encoding for the collective dephasing noise, our scheme can also be robust against the involved Z errors. In addition, we also outline the physical implementation of the protocol, which is insensitive to both X and Z errors. Therefore, our protocol provides a promising strategy for scalable fault-tolerant quantum computation.
Reliable execution of large-scale quantum algorithms requires robust underlying operations and this challenge is addressed by quantum error correction (QEC). Most modern QEC protocols rely on measurements and feed-forward operations, which are experimentally demanding, and often slow and prone to high error rates. Additionally, no single error-correcting code intrinsically supports the full set of logical operations required for universal quantum computing, resulting in an increased operational overhead. In this work, we present a complete toolbox for fault-tolerant universal quantum computing without the need for measurements during algorithm execution by combining the strategies of code switching and concatenation. To this end, we develop new fault-tolerant, measurement-free protocols to transfer encoded information between 2D and 3D color codes, which offer complementary and in combination universal sets of robust logical gates. We identify experimentally realistic regimes where these protocols surpass state-of-the-art measurement-based approaches. Moreover, we extend the scheme to higher-distance codes by concatenating the 2D color code with itself and by integrating code switching for operations that lack a natively fault-tolerant implementation. Our measurement-free approach thereby provides a practical and scalable pathway for universal quantum computing on state-of-the-art quantum processors.
Many current quantum error-correcting codes that achieve full fault tolerance suffer from having low ratios of logical to physical qubits and significant overhead. This makes them difficult to implement on current noisy intermediate-scale quantum (NISQ) computers and results in the inability to perform quantum algorithms at useful scales with near-term quantum processors. As a result, calculations are generally done without encoding. We propose a middle ground between these two approaches: constructions in the [[n,n−2,2]] quantum error-detecting code that can detect any error from a single faulty gate by measuring the stabilizer generators of the code and additional ancillas at the end of the computation. This achieves weak fault tolerance. As we show, this yields a significant improvement over no error correction for small computations with low enough physical error probabilities and requires much less overhead than codes that achieve full fault tolerance. We give constructions for a set of gates that achieve universal quantum computation in this error-detecting code, while satisfying weak fault tolerance up to analog imprecision on the physical rotation gate.
High-fidelity and robust quantum manipulation is the key for scalable quantum computation. Therefore, due to its intrinsic operational robustness, quantum manipulation induced by geometric phases is one of the promising strategies. However, the longer gate time for geometric operations and more physical difficulties with regard to implementation hinder its practical and wide application. Here, we propose a simplified implementation of universal holonomic quantum gates on superconducting circuits with experimentally demonstrated techniques, which can remove these two main challenges by introducing time-optimal control into the construction of quantum gates. Notably, our scheme is also based on a decoherence-free subspace encoding and requires minimal physical-qubit resources, which can be partially immune to error caused by qubit-frequency drift, one of the main sources of error for large-scale superconducting circuits. Meanwhile, gate error caused by unwanted leakage can also be eliminated by our deliberate design of quantum evolution paths. Finally, our scheme is numerically shown to be more robust than the conventional ones and thus provides a promising strategy for scalable solid-state fault-tolerant quantum computation.
Quantum error correction (QEC) is indispensable for scalable quantum computing, but implementing it with minimal hardware overhead remains a central challenge. Large spin systems with collective degrees of freedom offer a promising route to reducing the control complexity of qubit architectures while retaining a large Hilbert space for fault-tolerant encoding. However, existing proposals for logical gates and QEC in spin ensembles generally rely on inefficient higher-order interactions. Here we introduce spin-N-Cat codes, which encode logical qubits in superpositions of spin-coherent states and generalize bosonic Cat codes to the modular subspaces of permutationally symmetric spin ensembles. The code corrects collective and individual dephasing, excitation, and decay errors. We also present an efficient physical realization in central-spin systems, such as a quantum dot, where encoding, decoding, and a universal, fault-tolerant, and bias-preserving gate set are implemented using only first-order interactions. Numerical simulations demonstrate high logical fidelity under dephasing and excitation-decay noise, independent of noise bias, and that full QEC cycles are feasible with realistic microscopic parameters. For the large collective spins available in quantum dots, this translates into a substantial extension of coherence time. Our results establish spin-N-Cat codes as a scalable, hardware-efficient approach to QEC in spin-based quantum architectures.