Classical leakage-resilient circuits from quantum fault-tolerant computation

Tese (doutorado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Ciência da Computação, 2015.Implementações físicas de algoritmos criptográficos vazam informação, o que os torna vulneráveis aos chamados ataques de canal lateral. Atualmente, criptografia é utilizada em uma variedade crescente de cenários, e frequentemente a suposição de que a execução de criptossistemas é fisicamente isolada não é realista. A área de resistência a vazamentos propõe mitigar ataques de canal lateral projetando protocolos que são seguros mesmo se a informação vaza durante a execução. Neste trabalho, estudamos computação resistente a vazamento, que estuda o problema de executar computação universal segura na presença de vazamento. Computação quântica tolerante a falhas se preocupa com o problema de ruído em computadores quânticos. Uma vez que é extremamente difícil isolar sistemas quânticos de ruído, a área de tolerância a falhas propões esquemas para executar computações corretamente mesmo se há algum ruído. Existe uma conexão entre resistência a vazamento e tolerância a falhas. Neste trabalho, mostramos que vazamento em um circuito clássico é uma forma de ruído, quando o circuito é interpretado como um circuito quântico. Posteriormente, provamos que para um modelo de vazamento arbitrário, existe um modelo de ruído correspondente para o qual um circuito que é tolerante a falhas de acordo com um modelo de ruído também é resistente a vazamento de acordo com o modelo de vazamento dado. Também mostramos como utilizar construções para tolerância a falhas para implementar circuitos clássicos que são seguros em modelos de vazamento específicos. Isto é feito estabelecendo critérios para os quais circuitos quânticos podem ser convertidos em circuitos clássicos de certa forma que a propriedade de resistência a vazamentos é preservada. Usando estes critérios, convertemos uma implementação de computação quântica tolerante a falhas em um compilador resistente a vazamentos clássicos, isto é, um esquema que compila um circuito arbitrário em um circuito de mesma funcionalidade que é resistente a vazamentos.Physical implementations of cryptographic algorithms leak information, which makes them vulnerable to so-called side-channel attacks. Cryptography is now used in an ever-increasing variety of scenarios, and the assumption that the execution of cryptosystems is physically insulated is often not realistic. The field of leakage resilience proposes to mitigate side-channel attacks by designing protocols that are secure even if information leaks during execution. In this work, we study leakage-resilient computation, which concerns the problem of performing secure universal computation in the presence of leakage. Fault-tolerant quantum computation is concerned with the problem of noise in quantum computers. Since it is very hard to insulate quantum systems from noise, fault tolerance proposes schemes for performing computations correctly even if some noise is present. It turns out that there exists a connection between leakage resilience and fault tolerance. In this work, we show that leakage in a classical circuit is a form of noise, when the circuit is interpreted as quantum. We then prove that for an arbitrary leakage model, there exists a corresponding noise model in which a circuit that is fault-tolerant against the noise model is also resilient against the given leakage model. We also show how to use constructions for fault tolerance to implement classical circuits that are secure in specific leakage models. This is done by establishing criteria in which quantum circuits can be converted into classical circuits in such a way that the leakage resilience property is preserved. Using these criteria, we convert an implementation of universal fault-tolerant quantum computation into a classical leakageresilient compiler, i.e., a scheme that compiles an arbitrary circuit into a circuit of the same functionality that is leakage-resilient

A Silicon Surface Code Architecture Resilient Against Leakage Errors

Spin qubits in silicon quantum dots are one of the most promising building blocks for large scale quantum computers thanks to their high qubit density and compatibility with the existing semiconductor technologies. High fidelity single-qubit gates exceeding the threshold of error correction codes like the surface code have been demonstrated, while two-qubit gates have reached 98\% fidelity and are improving rapidly. However, there are other types of error --- such as charge leakage and propagation --- that may occur in quantum dot arrays and which cannot be corrected by quantum error correction codes, making them potentially damaging even when their probability is small. We propose a surface code architecture for silicon quantum dot spin qubits that is robust against leakage errors by incorporating multi-electron mediator dots. Charge leakage in the qubit dots is transferred to the mediator dots via charge relaxation processes and then removed using charge reservoirs attached to the mediators. A stabiliser-check cycle, optimised for our hardware, then removes the correlations between the residual physical errors. Through simulations we obtain the surface code threshold for the charge leakage errors and show that in our architecture the damage due to charge leakage errors is reduced to a similar level to that of the usual depolarising gate noise. Spin leakage errors in our architecture are constrained to only ancilla qubits and can be removed during quantum error correction via reinitialisations of ancillae, which ensure the robustness of our architecture against spin leakage as well. Our use of an elongated mediator dots creates spaces throughout the quantum dot array for charge reservoirs, measuring devices and control gates, providing the scalability in the design

Q-Pandora Unboxed: Characterizing Noise Resilience of Quantum Error Correction Codes

Quantum error correction codes (QECCs) are critical for realizing reliable quantum computing by protecting fragile quantum states against noise and errors. However, limited research has analyzed the noise resilience of QECCs to help select optimal codes. This paper conducts a comprehensive study analyzing two QECCs - rotated and unrotated surface codes - under different error types and noise models using simulations. Among them, rotated surface codes perform best with higher thresholds attributed to simplicity and lower qubit overhead. The noise threshold, or the point at which QECCs become ineffective, surpasses the error rate found in contemporary quantum processors. When confronting quantum hardware where a specific error or noise model is dominant, a discernible hierarchy emerges for surface code implementation in terms of resource demand. This ordering is consistently observed across unrotated, and rotated surface codes. Our noise model analysis ranks the code-capacity model as the most pessimistic and circuit-level model as the most realistic. The study maps error thresholds, revealing surface code's advantage over modern quantum processors. It also shows higher code distances and rounds consistently improve performance. However, excessive distances needlessly increase qubit overhead. By matching target logical error rates and feasible number of qubits to optimal surface code parameters, our study demonstrates the necessity of tailoring these codes to balance reliability and qubit resources. Conclusively, we underscore the significance of addressing the notable challenges associated with surface code overheads and qubit improvements.Comment: 15 pages; 9 figures; 3 table

Comparing the Overhead of Topological and Concatenated Quantum Error Correction

This work compares the overhead of quantum error correction with concatenated and topological quantum error-correcting codes. To perform a numerical analysis, we use the Quantum Resource Estimator Toolbox (QuRE) that we recently developed. We use QuRE to estimate the number of qubits, quantum gates, and amount of time needed to factor a 1024-bit number on several candidate quantum technologies that differ in their clock speed and reliability. We make several interesting observations. First, topological quantum error correction requires fewer resources when physical gate error rates are high, white concatenated codes have smaller overhead for physical gate error rates below approximately 10E-7. Consequently, we show that different error-correcting codes should be chosen for two of the studied physical quantum technologies - ion traps and superconducting qubits. Second, we observe that the composition of the elementary gate types occurring in a typical logical circuit, a fault-tolerant circuit protected by the surface code, and a fault-tolerant circuit protected by a concatenated code all differ. This also suggests that choosing the most appropriate error correction technique depends on the ability of the future technology to perform specific gates efficiently

Quantum Cryptography Beyond Quantum Key Distribution

Quantum cryptography is the art and science of exploiting quantum mechanical effects in order to perform cryptographic tasks. While the most well-known example of this discipline is quantum key distribution (QKD), there exist many other applications such as quantum money, randomness generation, secure two- and multi-party computation and delegated quantum computation. Quantum cryptography also studies the limitations and challenges resulting from quantum adversaries---including the impossibility of quantum bit commitment, the difficulty of quantum rewinding and the definition of quantum security models for classical primitives. In this review article, aimed primarily at cryptographers unfamiliar with the quantum world, we survey the area of theoretical quantum cryptography, with an emphasis on the constructions and limitations beyond the realm of QKD.Comment: 45 pages, over 245 reference