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The continuous growth of quantum computing and the increasingly complex quantum programs resulting from it lead to unprecedented obstacles in ensuring program correctness. Runtime assertions are, therefore, becoming a crucial tool in the…
The structure of satisfiability problems is used to improve search algorithms for quantum computers and reduce their required coherence times by using only a single coherent evaluation of problem properties. The structure of random k-SAT…
In this paper, we study quantum query complexity of the following rather natural tripartite generalisations (in the spirit of the 3-sum problem) of the hidden shift and the set equality problems, which we call the 3-shift-sum and the…
Quantum computing has demonstrated the potential to solve computationally intensive problems more efficiently than classical methods. Many software engineering tasks, such as test case selection, static analysis, code clone detection, and…
Computational methods are the most effective tools we have besides scientific experiments to explore the properties of complex biological systems. Progress is slowing because digital silicon computers have reached their limits in terms of…
Quantum computing leverages the principles of quantum mechanics to perform computations far beyond the capabilities of classical systems, particularly in fields such as cryptography and optimization. However, current quantum programming…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
With the constantly advancing capabilities of quantum computers, conventional cryptographic systems relying on complex math problems may encounter unforeseen vulnerabilities. Unlike regular computers, which are often deemed cost-ineffective…
It is imperative that useful quantum computers be very difficult to simulate classically; otherwise classical computers could be used for the applications envisioned for the quantum ones. Perfect quantum computers are unarguably…
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
Quantum computers show promise to solve select problems otherwise intractable on classical computers. However, noisy intermediate-scale quantum (NISQ) era devices are currently prone to various sources of error. Quantum error correction…
Quantum computers hold promise for solving problems intractable for classical computers, especially those with high time or space complexity. Practical quantum advantage can be said to exist for such problems when the end-to-end time for…
The future development of quantum technologies relies on creating and manipulating quantum systems of increasing complexity, with key applications in computation, simulation and sensing. This poses severe challenges in the efficient…
The power of quantum computers is still somewhat speculative. While they are certainly faster than classical ones at some tasks, the class of problems they can efficiently solve has not been mapped definitively onto known classical…
Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and…
In the past decade quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests…
The local Hamiltonian (LH) problem is the canonical $\mathsf{QMA}$-complete problem introduced by Kitaev. In this paper, we show its hardness in a very strong sense: we show that the 3-local Hamiltonian problem on $n$ qubits cannot be…
The Quantum Computer Condition (QCC) provides a rigorous and completely general framework for carrying out analyses of questions pertaining to fault-tolerance in quantum computers. In this paper we apply the QCC to the problem of…
The so-called "threshold" theorem says that, once the error rate per qubit per gate is below a certain value, indefinitely long quantum computation becomes feasible, even if all of the qubits involved are subject to relaxation processes,…
Quantum computing has the potential to revolutionize multiple fields by solving complex problems that can not be solved in reasonable time with current classical computers. Nevertheless, the development of quantum computers is still in its…