Related papers: On the Role of Coherence in Shor's Algorithm
Grover's algorithm constitutes the optimal quantum solution to the search problem and provides a quadratic speed-up over all possible classical search algorithms. Quantum interference between computational paths has been posited as a key…
Quantum coherence quantifies the amount of superposition in a quantum system, and is the reason and resource behind several phenomena and technologies. It depends on the natural basis in which the quantum state of the system is expressed,…
Shor's factoring algorithm, believed to provide an exponential speedup over classical computation, relies on finding the period of an exactly periodic quantum modular multiplication operator. This exact periodicity is the hallmark of an…
Control at the interface between the classical and the quantum world is fundamental in quantum physics. In particular, how classical control is enhanced by coherence effects is an important question both from a theoretical as well as from a…
Coherence is a cornerstone of quantum theory and a prerequisite for the advantage of quantum technologies. In recent work, the notion of coherence with respect to a general quantum measurement (POVM) was introduced and embedded into a…
The geometry of quantum states provides a unifying framework for estimation processes based on quantum probes, and it allows to derive the ultimate bounds of the achievable precision. We show a relation between the statistical distance…
The resource theory of coherence studies the operational value of superpositions in quantum technologies. A key question in this theory concerns the efficiency of manipulation and inter-conversion of the resource. Here we solve this…
Richard Feynman's observation that quantum mechanical effects could not be simulated efficiently on a computer led to speculation that computation in general could be done more efficiently if it used quantum effects. This speculation…
Quantum coherence is an essential ingredient in quantum information processing and plays a central role in emergent fields such as nanoscale thermodynamics and quantum biology. However, our understanding and quantitative characterization of…
We study effects of imperfections induced by residual couplings between qubits on the accuracy of Shor's algorithm using numerical simulations of realistic quantum computations with up to 30 qubits. The factoring of numbers up to N=943 show…
Quantum algorithms have the ability to reduce runtime for executing tasks beyond the capabilities of classical algorithms. Therefore, identifying the resources responsible for quantum advantages is an interesting endeavour. We prove that…
The peculiar uncertainty or randomness of quantum measurements stems from coherence, whose information-theoretic characterization is currently under investigation. Under the resource theory of coherence, it is interesting to investigate…
Quantum computing is a winsome field that concerns with the behaviour and nature of energy at the quantum level to improve the efficiency of computations. In recent years, quantum computation is receiving much attention for its capability…
In this review article we summarize all experiments claiming quantum computational advantage to date. Our review highlights challenges, loopholes, and refutations appearing in subsequent work to provide a complete picture of the current…
Quantum coherence plays a fundamental and operational role in different areas of physics. A resource theory has been developed to characterize the coherence of distinguishable particles systems. Here we show that indistinguishability of…
Shor's algorithm is one of the most important quantum algorithm proposed by Peter Shor [Proceedings of the 35th Annual Symposium on Foundations of Computer Science, 1994, pp. 124--134]. Shor's algorithm can factor a large integer with…
Quantum resource theories identify the features of quantum computers that provide their computational advantage over classical systems. We investigate the resources driving the complexity of classical simulation in the standard model of…
Two primary facets of quantum technological advancement that hold great promise are quantum communication and quantum computation. For quantum communication, the canonical resource is entanglement. For quantum gate implementation, the…
We show that given the order of a single element selected uniformly at random from $\mathbb Z_N^*$, we can with very high probability, and for any integer $N$, efficiently find the complete factorization of $N$ in polynomial time. This…
As a quantum resource, quantum coherence plays an important role in modern physics. Many coherence measures and their relations with entanglement have been proposed, and the dynamics of entanglement has been experimentally studied. However,…