相关论文: Sharp Quantum vs. Classical Query Complexity Separ…

Quantum computing promises to solve difficult optimization problems in chemistry, physics and mathematics more efficiently than classical computers, but requires fault-tolerant quantum computers with millions of qubits. To overcome errors…

Due to recent technological advances, actual quantum devices are being constructed and used to perform computations. As a result, many classical problems are being restated so as to be solved on quantum computers. Some examples include…

Attempts to separate the power of classical and quantum models of computation have a long history. The ultimate goal is to find exponential separations for computational problems. However, such separations do not come a dime a dozen: while…

We develop a classical model of computation (the S model) which captures some important features of quantum computation, and which allows to design fast algorithms for solving specific problems. In particular, we show that Deutsch's problem…

We present the detailed process of converting the classical Fourier Transform algorithm into the quantum one by using QR decomposition. This provides an example of a technique for building quantum algorithms using classical ones. The…

Quantum computing promises transformational gains for solving some problems, but little to none for others. For anyone hoping to use quantum computers now or in the future, it is important to know which problems will benefit. In this paper,…

Quantum computers are widely believed have an advantage over classical computers, and some have even published some empirical evidence that this is the case. However, these publications do not include a rigorous proof of this advantage,…

Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonabelian hidden subgroup problem, which generalizes the central problem solved by Shor's factoring algorithm. We suggest an…

Classical satisfiability (SAT) and quantum satisfiability (QSAT) are complete problems for the complexity classes NP and QMA which are believed to be intractable for classical and quantum computers, respectively. Statistical ensembles of…

We show that quantum theory allows for transformations of black boxes that cannot be realized by inserting the input black boxes within a circuit in a pre-defined causal order. The simplest example of such a transformation is the classical…

Quantum computational complexity estimates the difficulty of constructing quantum states from elementary operations, a problem of prime importance for quantum computation. Surprisingly, this quantity can also serve to study a completely…

These notes discuss the quantum algorithms we know of that can solve problems significantly faster than the corresponding classical algorithms. So far, we have only discovered a few techniques which can produce speed up versus classical…

Quantum computing promises the ability to compute properties of quantum systems exponentially faster than classical computers. Quantum advantage is achieved when a practical problem is solved more efficiently on a quantum computer than on a…

We initiate a systematic study of the time complexity of quantum divide and conquer algorithms for classical problems. We establish generic conditions under which search and minimization problems with classical divide and conquer algorithms…

We study quantum algorithms working on classical probability distributions. We formulate four different models for accessing a classical probability distribution on a quantum computer, which are derived from previous work on the topic, and…

A central problem in quantum computation is to understand which quantum circuits are useful for exponential speed-ups over classical computation. We address this question in the setting of query complexity and show that for almost any…

Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…

Alongside the development of quantum algorithms and quantum complexity theory in recent years, quantum techniques have also proved instrumental in obtaining results in classical (non-quantum) areas. In this paper we survey these results and…

One advantage of quantum algorithms over classical computation is the possibility to spread out, process, analyse and extract information in multipartite configurations in coherent superpositions of classical states. This will be discussed…

The standard setting of quantum computation for continuous problems uses deterministic queries and the only source of randomness for quantum algorithms is through measurement. This setting is related to the worst case setting on a classical…