相关论文: On Computational Power of Quantum Branching Progra…
In this paper we review our current results concerning the computational power of quantum read-once branching programs. First of all, based on the circuit presentation of quantum branching programs and our variant of quantum fingerprinting…
Classical branching programs are studied to understand the space complexity of computational problems. Prior to this work, Nakanishi and Ablayev had separately defined two different quantum versions of branching programs that we refer to as…
Branching programs are quite popular for studying time-space lower bounds. Bera et al. recently introduced the model of generalized quantum branching program aka. GQBP that generalized two earlier models of quantum branching programs. In…
Quantum branching programs (quantum binary decision diagrams, respectively) are a convenient tool for examining quantum computations using only a logarithmic amount of space. Recently several types of restricted quantum branching programs…
In this paper, the space complexity of nonuniform quantum computations is investigated. The model chosen for this are quantum branching programs, which provide a graphic description of sequential quantum algorithms. In the first part of the…
In this paper we show that one qubit polynomial time computations are at least as powerful as $\NC^1$ circuits. More precisely, we define syntactic models for quantum and stochastic branching programs of bounded width and prove upper and…
The paper presents the first nontrivial upper and lower bounds for (non-oblivious) quantum read-once branching programs. It is shown that the computational power of quantum and classical read-once branching programs is incomparable in the…
Loop is a powerful program construct in classical computation, but its power is still not exploited fully in quantum computation. The exploitation of such power definitely requires a deep understanding of the mechanism of quantum loop…
Kernel methods are used extensively in classical machine learning, especially in the field of pattern analysis. In this paper, we propose a kernel-based quantum machine learning algorithm that can be implemented on a near-term, intermediate…
According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a…
Understanding and predicting the properties of solid-state materials from first-principles has been a great challenge for decades. Owing to the recent advances in quantum technologies, quantum computations offer a promising way to achieve…
While quantum computers hold the promise of significant computational speedups, the limited size of early quantum machines motivates the study of space-bounded quantum computation. We relate the quantum space complexity of computing a…
A quantum processor is a programmable quantum circuit in which both the data and the program, which specifies the operation that is carried out on the data, are quantum states. We study the situation in which we want to use such a processor…
A model of computation for which reasonable yet still incomplete lower bounds are known is the read-once branching program. Here variants of complexity measures successful in the study of read-once branching programs are defined and…
Several upper bounds on the size of quantum codes are derived using the linear programming approach. These bounds are strengthened for the linear quantum codes.
Quantum computations promise the ability to solve problems intractable in the classical setting. Restricting the types of computations considered often allows to establish a provable theoretical advantage by quantum computations, and later…
In this paper we prove a space lower bound of $n^{\Omega(k)}$ for non-deterministic (syntactic) read-once branching programs ({\sc nrobp}s) on functions expressible as {\sc cnf}s with treewidth at most $k$ of their primal graphs. This lower…
A quantum computer has now solved a specialized problem believed to be intractable for supercomputers, suggesting that quantum processors may soon outperform supercomputers on scientifically important problems. But flaws in each quantum…
The "Power of One Qubit" refers to a computational model that has access to only one pure bit of quantum information, along with n qubits in the totally mixed state. This model, though not as powerful as a pure-state quantum computer, is…
The most powerful technique known at present for bounding the size of quantum codes of prescribed minimum distance is the quantum linear programming bound. Unlike the classical linear programming bound, it is not immediately obvious that if…