相关论文: Computation with Unitaries and One Pure Qubit
Deterministic quantum computation with one quantum bit (DQC1) is a restricted model of quantum computing where the input state is the completely mixed state except for a single clean qubit, and only a single output qubit is measured at the…
In our thesis, we try to shed more light onto the complexity of quantum complexity classes by refining the related part of the hierarchy. First, we review the basic concepts of quantum computing in general. Then, inspired by BQP, we define…
We prove that quantum computation is polynomially equivalent to classical probabilistic computation with an oracle for estimating the value of simple sums, quadratically signed weight enumerators. The problem of estimating these sums can be…
We study the computational complexity of certain integrable quantum theories in 1+1 dimensions. We formalize a model of quantum computation based on these theories. In this model, distinguishable particles start out with known momenta and…
Deterministic quantum computation with one quantum bit (DQC1) is a model of quantum computing where the input restricted to containing a single qubit in a pure state and with all other qubits in a completely-mixed state, with only a single…
We study the complexity of computational problems from quantum physics. Typically, they are studied using the complexity class QMA (quantum counterpart of NP) but some natural computational problems appear to be slightly harder than QMA. We…
This article surveys quantum computational complexity, with a focus on three fundamental notions: polynomial-time quantum computations, the efficient verification of quantum proofs, and quantum interactive proof systems. Properties of…
Deterministic quantum computation with one quantum bit (DQC1), or the one clean qubit model, [E. Knill and R. Laflamme, Phys. Rev. Lett. {\bf81}, 5672 (1998)] is a model of quantum computing where the input is the tensor product of a single…
We discuss a classical complexity of finite-dimensional unitary transformations, which can been seen as a computable approximation of classical descriptional complexity of a unitary transformation acting on a set of qubits.
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…
The computational complexity of a quantum state quantifies how hard it is to make. `Complexity geometry', first proposed by Nielsen, is an approach to defining computational complexity using the tools of differential geometry. Here we…
Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum…
What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field…
The complexity of quantum computation remains poorly understood. While physicists attempt to find ways to create quantum computers, we still do not have much evidence one way or the other as to how useful these machines will be. The tools…
A foundational question in quantum computational complexity asks how much more useful a quantum state can be in a given task than a comparable, classical string. Aaronson and Kuperberg showed such a separation in the presence of a quantum…
We construct a model of quantum metrology inspired by the computational model known as deterministic quantum computation with one quantum bit (DQC1). Using only one pure qubit together with $l$ fully-mixed qubits we obtain measurement…
We obtain the strongest separation between quantum and classical query complexity known to date -- specifically, we define a black-box problem that requires exponentially many queries in the classical bounded-error case, but can be solved…
The "quantum complexity" of a unitary operator measures the difficulty of its construction from a set of elementary quantum gates. While the notion of quantum complexity was first introduced as a quantum generalization of the classical…
The number of qubits used by a quantum algorithm will be a crucial computational resource for the foreseeable future. We show how to obtain the classical query complexity for continuous problems. We then establish a simple formula for a…
We develop a sound and complete equational theory for the functional quantum programming language QML. The soundness and completeness of the theory are with respect to the previously-developed denotational semantics of QML. The completeness…