Effective Pure States for Bulk Quantum Computation

An interferometric complementarity experiment in a bulk Nuclear Magnetic Resonance ensemble

We have experimentally demonstrated the interferometric complementarity, which relates the distinguishability $D$ quantifying the amount of which-way (WW) information to the fringe visibility $V$ characterizing the wave feature of a quantum entity, in a bulk ensemble by Nuclear Magnetic Resonance (NMR) techniques. We primarily concern on the intermediate cases: partial fringe visibility and incomplete WW information. We propose a quantitative measure of $D$ by an alternative geometric strategy and investigate the relation between $D$ and entanglement. By measuring $D$ and $V$ independently, it…

Are random pure states useful for quantum computation?

We show the following: a randomly chosen pure state as a resource for measurement-based quantum computation, is - with overwhelming probability - of no greater help to a polynomially bounded classical control computer, than a string of random bits. Thus, unlike the familiar "cluster states", the computing power of a classical control device is not increased from P to BQP, but only to BPP. The same holds if the task is to sample from a distribution rather than to perform a bounded-error computation. Furthermore, we show that our results can be extended to states with significantly less entangle…

Holographic Interpretation of Shannon Entropy of Coherence of Quantum Pure States

For a quantum pure state in conformal field theory, we generate the Shannon entropy of its coherence, that is, the von Neumann entropy obtained by introducing quantum measurement errors. We give a holographic interpretation of this Shannon entropy, based on Swingle's interpretation of anti-de Sitter space/conformal field theory (AdS/CFT) correspondence in the context of AdS$_3$/CFT$_2$. As a result of this interpretation, we conjecture a differential geometrical formula for the Shannon entropy of the coherence of a quantum pure or purified state in CFT$_2$ at thermal and momentum equilibrium a…

NMR Quantum Computation with a hyperpolarized nuclear spin bulk

We consider two new quantum gate mechanisms based on nuclear spins in hyperpolarized solid $^{129}Xe$ and HCl mixtures and inorganic semiconductors. We propose two schemes for implementing a controlled NOT (CNOT) gate based on nuclear magnetic resonance (NMR) spectroscopy and magnetic resonance imaging (MRI) from hyperpolarized solid $^{129}Xe$ and HCl mixtures and optically pumped NMR in semiconductors. Such gates might be built up with particular spins addressable based on MRI techniques and optical pumping and optical detection techniques. The schemes could be useful for implementing actual…

All pure fermionic non-Gaussian states are magic states for matchgate computations

Magic states were introduced in the context of Clifford circuits as a resource that elevates classically simulatable computations to quantum universal capability, while maintaining the same gate set. Here we study magic states in the context of matchgate (MG) circuits, where the notion becomes more subtle, as MGs are subject to locality constraints and also the SWAP gate is not available. Nevertheless a similar picture of gate-gadget constructions applies, and we show that every pure fermionic state which is non-Gaussian, i.e. which cannot be generated by MGs from a computational basis state, …

Verified Delegated Quantum Computing with One Pure Qubit

While building a universal quantum computer remains challenging, devices of restricted power such as the so-called one pure qubit model have attracted considerable attention. An important step in the construction of these limited quantum computational devices is the understanding of whether the verification of the computation within these models could be also performed in the restricted scheme. Encoding via blindness (a cryptographic protocol for delegated computing) has proven successful for the verification of universal quantum computation with a restricted verifier. In this paper, we presen…

学习可高效生成纯态的计算复杂度

Computational Complexity of Learning Efficiently Generatable Pure States

该研究探讨可高效生成量子态学习的计算复杂度，证明纯态场景下存在带PP谕示的量子多项式时间学习算法，并揭示量子态学习难度与量子密码学的等价/蕴含关联。

纯对数时间与常数空间开销的容错量子计算

Purely-logarithmic-time- and constant-space-overhead fault-tolerant quantum computation

本文证明常数空间开销的容错量子计算可实现严格对数时间开销，通过多项式子秩横向CCZ门和递归蒸馏电路，优于此前含次多对数因子的结果。

On a Geometric Structure of Pure Multi-qubit Quantum States and Its Applicability to a Numerical Computation

For one-qubit pure quantum states, it is already proved that the Voronoi diagrams with respect to two distances -- Euclidean distance and the quantum divergence -- coincide. This fact is a support for a known method to calculate the Holevo capacity. To consider an applicability of this method to quantum states of a higher level system, it is essential to check if the coincidence of the Voronoi diagrams also occurs. In this paper, we show a negative result for that expectation. In other words, we mathematically prove that those diagrams no longer coincide in a higher dimension. That indicates t…

Switching pure states of the dissipative Heisenberg XXZ chain by local magnetic fields

The effects of a local magnetic field on nonequilibrium stationary states (NESS) of the open quantum $XXZ$ spin chain are investigated with a Lindblad master equation approach in the limit of strong dissipation. The local magnetic field is applied to a single bulk spin of the chain while the ends are kept at fixed polarizations by dissipation. We show that suitable changes of the local magnetic field permit to invert the spin current by switching pure NESS with opposite chiralities, while preserving the state purity and achieving optimal transport.

量子控制的纯量子计算中的因果性

Causality in Pure Quantum Computation with Quantum Control

研究量子计算中因果性问题，提出带量子控制的类型化λ演算及范畴语义，用高阶函数和量子条件分支扩展纯量子计算，基于直觉主义BV逻辑设类型系统加强因果性，借新模型证某些不可实现过程不可定义。