Intermediate quantum maps for quantum computation

Quantum dynamical maps and Markovianity

It is known that the time evolution of a subsystem from an initial state to two later times, t1, t2 (t2 > t1), are both completely positive (CP) but it is shown here that in the intermediate times between t1 and t2, in general, it need not be CP. This reveals the key to the Markov (if CP) and nonMarkov (if NCP) avataras of the intermediate dynamics. This is brought out based on A and B dynamical maps - without resorting to Master equation approach. The choice of tensor product form for the global initial state points towards the system-environment interaction dynamics as the sole cause for Mar…

Interplay of quantum stochastic and dynamical maps to discern Markovian and non-Markovian transitions

It is known that the dynamical evolution of a system, from an initial tensor product state of system and environment, to any two later times, t1,t2 (t2>t1), are both completely positive (CP) but in the intermediate times between t1 and t2 it need not be CP. This reveals the key to the Markov (if CP) and nonMarkov (if it is not CP) avataras of the intermediate dynamics. This is brought out here in terms of the quantum stochastic map A and the associated dynamical map B -- without resorting to master equation approaches. We investigate these features with four examples which have entirely differ…

Divide-and-conquer verification method for noisy intermediate-scale quantum computation

Several noisy intermediate-scale quantum computations can be regarded as logarithmic-depth quantum circuits on a sparse quantum computing chip, where two-qubit gates can be directly applied on only some pairs of qubits. In this paper, we propose a method to efficiently verify such noisy intermediate-scale quantum computation. To this end, we first characterize small-scale quantum operations with respect to the diamond norm. Then by using these characterized quantum operations, we estimate the fidelity $\langleψ_t|\hatρ_{\rm out}|ψ_t\rangle$ between an actual $n$-qubit output state $\hatρ_{\rm …

连接经典与量子世界：映射、态与演化

Bridging Classical and Quantum Worlds: Maps, States, and Evolutions

本文通过分析希尔伯特空间算子空间线性映射中正性与完全正性的中间概念，探讨经典与量子理论的相互作用，提出从经典对应物推导量子态与演化及反之的构造方法。

Eliminating Intermediate Measurements in Space-Bounded Quantum Computation

A foundational result in the theory of quantum computation known as the "principle of safe storage" shows that it is always possible to take a quantum circuit and produce an equivalent circuit that makes all measurements at the end of the computation. While this procedure is time efficient, meaning that it does not introduce a large overhead in the number of gates, it uses extra ancillary qubits and so is not generally space efficient. It is quite natural to ask whether it is possible to defer measurements to the end of a quantum computation without increasing the number of ancillary qubits. W…

带中间测量的IQP计算

IQP computations with intermediate measurements

该研究分析带中间测量的IQP电路，证明非自适应或自适应X基测量及非自适应Z基测量不改变计算能力，而自适应Z基测量或特定CZ门与自适应X基测量模型达到量子普适，且结果对实现误差稳定。