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Quantum computer possesses quantum parallelism and offers great computing power over classical computer cite{er1,er2}. As is well-know, a moving quantum object passing through a double-slit exhibits particle wave duality. A quantum computer is static and lacks this duality property. The recently proposed duality computer has exploited this particle wave duality property, and it may offer additional computing power cite{r1}. Simply put it, a duality computer is a moving quantum computer passing through a double-slit. A duality computer offers the capability to perform separate operations on the sub-waves coming out of the different slits, in the so-called duality parallelism. Here we show that an $n$-dubit duality computer can be modeled by an $(n+1)$-qubit quantum computer. In a duality mode, computing operations are not necessarily unitary. A $n$-qubit quantum computer can be used as an $n$-bit reversible classical computer and is energy efficient. Our result further enables a $(n+1)$-qubit quantum computer to run classical algorithms in a $O(2^n)$-bit classical computer. The duality mode provides a natural link between classical computing and quantum computing. Here we also propose a recycling computing mode in which a quantum computer will continue to compute until the result is obtained. These two modes provide new tool for algorithm design. A search algorithm for the unsorted database search problem is designed.
Quantum computers are capable of efficiently contracting unitary tensor networks, a task that is likely to remain difficult for classical computers. For instance, networks based on matrix product states or the multi-scale entanglement renormalization
Fluctuation relations allow for the computation of equilibrium properties, like free energy, from an ensemble of non-equilibrium dynamics simulations. Computing them for quantum systems, however, can be difficult, as performing dynamic simulations of
The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment. Recovery from e
This article introduces quantum computation by analogy with probabilistic computation. A basic description of the quantum search algorithm is given by representing the algorithm as a C program in a novel way.
Benchmarking is how the performance of a computing system is determined. Surprisingly, even for classical computers this is not a straightforward process. One must choose the appropriate benchmark and metrics to extract meaningful results. Different