A hierarchical, reversible mapping between levels of tree structured computation, applicable for structuring the Quantum Computation algorithm for NP-complete problem is presented. It is proven that confining the state of a quantum computer to a subspace of the available Hilbert space, where states are consistent with the problem constraints, can be done in polynomial time. The proposed mapping, together with the method of state reduction can be potentially used for solving NP-complete problems in polynomial time.
We demonstrate the reversible mapping of a coherent state of light with mean photon number n-bar ~= 1.1 to and from the hyperfine states of an atom trapped within the mode of a high finesse optical cavity. The coherence of the basic processes is verified by mapping the atomic state back onto a field state in a way that depends on the phase of the original coherent state. Our experiment represents an important step towards the realization of cavity QED-based quantum networks, wherein coherent transfer of quantum states enables the distribution of quantum information across the network.
In previous work and motivated by a theoretical discussion on physical realizations, a new quantum gate library (the NCV-v1 library) for electronic design automation of quantum circuits has been proposed. Here, qudits instead of qubits are assumed, i.e. a basic building block which does not rely on a two level quantum system but a (multiple-valued) d-level quantum system is assumed. However, the descriptions on the foundation of this new library remained brief. This technical report provides an extended description of the applied ideas and concepts.
The paper introduces dual Toffoli and Peres reversible gates, which operate under disjunctive control, and shows their functionality based on the Barenco et al. quantum model. Both uniform and mixed polarity are considered for the controls. Rewriting rules are presented, which provide a possible reduction of the number of gates and quantum cost of reversible (sub)circuits using standard Toffoli or Peres gates. Finally, a Clifford+T realization of a dual Toffoli and a dual Peres gate is shown, which may be used when mapping reversible circuits to the IBM quantum computers.
Reversible Boolean function is a one-to-one function which maps $n$-bit input to $n$-bit output. Reversible logic synthesis has been widely studied due to its relationship with low-energy computation as well as quantum computation. In this work, we give a structured decomposition for even reversible Boolean functions (RBF). Specifically, for $n\geq 6$, any even $n$-bit RBF can be decomposed to $7$ blocks of $(n-1)$-bit RBF, where $7$ is a constant independent of $n$; and the positions of those blocks have large degree of freedom. Moreover, if the $(n-1)$-bit RBFs are required to be even as wel…
The future challenge of quantum communication are scalable quantum networks, which require coherent and reversible mapping of photonic qubits onto stationary atomic systems (quantum memories). A crucial requirement for realistic networks is the ability to efficiently store multiple qubits in one quantum memory. Here we demonstrate coherent and reversible mapping of 64 optical modes at the single photon level in the time domain onto one solid-state ensemble of rare-earth ions. Our light-matter interface is based on a high-bandwidth (100 MHz) atomic frequency comb, with a pre-determined storage …
Mappings of classical computation onto statistical mechanics models have led to remarkable successes in addressing some complex computational problems. However, such mappings display thermodynamic phase transitions that may prevent reaching solution even for easy problems known to be solvable in polynomial time. Here we map universal reversible classical computations onto a planar vertex model that exhibits no bulk classical thermodynamic phase transition, independent of the computational circuit. Within our approach the solution of the computation is encoded in the ground state of the vertex …
Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms --- search…
The generation of reversible circuits from high-level code is an important problem in several application domains, including low-power electronics and quantum computing. Existing tools compile and optimize reversible circuits for various metrics, such as the overall circuit size or the total amount of space required to implement a given function reversibly. However, little effort has been spent on verifying the correctness of the results, an issue of particular importance in quantum computing. There, compilation allows not only mapping to hardware, but also the estimation of resources required…
Coherent and reversible mapping of quantum information between light and matter is an important experimental challenge in quantum information science. In particular, it is a decisive milestone for the implementation of quantum networks and quantum repeaters. So far, quantum interfaces between light and atoms have been demonstrated with atomic gases, and with single trapped atoms in cavities. Here we demonstrate the coherent and reversible mapping of a light field with less than one photon per pulse onto an ensemble of 10 millions atoms naturally trapped in a solid. This is achieved by coherent…
Our main models of computation (the Turing Machine and the RAM) make fundamental assumptions about which primitive operations are realizable. The consensus is that these include logical operations like conjunction, disjunction and negation, as well as reading and writing to memory locations. This perspective conforms to a macro-level view of physics and indeed these operations are realizable using macro-level devices involving thousands of electrons. This point of view is however incompatible with quantum mechanics, or even elementary thermodynamics, as both imply that information is a conserv…
We exploit the properties of chain mapping transformations of bosonic environments to identify a finite collection of modes able to capture the characteristic features, or fingerprint, of the environment. Moreover we show that the countable infinity of residual bath modes can be replaced by a universal Markovian closure, namely a small collection of damped modes undergoing a Lindblad-type dynamics whose parametrization is independent of the spectral density under consideration. We show that the Markovian closure provides a quadratic speed-up with respect to standard chain mapping techniques an…
In this paper we present a hybrid scheme for topological quantum computation in a system of cold atoms trapped in an atomic lattice. A topological qubit subspace is defined using Majorana fermions which emerge in a network of atomic Kitaev one-dimensional wires. We show how braiding can be efficiently implemented in this setup and propose a direct way to demonstrate the non-Abelian nature of Majorana fermions via a single parity measurement. We then introduce a proposal for the efficient, robust and reversible mapping of the topological qubits to a conventional qubit stored in a single atom. T…
Considering the large-scale quantum computer, it is important to know how much quantum computational resources is necessary precisely and quickly. Unfortunately the previous methods so far cannot support a large-scale quantum computing practically and therefore the analysis because they usually use a non-structured code. To overcome this problem, we propose a fast mapping by using the hierarchical assembly code which is much more compact than the non-structured code. During the mapping process, the necessary modules and their interconnection can be dynamically mapped by using the communication…
INESC-ID / IST - Technical University of Lisboa（INESC-ID／高等理工学院（IST）-里斯本技术大学）
The production system is a theoretical model of computation relevant to the artificial intelligence field allowing for problem solving procedures such as hierarchical tree search. In this work we explore some of the connections between artificial intelligence and quantum computation by presenting a model for a quantum production system. Our approach focuses on initially developing a model for a reversible production system which is a simple mapping of Bennett's reversible Turing machine. We then expand on this result in order to accommodate for the requirements of quantum computation. We prese…
Hybrid quantum memory leveraging slow-light and gradient-echo duality
Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw（华沙大学新技术中心量子光学技术研究中心）；Faculty of Physics, University of Warsaw（华沙大学物理学院）
The reaction-coordinate mapping is a useful technique to study complex quantum dissipative dynamics into structured environments. In essence, it aims to mimic the original problem by means of an 'augmented system', which includes a suitably chosen collective environmental coordinate---the 'reaction coordinate'. This composite then couples to a simpler 'residual reservoir' with short-lived correlations. If, in addition, the residual coupling is weak, a simple quantum master equation can be rigorously applied to the augmented system, and the solution of the original problem just follows from tra…
