Reversible and irreversible dynamics of a qubit interacting with a small environment

Reversible state transfer between superconducting qubits and atomic ensembles

We examine the possibility of coherent, reversible information transfer between solid-state superconducting qubits and ensembles of ultra-cold atoms. Strong coupling between these systems is mediated by a microwave transmission line resonator that interacts near-resonantly with the atoms via their optically excited Rydberg states. The solid-state qubits can then be used to implement rapid quantum logic gates, while collective metastable states of the atoms can be employed for long-term storage and optical read-out of quantum information.

A Model for an Irreversible Bias Current in the Superconducting Qubit Measurement Process

The superconducting charge-phase `Quantronium' qubit is considered in order to develop a model for the measurement process used in the experiment of Vion et. al. [Science 296 886 (2002)]. For this model we propose a method for including the bias current in the read-out process in a fundamentally irreversible way, which to first order, is approximated by the Josephson junction tilted-washboard potential phenomenology. The decohering bias current is introduced in the form of a Lindblad operator and the Wigner function for the current biased read-out Josephson junction is derived and analyzed. Du…

General structures of reversible and quantum gates

The most general structure (in matrix form) of a single-qubit gate is presented. Subsequently, used that to obtain a set of conditions for testing (a) whether a given 2-qubit gate is genuinely a 2-qubit gate, i.e., not decomposable into two single qubit gates and (b) whether a given single qubit gate is self-inverse? Relevance of the results reported here is discussed in the context of optimization of reversible and quantum circuits, especially for the optimization of quantum cost. A systematic procedure is developed for the identification of the non-decomposable 2-qubit gates. Such a non-deco…

一种使用可逆纳米粒子指针的连续自发定位的类测量测试

Can a Measurement Be Undone? Recovering the State of a Measured Microscopic System with a Reversible Measuring Apparatus

提出一种类测量干涉测试连续自发定位（CSL）模型的方法，利用可逆纳米粒子指针放大分支信息，通过相干性恢复与否检测CSL效应，灵敏度显著优于直接物质波测试。

Reversible Fault-Tolerant Logic

It is now widely accepted that the CMOS technology implementing irreversible logic will hit a scaling limit beyond 2016, and that the increased power dissipation is a major limiting factor. Reversible computing can potentially require arbitrarily small amounts of energy. Recently several nano-scale devices which have the potential to scale, and which naturally perform reversible logic, have emerged. This paper addresses several fundamental issues that need to be addressed before any nano-scale reversible computing systems can be realized, including reliability and performance trade-offs and ar…

Ancilla-Input and Garbage-Output Optimized Design of a Reversible Quantum Integer Multiplier

A reversible logic has application in quantum computing. A reversible logic design needs resources such as ancilla and garbage qubits to reconfigure circuit functions or gate functions. The removal of garbage qubits and ancilla qubits are essential in designing an efficient quantum circuit. In the literature, there are multiple designs that have been proposed for a reversible multiplication operation. A multiplication hardware is essential for the circuit design of quantum algorithms, quantum cryptanalysis, and digital signal processing (DSP) applications. The existing designs of reversible qu…

Reversible circuit compilation with space constraints

We develop a framework for resource efficient compilation of higher-level programs into lower-level reversible circuits. Our main focus is on optimizing the memory footprint of the resulting reversible networks. This is motivated by the limited availability of qubits for the foreseeable future. We apply three main techniques to keep the number of required qubits small when computing classical, irreversible computations by means of reversible networks: first, wherever possible we allow the compiler to make use of in-place functions to modify some of the variables. Second, an intermediate repres…

Reversibility and Adiabatic Computation: Trading Time and Space for Energy

Future miniaturization and mobilization of computing devices requires energy parsimonious `adiabatic' computation. This is contingent on logical reversibility of computation. An example is the idea of quantum computations which are reversible except for the irreversible observation steps. We propose to study quantitatively the exchange of computational resources like time and space for irreversibility in computations. Reversible simulations of irreversible computations are memory intensive. Such (polynomial time) simulations are analysed here in terms of `reversible' pebble games. We show that…

One Additional Qubit is Enough: Encoded Embeddings for Boolean Components in Quantum Circuits

Research on quantum computing has recently gained significant momentum since first physical devices became available. Many quantum algorithms make use of so-called oracles that implement Boolean functions and are queried with highly superposed input states in order to evaluate the implemented Boolean function for many different input patterns in parallel. To simplify or enable a realization of these oracles in quantum logic in the first place, the Boolean reversible functions to be realized usually need to be broken down into several non-reversible sub-functions. However, since quantum logic i…

Reversible Circuit Optimization via Leaving the Boolean Domain

For years, the quantum/reversible circuit community has been convinced that: a) the addition of auxiliary qubits is instrumental in constructing a smaller quantum circuit; and, b) the introduction of quantum gates inside reversible circuits may result in more efficient designs. This paper presents a systematic approach to optimizing reversible (and quantum) circuits via the introduction of auxiliary qubits and quantum gates inside circuit designs. This advances our understanding of what may be achieved with a) and b).

Deviations from reversible dynamics in a qubit-oscillator system coupled to a very small environment

In this contribution it is considered a simple and solvable model consisting of a qubit in interaction with an oscillator exposed to a very small "environment" (a second qubit). An isolated qubit-oscillator system having the oscillator initially in one of its energy eigenstates exhibits Rabi oscillations, an evidence of coherent quantum behaviour. It is shown here in which way the coupling to a small "environment" disrupts such regular behaviour, leading to a quasi-periodic dynamics for the qubit linear entropy. In particular, it is found that the linear entropy is very sensitive to the amount…