Quantum random access memory

A random access memory (RAM) uses n bits to randomly address N=2^n distinct memory cells. A quantum random access memory (qRAM) uses n qubits to address any quantum superposition of N memory cells. We present an architecture that exponentially reduces the requirements for a memory call: O(log N) switches need be thrown instead of the N used in conventional (classical or quantum) RAM designs. This yields a more robust qRAM algorithm, as it in general requires entanglement among exponentially less gates, and leads to an exponential decrease in the power needed for addressing. A quantum optical implementation is presented.Comment: 4 pages, 3 figures. Accepted for publication on Phys. Rev. Let

The conditional entropy power inequality for quantum additive noise channels

We prove the quantum conditional Entropy Power Inequality for quantum additive noise channels. This inequality lower bounds the quantum conditional entropy of the output of an additive noise channel in terms of the quantum conditional entropies of the input state and the noise when they are conditionally independent given the memory. We also show that this conditional Entropy Power Inequality is optimal in the sense that we can achieve equality asymptotically by choosing a suitable sequence of Gaussian input states. We apply the conditional Entropy Power Inequality to find an array of information-theoretic inequalities for conditional entropies which are the analogues of inequalities which have already been established in the unconditioned setting. Furthermore, we give a simple proof of the convergence rate of the quantum Ornstein-Uhlenbeck semigroup based on Entropy Power Inequalities.Comment: 26 pages; updated to match published versio

An AC Stark Gradient Echo Memory in Cold Atoms

The burgeoning fields of quantum computing and quantum key distribution have created a demand for a quantum memory. The gradient echo memory scheme is a quantum memory candidate for light storage that can boast efficiencies approaching unity, as well as the flexibility to work with either two or three level atoms. The key to this scheme is the frequency gradient that is placed across the memory. Currently the three level implementation uses a Zeeman gradient and warm atoms. In this paper we model a new gradient creation mechanism - the ac Stark effect - to provide an improvement in the flexibility of gradient creation and field switching times. We propose this scheme in concert with a move to cold atoms (~1 mK). These temperatures would increase the storage times possible, and the small ensemble volumes would enable large ac Stark shifts with reasonable laser power. We find that memory bandwidths on the order of MHz can be produced with experimentally achievable laser powers and trapping volumes, with high precision in gradient creation and switching times on the order of nanoseconds possible. By looking at the different decoherence mechanisms present in this system we determine that coherence times on the order of 10s of milliseconds are possible, as are delay-bandwidth products of approximately 50 and efficiencies over 90%

Quantum repeaters with imperfect memories: cost and scalability

Memory dephasing and its impact on the rate of entanglement generation in quantum repeaters is addressed. For systems that rely on probabilistic schemes for entanglement distribution and connection, we estimate the maximum achievable rate per employed memory for our optimized partial nesting protocol. We show that, for any given distance $L$, the polynomial scaling of rate with distance can only be achieved if quantum memories with coherence times on the order of $L/c$ or longer, with $c$ being the speed of light in the channel, are available. The above rate degrades as a power of $\exp[-\sqrt{(L/c)/ \tau_c}]$ with distance when the coherence time $\tau_c \ll L/c$.Comment: Extended version with 5 figure

Quantum computation with devices whose contents are never read

In classical computation, a "write-only memory" (WOM) is little more than an oxymoron, and the addition of WOM to a (deterministic or probabilistic) classical computer brings no advantage. We prove that quantum computers that are augmented with WOM can solve problems that neither a classical computer with WOM nor a quantum computer without WOM can solve, when all other resource bounds are equal. We focus on realtime quantum finite automata, and examine the increase in their power effected by the addition of WOMs with different access modes and capacities. Some problems that are unsolvable by two-way probabilistic Turing machines using sublogarithmic amounts of read/write memory are shown to be solvable by these enhanced automata.Comment: 32 pages, a preliminary version of this work was presented in the 9th International Conference on Unconventional Computation (UC2010

An Application of Quantum Finite Automata to Interactive Proof Systems

Quantum finite automata have been studied intensively since their introduction in late 1990s as a natural model of a quantum computer with finite-dimensional quantum memory space. This paper seeks their direct application to interactive proof systems in which a mighty quantum prover communicates with a quantum-automaton verifier through a common communication cell. Our quantum interactive proof systems are juxtaposed to Dwork-Stockmeyer's classical interactive proof systems whose verifiers are two-way probabilistic automata. We demonstrate strengths and weaknesses of our systems and further study how various restrictions on the behaviors of quantum-automaton verifiers affect the power of quantum interactive proof systems.Comment: This is an extended version of the conference paper in the Proceedings of the 9th International Conference on Implementation and Application of Automata, Lecture Notes in Computer Science, Springer-Verlag, Kingston, Canada, July 22-24, 200

Anderson localisation in steady states of microcavity polaritons

We present an experimental signature of the Anderson localisation of microcavity polaritons, and provide a systematic study of the dependence on disorder strength. We reveal a controllable degree of localisation, as characterised by the inverse-participation ratio, by tuning the positional disorder of arrays of interacting mesas. This constitutes the realisation of disorder-induced localisation in a driven-dissipative system. In addition to being an ideal candidate for investigating localisation in this regime, microcavity polaritons hold promise for low-power, ultra-small devices and their localisation could be used as a resource in quantum memory and quantum information processing.Comment: 7 pages, 3 figure