Experimental realization of the one qubit Deutsch-Jozsa algorithm in a quantum dot

Abstract

We perform quantum interference experiments on a single self-assembled semiconductor quantum dot. The presence or absence of a single exciton in the dot provides a qubit that we control with femtosecond time resolution. We combine a set of quantum operations to realize the singlequbit Deutsch-Jozsa algorithm. The results show the feasibility of single qubit quantum logic in a semiconductor quantum dot using ultrafast optical control.PACS numbers: 78.55. Cr,03.67.Lx Time-resolved optical spectroscopy in semiconductor quantum dots has recently progressed toward the full quantum control of excitons trapped inside a single dot. 1,2,3,4 These advances have stimulated proposals to use excitons in quantum dots as quantum bits 5,6,7 for implementation of quantum computing. Very recently, the ability to operate a two-qubit gate using exciton and biexciton states was demonstrated in a single quantum dot. 8 These achievements represent a step toward an alloptical implementation of quantum computing using excitonic qubits. The first algorithm that comes to mind in order to check the feasibility of quantum computation in this context is the Deutsch-Jozsa (DJ) algorithm. 9 This algorithm is one of the simplest quantum algorithms that provides an exponential speed-up with respect to classical algorithms. As such, it has been extensively studied and has been used in experimental demonstrations of simple quantum computation in a variety of systems. 10,11,12 In this Rapid Communication we report the experimental realization of the DJ algorithm for a single qubit using an optimized version of the algorithm 13 .The Deutsch problem 9 involves global properties of binary functions on a subset of the natural numbers. Given a natural number N , we can define a set called X N with all the natural numbers that can be represented with N bits. A binary function f : X N → {0, 1} is called balanced if it returns 0 for exactly half of the elements of X N and 1 for the other half. Given a function that is either balanced or constant, the Deutsch problem consists of finding out which type it is. A general classical algorithm requires evaluating the function on more than half of the elements, requiring at least 2 N −1 + 1 evaluations. This causes the classical run time to grow exponentially with the input size. The Deutsch-Jozsa algorithm provides a way to solve the Deutsch problem on a quantum computer using a quantum subroutine that evaluates f . The problem and its solution provide an example of Oracle-based quantum computation. 14,15 It is assumed that a quantum subroutine or Oracle contains the information about the unknown function. The algorithm gives a recipe on how to prepare (encoding) and read out (decoding) the qubit in an efficient way. In an experimental demonstration, we have not only to implement the algorithm (encoding and decoding operations), but we also have to build the Oracle. The specific structure of the Oracle, encoding and decoding is not unique and several versions can be found in the literature. 9,13,16,17 . The on...

Non-Markovianity-assisted high-fidelity Deutsch–Jozsa algorithm in diamond

“…39,40,42 However, a recent study revealed that the memory effects of a non-Markovian environment can be regarded as important physical resources 28,33 to improve QIP in an open quantum system. To further enhance the POS of the RDJA, we utilized the memory effects of the non-Markovian environment, which can be extracted by the DD method 26,39 to mitigate imperfect operations and decoherence.…”

“…The RDJA can be decomposed into two different unitary transformations: rotation operation and phase-controlled gate. 39,40,42 The rotation operation can be realized by a (π/2) X pulse resonant with the transition between 0 j i and 1 j i. Here ϕ X(Y) denotes the rotation with angle ϕ around the X(Y) axis.…”

“…This result obviously contradicts previous results. 40,42 In the Born-Markovian decoherence region, 43 as the duration of the interaction of the quantum system with the environment increases, the degeneration of the coherence of the quantum system also increases. Consequently, the POS should decrease monotonically with the delay time of the measurement.…”

“…Because of the turnoff of the information reflow from the spin bath to the electron spin of the NV center, the POS of the RDJA decreased monotonically with the delay time of the measurement. 40,42 The memory effects in the non-Markovian process, obtaining the final measurement immediately after the operation is not an optimal strategy when the operation speed is comparable to the rate of information exchange between the system and the environment. However, using an appropriate delay time recovers the result.…”

“…This result represents a substantial improvement over previous results. 39,42 In contrast, the transition from non-Markovian to Markovian dynamics of the NV center was experimentally realized with a magnetic field, where the POS of the RDJA decreases monotonically with the delay time of the measurement, as expected in the Markovian region. The experimental result clearly confirmed that the performance of a practical quantum algorithm can be improved by incorporating the memory effects from the non-Markovian environment as important quantum resources.…”