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arXiv:quant-ph/0403159 · Physical Review A

Interaction-free quantum computation

Hiroo Azuma

Published Jul 29, 2004• 13 citations
arXivHTMLPDF

Abstract

In this paper, we study the quantum computation realized by an interaction-free measurement (IFM). Using the interferometer of Kwiat et al., we construct a two-qubit quantum gate that changes one particle's trajectory according to whether or not the other particle exists in the interferometer. We propose a method for distinguishing Bell-basis vectors, each of which consists of a pair of an electron and a positron, by this gate. (This is called the Bell-basis measurement.) This method succeeds with probability $1$ in the limit of $N\ensuremath{\rightarrow}\ensuremath{\infty}$, where $N$ is the number of beam splitters in the interferometer. Moreover, we can carry out a controlled-NOT gate operation by the above Bell-basis measurement and the method proposed by Gottesman and Chuang. Therefore, we can prepare a universal set of quantum gates by the IFM. This means that we can execute any quantum algorithm by the IFM.

DOI
10.1103/physreva.70.012318

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arXiv:quant-ph/0005128•May 31, 2000•1 citation
In this paper, we study the quantum computation realized by an interaction-free measurement (IFM). Using the interferometer of Kwiat et al., we construct a two-qubit quantum gate that changes one particle's trajectory according to whether or not the other particle exists in the interferometer. We propose a method for distinguishing Bell-basis vectors, each of which consists of a pair of an electron and a positron, by this gate. (This is called the Bell-basis measurement.) This method succeeds with probability 111 in the limit of N\ensuremath→\ensuremath∞N\ensuremath{\rightarrow}\ensuremath{\infty}N\ensuremath→\ensuremath∞, where NNN is the number of beam splitters in the interferometer. Moreover, we can carry out a controlled-NOT gate operation by the above Bell-basis measurement and the method proposed by Gottesman and Chuang. Therefore, we can prepare a universal set of quantum gates by the IFM. This means that we can execute any quantum algorithm by the IFM.
In this paper, we study the generation of entanglement by interaction-free measurements. Using Kwiat et al.'s interferometer, we construct a two-qubit quantum gate that changes one particle's trajectory according to the other particle's trajectory. We propose methods for generating the Bell state from an electron and a positron and from a pair of photons using this gate. We also show that, by using this gate, we can carry out the Bell measurement with a probability of 3/4 at the maximum and execute a controlled-NOT operation by the method proposed by Gottesman and Chuang with a probability of 9/16 at the maximum. We estimate the success probability for generating the Bell state by our procedure under imperfect interaction.
Recently, it has been pointed out that it is possible to make a quantum-mechanical interaction-free measurement (IFM), in which the existence of an object in a given region of space may be determined seemingly without interacting with it.1,2 In the embodiment first proposed by Elitzur and Vaidman,3 a standard Michelson interferometer is aligned so that incident single photons (obtained in our experiment by using parametric downconversion; see Fig. 1) must exit by the same port in which they entered, in the absence of any object within the interferometer. The presence of an object (e.g., the mirror leading to detector DB) in one of the arms completely changes the possible outcomes because the constructive interference is interrupted. Now it is possible that the photon will exit from the other exit port, to detector DIfm. By detecting the photon in this case, one can claim with certainty that an object was within the interferometer, even though the photon could not have interacted with it. If the beam splitter has a very low reflectivity, then the fraction of IFMs approaches 1/2.
In this paper, we propose a new direction of research for the realization of the quantum controlled-not gate based on a technique called ``interaction-free measurement'', where qubits are two-level atoms (or ions) and information is mediated from one qubit to another by lasers in superpositions of πππ and 2π2π2π pulses. We investigate the advantages and limitations of such a gate and discuss possible applicability.
"Interaction-free measurements" (IFM) originate from the latest quantum interferometric technologies. The latest research of quantum optics demonstrates, by using the complementary wavelike and particlelike natures of photons, it is possible to make interaction-free measurements by which the presence of an object can be determined with no photons being absorbed. The paper introduces the concept of "Interaction-free Measurement" (IFM), the original Elitzur-Vaidman scheme, the "High Efficiency Interaction-free Measurement", the application of quantum Zeno effect and the improved scheme proposed by Kwiat et al. The EV scheme is implemented in a Mach-Zehnder interferometer. Theoretically this paper also draws a conclusion in IFM feasibility by analyzing the wave functions of photon at various locations in the interferometer.
A theoretical unified interferometric framework is developed for interaction-free measurement (IFM) and delayed-choice (DC) experiments. The proposed model leads to a quantum circuit based architecture in which an ancillary qubit coherently controls the interaction between a photon and a bomb, allowing the system to evolve in a superposition of interaction and non-interaction regimes. The ancillary control qubit serves as a quantum switch that continuously interpolates between IFM and DC behavior, revealing a common operational origin for both phenomena. We demonstrate that both the phenomena can be realized within this framework through controlled quantum-gate operations. The analysis shows that the framework enables a continuous transition between the particle-like and wave-like behavior in DC setup. The framework is shown to be consistent with standard quantum mechanics, preserving unitary evolution, quantum superposition and the measurement postulate.
A quantum computer is a multi-particle interferometer that comprises beam splitters at both ends and arms, where the n two-level particles undergo the interactions among them. The arms are designed so that relevant functions required to produce a computational result is stored in the phase shifts of the 2^n arms. They can be detected by interferometry that allows us to utilize quantum parallelism. Quantum algorithms are accountable for what interferometers to be constructed to compute particular problems. A standard formalism for constructing the arms has been developed by the extension of classical reversible gate arrays. By its nature of sequential applications of logic operations, the required number of gates increases exponentially as the problem size grows. This may cause a crucial obstacle to perform a quantum computation within a limited decoherence time. We propose a direct and concurrent construction of the interferometer arms by one-time evolution of a physical system with arbitrary multi-particle interactions. It is inherently quantum mechanical and has no classical analogue. Encoding the functions used in Shor's algorithm for prime factoring, Grover's algorithm and Deutsch-Jozsa algorithm requires only one-time evolution of such a system regardless of the problem size n as opposed to its standard sequential counterpart that takes O(n^3), O(n) and O(n2^n).