In order for quantum communications systems to become widely used, it will probably be necessary to develop quantum repeaters that can extend the range of quantum key distribution systems and correct for errors in the transmission of quantum information. Quantum logic gates based on linear optical techniques appear to be a promising approach for the development of quantum repeaters, and they may have applications in quantum computing as well. Here we describe the basic principles of logic gates based on linear optics, along with the results from several experimental demonstrations of devices of this kind. A prototype source of single photons and a quantum memory device for photons are also discussed. These devices can be combined with a four-qubit encoding to implement a quantum repeater.
We present a feasible scheme to implement the non-deterministic quantum logic operation of Knill, Laflamme and Milburn (Nature, 409, 46-52(2001)) by using a teleportation protocol, which requires only single-photon sources, linear optical elements and photon detectors.
We propose a scheme for concentrating nonmaximally pure and mixed polarization-entangled state of individual photon pairs. The scheme uses only simple linear optical elements and may be feasible within current optical technology.
We discuss the unique capabilities of programmable logic devices (PLD's) for experimental quantum optics and describe basic procedures of design and implementation. Examples of advanced applications include optical metrology and feedback control of quantum dynamical systems. As a tutorial illustration of the PLD implementation process, a field programmable gate array (FPGA) controller is used to stabilize the output of a Fabry-Perot cavity.
We describe a feasible logic Bell-state analysis protocol by employing the logic entanglement to be the robust concatenated Greenberger-Horne-Zeilinger (C-GHZ) state. This protocol only uses polarization beam splitters and half-wave plates, which are available in current experimental technology. We can conveniently identify two of the logic Bell states. This protocol can be easily generalized to the arbitrary C-GHZ state analysis. We can also distinguish two $N$-logic-qubit C-GHZ states. As the previous theory and experiment both showed that the C-GHZ state has the robustness feature, this log…
Knill, Laflamme, and Milburn [Nature 409, 46 (2001)] have shown that quantum logic operations can be performed using linear optical elements and additional ancilla photons. Their approach is probabilistic in the sense that the logic devices fail to produce an output with a failure rate that scales as 1/n, where n is the number of ancilla. Here we present an alternative approach in which the logic devices always produce an output with an intrinsic error rate that scales as 1/n^2,which may have several advantages in quantum computing applications.
Knill, Laflamme, and Milburn recently showed that non-deterministic quantum logic operations could be performed using linear optical elements, additional photons (ancilla), and post-selection based on the output of single-photon detectors [Nature 409, 46 (2001)]. Here we report the experimental demonstration of two logic devices of this kind, a destructive controlled-NOT (CNOT) gate and a quantum parity check. These two devices can be combined with a pair of entangled photons to implement a conventional (non-destructive) CNOT that succeeds with a probability of 1/4.
We propose a new system for implementing quantum logic gates: neutral atoms trapped in a very far-off-resonance optical lattice. Pairs of atoms are made to occupy the same well by varying the polarization of the trapping lasers, and then a near-resonant electric dipole is induced by an auxiliary laser. A controlled-NOT can be implemented by conditioning the target atomic resonance on a resolvable level shift induced by the control atom. Atoms interact only during logical operations, thereby suppressing decoherence.
We analyse the design and optimisation of quantum logic circuits suitable for the experimental demonstration of a three-qubit quantum computation prototype based on optically-controlled, solid-state quantum logic gates. In these gates, the interaction between two qubits carried by the electron-spin of donors is mediated by the optical excitation of a control particle placed in their proximity. First, we use a geometrical approach for analysing the entangling characteristics of these quantum gates. Then, using a genetic programming algorithm, we develop circuits for the refined Deutsch-Jozsa al…
A systematic method for simulating small-scale quantum circuits by use of linear optical devices is presented. It relies on the representation of several quantum bits by a single photon, and on the implementation of universal quantum gates using simple optical components (beam splitters, phase shifters, etc.). This suggests that the optical realization of small quantum networks is reasonable given the present technology in quantum optics, and could be a useful technique for testing simple quantum algorithms or error-correction schemes. The optical circuit for quantum teleportation is presented…
We present a detailed analysis and design of a neutral atom quantum logic device based on atoms in optical traps interacting via dipole-dipole coupling of Rydberg states. The dominant physical mechanisms leading to decoherence and loss of fidelity are enumerated. Our results support the feasibility of performing single and two-qubit gates at MHz rates with decoherence probability and fidelity errors at the level of $10^{-3}$ for each operation. Current limitations and possible approaches to further improvement of the device are discussed.
The Toffoli gate is an essential logic element, which permits implementation of a reversible processor. It is of relevance both for classical as well as quantum logics. We propose and theoretically study all-optical implementations of three-bit and four-bit Toffoli gates by application of adiabatic population transfer techniques. For a three-bit Toffoli gate we use variants of stimulated Raman adiabatic passage (STIRAP) processes in a $Λ$-type level scheme, driven by two laser pulses at sufficiently large detunings. For the implementation of a four-bit Toffoli gate, we apply reversible adiabat…
We show how the efficiency of a logical Bell measurement (BM) can be calculated for arbitrary CSS codes with the experimentally important constraint of using only transversal static linear-optical BMs on the physical single-photon qubit level. For this purpose, we utilize the codes' description in terms of stabilizers in order to calculate general efficiencies for the loss-free case, but also for specific cases including photon loss. These efficiencies can be, for instance, used for obtaining transmission rates of all-optical quantum repeaters. In the loss-free case, we demonstrate that the im…
Optical qubits uniquely combine information transfer in optical fibers with a good processing capability and are therefore attractive tools for quantum technologies. A large challenge, however, is to overcome the low efficiency of two-qubit logic gates. The experimentally achieved efficiency in an optical controlled NOT (CNOT) gate reached approximately 11% in 2003 and has seen no increase since. Here we report on a new platform that was designed to surpass this long-standing record. The new scheme avoids inherently probabilistic protocols and, instead, combines aspects of two established quan…
We introduce the method of using an annealing genetic algorithm to the numerically complex problem of looking for quantum logic gates which simultaneously have highest fidelity and highest success probability. We first use the linear optical quantum nonlinear sign (NS) gate as an example to illustrate the efficiency of this method. We show that by appropriately choosing the annealing parameters, we can reach the theoretical maximum success probability (1/4 for NS) for each attempt. We then examine the controlled-z (CZ) gate as the first new problem to be solved. We show results that agree with…
We study a means of creating multiparticle entanglement of neutral atoms using pairwise controlled dipole-dipole interactions in a three dimensional optical lattice. For tightly trapped atoms the dipolar interaction energy can be much larger than the photon scattering rate, and substantial coherent evolution of the two-atom state can be achieved before decoherence occurs. Excitation of the dipoles can be made conditional on the atomic states, allowing for deterministic generation of entanglement. We derive selection rules and a figure-of-merit for the dipole-dipole interaction matrix elements,…
We report on the usage of a linear optics phase gate for distinguishing all four Bell states simultaneously in a quantum teleportation and entanglement swapping protocol. This is demonstrated by full state tomography of the one and two qubit output states of the two protocols, yielding average state fidelities of about 0.83 and 0.77, respectively. In addition, the performance of the teleportation channel is characterised by quantum process tomography. The non classical properties of the entanglement swapping output states are further confirmed by the violation of a CHSH-type Bell inequality of…
We propose a protocol for conditional quantum logic between two 4-state atoms inside a high Q optical cavity. The process detailed in this paper utilizes a direct 4-photon 2-atom resonant process and has the added advantage of commonly addressing the two atoms when they are inside the high Q optical cavity.
We develop a theory for the interaction of multi-level atoms with multi-mode cavities yielding cavity-enhanced multi-photon resonances. The locations of the resonances are predicted from the use of effective two- and three-level Hamiltonians. As an application we show that quantum gates can be realised when photonic qubits are encoded on the cavity modes in arrangements where ancilla atoms transit the cavity. The fidelity of operations is increased by conditional measurements on the atom and by the use of a selected, dual-rail, Hilbert space. A universal set of gates is proposed, including the…
We discuss techniques for producing, manipulating and measureing qubits encoded optically as vacuum and single photon states. We show that a universal set of non-deterministic gates can be constructed using linear optics and photon counting. We investigate the efficacy of a test gate given realistic detector efficiencies.
Quantum interrogation can be used as a basic resource for quantum information. This paper presents its applications to entanglement creation and to optical quantum computation. The starting point will be a photon to particle quantum interrogation CZ gate, from which three families of optical CNOT gates will be derived. These gates are nondestructive and can work with probabilities arbitrarily close to 1. A possible experimental implementation with atomic ensembles is also discussed.
Interactions among qubits are essential for performing two-qubit quantum logic operations. However, nature gives us only nearest neighbor interactions in simple and controllable settings. Here we propose a strategy to induce interactions among two atomic entities that are not necessarily neighbors of each other through their common coupling with a cavity field. This facilitates fast multiqubit quantum logic operations through a set of two-qubit operations. The ideas presented here are applicable to various quantum computing proposals for atom based qubits such as, trapped ions, atoms trapped i…
A logical system derived from linear logic and called QMLL is introduced and shown able to capture all unitary quantum circuits. Conversely, any proof is shown to compute, through a concrete GoI interpretation, some quantum circuits. The system QMLL, which enjoys cut-elimination, is obtained by endowing multiplicative linear logic with a quantum modality.
University of Toronto（多伦多大学）；Barcelona Supercomputing Center（巴塞罗那超级计算中心）；Vector Institute for Artificial Intelligence（向量人工智能研究所）；Max Planck Institute for the Science of Light（马克斯·普朗克光科学研究所）；Canadian Institute for Advanced Research（加拿大高等研究院）
Logic Artificial Intelligence (AI) is a subfield of AI where variables can take two defined arguments, True or False, and are arranged in clauses that follow the rules of formal logic. Several problems that span from physical systems to mathematical conjectures can be encoded into these clauses and solved by checking their satisfiability (SAT). In contrast to machine learning approaches where the results can be approximations or local minima, Logic AI delivers formal and mathematically exact solutions to those problems. In this work, we propose the use of logic AI for the design of optical qua…
We show that a set of optical memories can act as a configurable linear optical network operating on frequency-multiplexed optical states. Our protocol is applicable to any quantum memories that employ off-resonant Raman transitions to store optical information in atomic spins. In addition to the configurability, the protocol also offers favourable scaling with an increasing number of modes where N memories can be configured to implement an arbitrary N-mode unitary operations during storage and readout. We demonstrate the versatility of this protocol by showing an example where cascaded memori…
Practical and useful quantum information processing (QIP) requires significant improvements with respect to current systems, both in error rates of basic operations and in scale. Individual trapped-ion qubits' fundamental qualities are promising for long-term systems, but the optics involved in their precise control are a barrier to scaling. Planar-fabricated optics integrated within ion trap devices can make such systems simultaneously more robust and parallelizable, as suggested by previous work with single ions. Here we use scalable optics co-fabricated with a surface-electrode ion trap to …
