A Simple Quantum Computer

Abstract

We propose an implementation of a quantum computer to solve Deutsch's problem, which requires exponential time on a classical computer but only linear time with quantum parallelism. By using a dual-rail qubit representation as a simple form of error correction, our machine can tolerate some amount of decoherence and still give the correct result with high probability. The design which we employ also demonstrates a signature for quantum parallelism which unambiguously delineates the desired quantum behavior from the merely classical. The experimental demonstration of our proposal using quantum optical components calls for the development of several key technologies common to single photonics.

8 pages RevTeX + 6 figures in postscript

Cited by in corpus (171)

• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Elementary gates for quantum computation
• Review article: Linear optical quantum computing
• Good Quantum Error-Correcting Codes Exist
• Quantum Teleportation is a Universal Computational Primitive
• Scalable photonic quantum computation through cavity-assisted interaction
• Preserving coherence in quantum computation by pairing quantum bits
• Universal computation by multi-particle quantum walk
• Efficient Simulation of Quantum Systems by Quantum Computers
• Optical Simulation of Quantum Logic
• Multiphoton Quantum Optics and Quantum State Engineering
• Performance and structure of single-mode bosonic codes
• Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer
• Quantum Computers, Factoring, and Decoherence
• Single-Photon Generation from Stored Excitation in an Atomic Ensemble
• Quantum computation using electrons trapped by surface acoustic waves
• Long-range interactions and entanglement of slow single-photon pulses
• Bosonic Quantum Codes for Amplitude Damping
• Ultrafast photon-photon interaction in a strongly coupled quantum dot-cavity system
• Giant electro-optic effect using polarizable dark states
• 3/4-efficient Bell measurement with passive linear optics and unentangled ancillae
• Impossibility of large phase shifts via the "giant Kerr effect" with single-photon wavepackets
• Universal continuous-variable quantum computation: Requirement of optical nonlinearity for photon counting
• Large Cross-Phase Modulation between Slow Co-propagating Weak Pulses in Rb
• Continuous-time cross-phase modulation and quantum computation
• Deutsch-Jozsa algorithm as a test of quantum computation
• Realizing Quantum Controlled Phase Flip through Cavity-QED
• Equivalence between an optomechanical system and a Kerr medium
• Quantum Bit Regeneration
• Quantum amplification and simulation of strong and ultrastrong coupling of light and matter
• Polarization state of a biphoton: quantum ternary logic
• Predicting Research Trends with Semantic and Neural Networks with an application in Quantum Physics
• Maximizing the Hilbert space for a finite number of distinguishable quantum states
• Optimal Decoherence Control in non-Markovian Open, Dissipative Quantum Systems
• Coherent Population Trapping of Electron Spins in a Semiconductor
• Atomic-waveguide quantum electrodynamics
• Pair-cat codes: autonomous error-correction with low-order nonlinearity
• Large conditional single-photon cross-phase modulation
• A passive CPHASE gate via cross-Kerr nonlinearities
• Quantum Phase Gate Operation Based on Nonlinear Optics: Full Quantum Analysis
• Prospects for Quantum Computing with an Array of Ultracold Polar Paramagnetic Molecules
• Single-molecule vacuum Rabi splitting: four-wave mixing and optical switching at the single-photon level
• Experimental nonlinear sign shift for linear optics quantum computation
• Optimum unambiguous discrimination among linearly-independent non-orthogonal quantum states and its optical realization
• Quantum error correction using squeezed Schrödinger cat states
• Quantum logic and entanglement by neutral Rydberg atoms: methods and fidelity
• Nonlinear coupling of continuous variables at the single quantum level
• Dual-rail encoding with superconducting cavities
• Quantum gates on hybrid qudits
• Quantum Computation with Ballistic Electrons
• Efficient Classical Simulation of Optical Quantum Circuits
• Factoring in a Dissipative Quantum Computer
• How to decompose arbitrary continuous-variable quantum operations
• Entangling two atoms in spatially separated cavities through both photon emission and absorption processes
• Prevention of dissipation with two particles
• Quantum Coherent Nonlinear Feedbacks with Applications to Quantum Optics on Chip
• Universal Quantum Computing with Arbitrary Continuous-Variable Encoding
• Demonstrating a long-coherence dual-rail erasure qubit using tunable transmons
• Cross-Kerr nonlinearity for phonon counting
• Photon-photon gate via the interaction between two collective Rydberg excitations
• Experimental realization of the one qubit Deutsch-Jozsa algorithm in a quantum dot
• Controlled coupling of spin-resolved quantum Hall edge states
• Qubits as Parafermions
• Efficient sorting of quantum-optical wave packets by temporal-mode interferometry
• Transverse multi-mode effects on the performance of photon-photon gates
• Breakdown of the cross-Kerr scheme for Photon Counting
• Schumacher's quantum data compression as a quantum computation
• Quantum computation with Kerr-nonlinear photonic crystals
• Theory of Cross Phase Modulation for the Vibrational Modes of Trapped Ions
• Qudit-Basis Universal Quantum Computation using ${\chi }^{(2)}$ Interactions
• Encoding qubits in multimode grid states
• Generalized Quantum Search with Parallelism
• Quantum information processing in bosonic lattices
• Fast simulation of bosonic qubits via Gaussian functions in phase space
• Two photons co- and counter-propagating through $N$ cross-Kerr sites
• Probabilistic quantum cloning via Greenberger-Horne-Zeilinger states
• Hardware-Efficient Bosonic Quantum Error-Correcting Codes Based on Symmetry Operators
• Quantum circuits for amplification of Kerr nonlinearity via quadrature squeezing
• Temporal trapping: a route to strong coupling and deterministic optical quantum computation
• Decoherence, Control, and Symmetry in Quantum Computers
• Giant Kerr nonlinearities and magneto-optical rotations in a Rydberg-atom gas via double electromagnetically induced transparency
• Synthesis and Analysis of Entangled Photonic Qubits in Spatial-Parity Space
• Interaction of Independent Single Photons based on Integrated Nonlinear Optics
• A brief introduction to quantum algorithms
• Generation of two-mode nonclassical motional states and a Fredkin gate operation in a two-dimensional ion trap
• Few-photon all-optical phase rotation in a quantum-well micropillar cavity
• Conditional $\pi$-Phase Shift of Single-Photon-Level Pulses at Room Temperature
• Photonic Nonlinearities via Quantum Zeno Blockade
• Perturbative expansions for the fidelities and spatially correlated dissipation of quantum bits
• Enhancing a slow and weak optomechanical nonlinearity with delayed quantum feedback
• Asymptotically noise decoupling for Markovian open quantum systems
• Decoherence on Grover's quantum algorithm: perturbative approach
• Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications
• Geometry of mixed states and degeneracy structure of geometric phases for multi-level quantum systems. A unitary group approach
• Phase-noise limitations on single-photon cross-phase modulation with differing group velocities
• Automatically Differentiable Quantum Circuit for Many-qubit State Preparation
• A measurement-induced optical Kerr interaction
• Interaction-free generation of entanglement
• Mesoscopic ultrafast nonlinear optics -- The emergence of multimode quantum non-Gaussian physics
• Two-photon self-Kerr nonlinearities for quantum computing and quantum optics
• Information processing at the speed of light
• Uniform cross phase modulation for nonclassical radiation pulses
• Theory of semiconductor quantum-wire based single- and two-qubit gates
• Limitations of two-level emitters as non-linearities in two-photon controlled phase gates
• Quantum interferometric generation of polarization entangled photons
• Phase-space methods for representing, manipulating, and correcting Gottesman-Kitaev-Preskill qubits
• Deterministic teleportation using single-photon entanglement as a resource
• A Quick Glance at Quantum Cryptography
• Quantum Annealing - Foundations and Frontiers
• Multiphoton Tomography with Linear Optics and Photon Counting
• Assessment of a quantum phase gate operation based on nonlinear optics
• Experimental Observation of Simultaneous Wave and Particle Behaviors in a Narrowband Single Photon's Wave Packe
• Designing Kerr interactions using multiple superconducting qubit types in a single circuit
• Æ codes
• Deterministic nonlinear gates with oscillators mediated by a qubit
• Proposal for a Datta-Das transistor in the quantum Hall regime
• Stationary light in atomic media
• Integrated photonic qubit quantum computing on a superconducting chip
• Photonic Realization of a Quantum Finite Automaton
• Analytical results for a conditional phase shift between single-photon pulses in a nonlocal nonlinear medium
• Chiral Majorana Interference as a Source of Quantum Entanglement
• Optimizing quantum error correction protocols with erasure qubits
• The $2T$-qutrit, a two-mode bosonic qutrit
• Interaction-free quantum computation
• Quantifying coherence in terms of Fisher information
• Addendum to "Single photon logic gates using minimum resources"
• Fault-tolerant quantum architectures based on erasure qubits
• Interactions in Electronic Mach-Zehnder Interferometers with Copropagating Edge Channels
• Characterizing the performance of continuous-variable Gaussian quantum gates
• Multiphoton resonances for all-optical quantum logic with multiple cavities
• Universal Continuous Variable Quantum Computation Without Cooling
• Photon counting schemes and performance of non-deterministic nonlinear gates in linear optics
• A Quantum Hopfield Associative Memory Implemented on an Actual Quantum Processor
• Universal quantum computing with thermal state bosonic systems
• Passive, deterministic photonic CPHASE gate via two-level systems
• One-step implementation of the genuine Fredkin gate in high-$Q$ coupled three-cavity arrays
• Low-Power Cross-Phase Modulation in a Metastable Xenon-Filled Cavity for Quantum Information Applications
• Generation of four-photon polarization entangled state based on EPR entanglers
• Two-qubit gates for decoherence-free qubits using a ring exchange interaction
• Nonclassical states that generate zero entanglement with a beam splitter
• Entanglement gauge and the non-Abelian geometric phase with two photonic qubits
• Using excited states and degeneracies to enhance the electric polarizability and first hyperpolarizability
• Mixed-Integer Programming Using a Bosonic Quantum Computer
• State preparation by photon filtering
• Pre-detection squeezing as a resource for high-dimensional Bell-state measurements
• Surface Code with Imperfect Erasure Checks
• Letting the tiger out of its cage: bosonic coding without concatenation
• Manipulating time-bin qubits with fiber optics components
• A method of enciphering quantum states
• Effects of Loss and Decoherence on a Simple Quantum Computer
• Study of optical nonlinearity of a highly dispersive medium using optical heterodyne detection technique
• Boson-boson pure-dephasing model with non-Markovian properties
• Universal quantum circuit for n-qubit quantum gate: A programmable quantum gate
• Superselection rules and bosonic quantum computational resources
• Quantum Information, Thermofield Dynamics and Thermalized Bosonic Oscillator
• Generation of perfectly entangled two and three qubits states by classical random interaction
• Communication over Continuous Quantum Secure Dialogue using Einstein-Podolsky-Rosen States
• Coherent edge mixing and interferometry in quantum Hall bilayers
• Quantum logic as a sum over classical logic gates
• Quantum Zeno dynamics induced atomic entanglement in a hybrid atom-cavity-fiber system
• Deterministic photonic entanglement arising from non-Abelian quantum holonomy
• Demonstration of Scully-Drühl-type quantum erasers on quantum computers
• Factoring an integer with three oscillators and a qubit
• Quantum Computing @ MIT: The Past, Present, and Future of the Second Revolution in Computing
• Doubling Qubits in a Trapped-Ion System via Vibrational Dual-Rail Encoding
• Loss tolerant cross-Kerr enhancement via modulated squeezing
• Quantum Algorithms in Cybernetics
• Deterministic linear-optical computing with symmetry-based qubits
• Photon Frequency Bears More At Less
• Topological structures of adiabatic phase for multi-level quantum systems
• Decoherence of the quantum logic gate implemented with the Jaynes-Cummings model: A semiclassical approach