Lecture Notes of my Course on Quantum Computing
... of T . This operation is also referred to as the Hermitian conjugate or adjoint operator. Notice that for permutation matrices we have P T P = I, and, more generally, for real orthogonal matrices U T U = I. Generalizing even further, a matrix with complex entries is called unitary if U † U = I. It ...
... of T . This operation is also referred to as the Hermitian conjugate or adjoint operator. Notice that for permutation matrices we have P T P = I, and, more generally, for real orthogonal matrices U T U = I. Generalizing even further, a matrix with complex entries is called unitary if U † U = I. It ...
Qubit Quantum Mechanics with Correlated-photon Experiments,
... alignment. The setup is designed so that the light paths through the interferometer are parallel to the rows of holes in the optical breadboard. This layout makes the alignment straightforward with the help of an iris.28 The light is sent to a fiber-coupled four-detector module 共Perkin Elmer model S ...
... alignment. The setup is designed so that the light paths through the interferometer are parallel to the rows of holes in the optical breadboard. This layout makes the alignment straightforward with the help of an iris.28 The light is sent to a fiber-coupled four-detector module 共Perkin Elmer model S ...
Nonlocal Labeling of Paths in a Single-Photon Interferometer
... We performed experiments to verify these predictions. The laboratory arrangement is shown in Fig. 2. A 457.9-nm beam from an argon-ion laser was incident on a pair of crossed beta-barium-borate crystals to produce polarizationentangled photon pairs via type-I spontaneous parametric down conversion 关 ...
... We performed experiments to verify these predictions. The laboratory arrangement is shown in Fig. 2. A 457.9-nm beam from an argon-ion laser was incident on a pair of crossed beta-barium-borate crystals to produce polarizationentangled photon pairs via type-I spontaneous parametric down conversion 关 ...
Quantum Computing Lecture 1 What is Quantum Computing?
... Entangled States The following states of a 2-qubit system cannot be separated into components parts. ...
... Entangled States The following states of a 2-qubit system cannot be separated into components parts. ...
A crack method, on the BB84 protocol
... the angle between the two linear polarization directions is 45 degrees. For each of the four optical paths described above, a "45 degree linearly polarized beam splitter" is further connected (as shown in the figure below) ...
... the angle between the two linear polarization directions is 45 degrees. For each of the four optical paths described above, a "45 degree linearly polarized beam splitter" is further connected (as shown in the figure below) ...
Achieving quantum supremacy with sparse and noisy commuting
... challenge that this poses is twofold: firstly we must identify the physically least expensive quantum computations that are classically unachievable; and we must also determine if this advantage can be maintained in the presence of physical noise. There are several intermediate quantum computing mod ...
... challenge that this poses is twofold: firstly we must identify the physically least expensive quantum computations that are classically unachievable; and we must also determine if this advantage can be maintained in the presence of physical noise. There are several intermediate quantum computing mod ...
Closed timelike curves make quantum and classical computing
... To state our results, it is crucial to have a formal model of computation in the presence of CTCs. We define a deterministic CTC algorithm A to be deterministic polynomial-time algorithm that takes as input a string x ∈ {0, 1}n , and that produces as output a Boolean circuit C = Cx , consisting of A ...
... To state our results, it is crucial to have a formal model of computation in the presence of CTCs. We define a deterministic CTC algorithm A to be deterministic polynomial-time algorithm that takes as input a string x ∈ {0, 1}n , and that produces as output a Boolean circuit C = Cx , consisting of A ...
Hong-Ou-Mandel interference between triggered and heralded
... by a short resonant optical pulse generated using a fast electro-optic modulator (EOM). The beams used for optical pumping and excitation are collinear with the dipole trap, and are focused onto the atom by the same aspheric lens. The excitation pulse duration τe = 3 ns is much shorter than the exci ...
... by a short resonant optical pulse generated using a fast electro-optic modulator (EOM). The beams used for optical pumping and excitation are collinear with the dipole trap, and are focused onto the atom by the same aspheric lens. The excitation pulse duration τe = 3 ns is much shorter than the exci ...
Optimal quantum cloning of orbital angular momentum photon
... guishable. If the two photons are made distinguishable by their internal quantum state, for example encoded in the polarization π or in other degrees of freedom, the coalescence effect vanishes. Now, if one of the two photons involved in the process is in a given input state to be cloned and the othe ...
... guishable. If the two photons are made distinguishable by their internal quantum state, for example encoded in the polarization π or in other degrees of freedom, the coalescence effect vanishes. Now, if one of the two photons involved in the process is in a given input state to be cloned and the othe ...
Quantum Computing Lecture 1 Bits and Qubits What is Quantum
... Entangled States The following states of a 2-qubit system cannot be separated into components parts. ...
... Entangled States The following states of a 2-qubit system cannot be separated into components parts. ...
Quantum state majorization at the output of bosonic Gaussian
... beamsplitter which is known from the field of quantum optics [34–36], namely that only coherent states remain pure under the action of a beamsplitter (Lemma 2 in section Methods). Therefore, since Eq. (21) is valid for every choice of |ψi ∈ K, then K necessarily contains only coherent states. Moreov ...
... beamsplitter which is known from the field of quantum optics [34–36], namely that only coherent states remain pure under the action of a beamsplitter (Lemma 2 in section Methods). Therefore, since Eq. (21) is valid for every choice of |ψi ∈ K, then K necessarily contains only coherent states. Moreov ...
Concrete analysis of Regev`s worst-case to average
... shows that an algorithm W4 that solves LWEq,Ψα given m samples can be used to construct a quantum algorithm W9 for DGS√2n·η (L)/α . Here, η (L) is the “smoothing parameter with accuracy ”, and DGSr0 (discrete Gaussian sampling problem) is the problem√of computing a sample from distribution DL,r0 ...
... shows that an algorithm W4 that solves LWEq,Ψα given m samples can be used to construct a quantum algorithm W9 for DGS√2n·η (L)/α . Here, η (L) is the “smoothing parameter with accuracy ”, and DGSr0 (discrete Gaussian sampling problem) is the problem√of computing a sample from distribution DL,r0 ...
A high-speed tunable beam splitter for feed
... a, in the outputs of spatial modes f and e: T = cos2 φ (U) 2 and R = sin 2 . Additionally, the input polarization will be rotated from α |+ + β |− to α |+ − β |− in the spatial mode e. This polarization rotation can be dynamically compensated with an additional EOM on path e applied with a half ...
... a, in the outputs of spatial modes f and e: T = cos2 φ (U) 2 and R = sin 2 . Additionally, the input polarization will be rotated from α |+ + β |− to α |+ − β |− in the spatial mode e. This polarization rotation can be dynamically compensated with an additional EOM on path e applied with a half ...
Quantum Process Tomography: Theory and Experiment
... FULL QPT IS ALWAYS HARD. STANDARD METHODS FOR PARTIAL QPT ARE ALSO EXPONENTIALLY HARD • THERE IS AN ALTERNATIVE METHOD FOR EFFICIENT AND SELECTIVE PARTIAL QUANTUM PROCESS TOMOGRAPHY • IT INVOLVES ESTIMATION OF „SURVIVAL PROBABILITIES‟ OF A SET OF STATES FORMING A 2-DESIGN (VERY USEFUL RESOURCE!) • T ...
... FULL QPT IS ALWAYS HARD. STANDARD METHODS FOR PARTIAL QPT ARE ALSO EXPONENTIALLY HARD • THERE IS AN ALTERNATIVE METHOD FOR EFFICIENT AND SELECTIVE PARTIAL QUANTUM PROCESS TOMOGRAPHY • IT INVOLVES ESTIMATION OF „SURVIVAL PROBABILITIES‟ OF A SET OF STATES FORMING A 2-DESIGN (VERY USEFUL RESOURCE!) • T ...
RST3
... • Complexity-based pseudorandomness is a deep concept in theoretical CS (with wide applications in scientific computing such as Monte Carlo methods) • Engineers generate pseudorandom numbers by arithmetic algorithms such as linear congruential generators and linear feedback shift registers (LFSR) ...
... • Complexity-based pseudorandomness is a deep concept in theoretical CS (with wide applications in scientific computing such as Monte Carlo methods) • Engineers generate pseudorandom numbers by arithmetic algorithms such as linear congruential generators and linear feedback shift registers (LFSR) ...
Collège de France abroad Lectures Quantum information with real
... the dispersive regime realizes a generalized measurement of the POVM kind which extracts partial information from the field. By a succession of such POVM’s, a complete quantum non demolition (QND) measurement of the photon number is realized. This QND procedures allows us to observe directly the qua ...
... the dispersive regime realizes a generalized measurement of the POVM kind which extracts partial information from the field. By a succession of such POVM’s, a complete quantum non demolition (QND) measurement of the photon number is realized. This QND procedures allows us to observe directly the qua ...
Quantum Dot Single Photon Sources Quantum Dots
... Indistiguishable Photons The KLM Proposal Knill, Laflamme, and Milburn [Knill, Laflamme, Milburn, Nature 409, 46 (2001)] suggested a probilistic two-qubit gate implemented with single photons and linear optical elements. The gate requires photon number resolving counters and additional so-called an ...
... Indistiguishable Photons The KLM Proposal Knill, Laflamme, and Milburn [Knill, Laflamme, Milburn, Nature 409, 46 (2001)] suggested a probilistic two-qubit gate implemented with single photons and linear optical elements. The gate requires photon number resolving counters and additional so-called an ...