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Semi-classical formula beyond the Ehrenfest time in
Semi-classical formula beyond the Ehrenfest time in

... [16][4][36][9] describe the evolved quantum state ψ (t), in the linear dispersion regime, which means that non linear effects on the dispersion of the coherent state are supposed to be negligible with respect to the linear effects. Because the first non linear effects correspond to cubic terms in th ...
Computing prime factors with a Josephson phase qubit quantum
Computing prime factors with a Josephson phase qubit quantum

... this algorithm involves the challenge of combining both single- and coupled-qubit gates in a meaningful sequence. We constructed the full factoring sequence by first performing automatic calibration of the individual gates and then combined them, without additional tuning, so as to factor the compos ...
Quantum Error Correction - Quantum Theory Group at CMU
Quantum Error Correction - Quantum Theory Group at CMU

... A somewhat abstract definition is given in Sec. 7 below. The general idea is that δ is the smallest number such that if the carriers are in a state corresponding to one of the code words and errors occur on at most δ − 1 of the carrier bits, the result will be orthogonal to all of the other code wor ...
Document
Document

... A quantum computer engineer needs to detect this entanglement as a way to benchmark or debug the processor. ...
Qubit metrology for building a fault-tolerant quantum
Qubit metrology for building a fault-tolerant quantum

... metrics are shown together. In level I, one- and two-qubit experiments measure coherence times T1 and T2, and show basic functionality of qubit gates. Along with the one-qubit gate time tg1, an initial estimate of gate error can be made. Determining the performance of a two-qubit gate is much harder ...
Document
Document

... Experimental results presented mostly reflect work in the Yacoby and Marcus groups at Harvard. ...
Deriving new operator identities by alternately using normally
Deriving new operator identities by alternately using normally

... better understood and its own special mathematics gets developed [1].” Following his expectation, the technique of integration within an ordered product (IWOP) of operators was invented which can directly apply the Newton-Leibniz integration rule to ket-bra projective operators [2,3]. The essence of ...
CS286.2 Lectures 5-6: Introduction to Hamiltonian Complexity, QMA
CS286.2 Lectures 5-6: Introduction to Hamiltonian Complexity, QMA

... Theorem 11. (Kempe-Kitaev-Regev) 2 − LHa,b is QMA-complete for some a = 2− poly(n) and b = 1/ poly(n). The first result along these lines came from Kitaev, who showed that 5 − LH is QMA-complete. We shall show a slightly weaker version of the theorem, which will contain all the key ideas: Theorem 12 ...
QUANTUM DARWINISM, CLASSICAL REALITY, and the
QUANTUM DARWINISM, CLASSICAL REALITY, and the

... superluminal communication. The loss of phase coherence is decoherence. Superpositions decohere as the ∣↑⟩ and ∣↓⟩ states are recorded by E. As phases no longer matter for S, phase information about S is lost. As promised earlier, that information loss was established without reduced density matrice ...
Quantum mechanical modeling of the CNOT (XOR) gate
Quantum mechanical modeling of the CNOT (XOR) gate

... However, in Section 4 we have considered the two-qubit system as an isolated system, but we have obtained that Ĥint does not have any global symmetry - which, also, directly follows from eq. (5). This produces a contradiction. 5.2 The contradiction It is worth emphasizing the above distinguished co ...
QUANTUM ERROR CORRECTING CODES FROM THE
QUANTUM ERROR CORRECTING CODES FROM THE

... primarily to mitigate the effects of such operators on quantum information encoded in evolving systems. By “active quantum error correction”, we mean protocols that involve active intervention into the system to correct errors. The basic method for active quantum error correction [1–4] identifies qu ...
QUANTUM ERROR CORRECTING CODES FROM THE
QUANTUM ERROR CORRECTING CODES FROM THE

... formalism" that may lead to such a general method. In particular, we cast the general problem of finding correctable codes for quantum channels into a matrix analysis framework. We then utilize a new tool recently introduced in [15]---called the "higher-rank numerical range"--the study of which was ...
Lecture 4: Some Properties of Qubits Introduction A Brief Recap
Lecture 4: Some Properties of Qubits Introduction A Brief Recap

... • So we can deduce a0 and a1 by making lots of measurements and just counting n(0) and n(1), right? • No: remember that after the measurement, the state of the system collapses onto the result of the measurement • We could prepare a large number of qubits in the same state and measure them all: this ...
superconducting qubits solid state qubits
superconducting qubits solid state qubits

... “Charge qubits” and “spin qubits” The qubits levels can be formed by either the energy levels of an electron in a potential well (such as a quantum dot or an impurity ion) or by the spin states of the electron (or the nucleus). The former are examples of charge qubits. The charge qubits have high e ...
Unitary time evolution
Unitary time evolution

... This simple result has many profound consequences. For one, the state |ψi of a system is not an observable. Given a quantum system, there is no way to tell in what state |ψi it was prepared. If the state |ψi is known, the state can be “copied” by preparing another system. But it is impossible to co ...
Coherent and incoherent evolution of qubits in
Coherent and incoherent evolution of qubits in

... waves and double defects • Spin qubits at defects and the use of control spins ...
ppt - QEC14
ppt - QEC14

... Single Qubit Rotations ...
MORE ON ERROR CORRECTION. Slides in PPT.
MORE ON ERROR CORRECTION. Slides in PPT.

... Nuclear spin ...
The Quantum Error Correcting Criteria
The Quantum Error Correcting Criteria

... where Ckl is a hermitian matrix. This equation is called the quantum error correcting criteria. It tells us when our encoding into a subspace can protect us from quantum errors Ek . As such it is a very important criteria for the theory of quantum error correction. Let’s show that this is a necessar ...
Quantum State Reconstruction From Incomplete Data
Quantum State Reconstruction From Incomplete Data

... prepared in the state , which is arbitrary but same for all qubits. The state of reservoir is described by the density matrix ...
High-fidelity Z-measurement error encoding of optical qubits
High-fidelity Z-measurement error encoding of optical qubits

... in Fig. 4. The average fidelity for all of these states 共excluding ␪, ␾ = 0° and 90°兲 is 0.96± 0.03, which is the same, to within error, as for the reconstructed states shown in Fig. 3. The behavior observed in Fig. 4 can be explained in terms of the classical and nonclassical interference requireme ...
PPT - Institute of Physics, Bhubaneswar
PPT - Institute of Physics, Bhubaneswar

... • If two parties don’t share a reference frame, rotationally invariant states are required to communicate. Bartlett et al., Rev. Mod. Phys. 79, 555 (2007) • If we encode in a DFS, universal quantum computing can be performed on a subspace even though it is not possible on the whole Hilbert space. Ke ...
On a Quantum Version of Pieri`s Formula
On a Quantum Version of Pieri`s Formula

... substitution is well defined, due to Lemma 2.1. Our main result can be stated as follows: Theorem 3.1 (Quantum Pieri’s formula) Let I be a subset in {1, 2, . . . , n}, and let J = {1, 2, . . . , n} \ I. Then, for k ≥ 1, we have in the algebra Enp : X Ek (θI ; p) = τa1 b1 τa2 b2 · · · τak bk , ...
A DIRECT PROOF OF THE QUANTUM VERSION OF MONK`S
A DIRECT PROOF OF THE QUANTUM VERSION OF MONK`S

... Ωw (F• ) = {V• ∈ F`(E) | dim(Vp ∩ Fq ) ≥ p − rw (p, n − q) ∀p, q} where rw (p, q) = #{i ≤ p | w(i) ≤ q}. The codimension of this variety is equal to the length `(w) of w. Notice that the rank conditions on Vp are redundant unless w has a descent at position p, i.e. w(p) > w(p + 1). Given a sequence ...
Quantum Error Correction and Orthogonal Geometry
Quantum Error Correction and Orthogonal Geometry

... A quantum error-correcting code is a way of encoding quantum states into qubits (two-state quantum systems) so that error or decoherence in a small number of individual qubits has little or no effect on the encoded data. The existence of quantum error-correcting codes was discovered only recently [1 ...
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Decoherence-free subspaces

A decoherence-free subspace (DFS) is a subspace of a system's Hilbert space that is invariant to non-unitary dynamics. Alternatively stated, they are a small section of the system Hilbert space where the system is decoupled from the environment and thus its evolution is completely unitary. DFSs can also be characterized as a special class of quantum error correcting codes. In this representation they are passive error-preventing codes since these subspaces are encoded with information that (possibly) won't require any active stabilization methods. These subspaces prevent destructive environmental interactions by isolating quantum information. As such, they are an important subject in quantum computing, where (coherent) control of quantum systems is the desired goal. Decoherence creates problems in this regard by causing loss of coherence between the quantum states of a system and therefore the decay of their interference terms, thus leading to loss of information from the (open) quantum system to the surrounding environment. Since quantum computers cannot be isolated from their environment (i.e. we cannot have a truly isolated quantum system in the real world) and information can be lost, the study of DFSs is important for the implementation of quantum computers into the real world.
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