6,510 research outputs found
Quantum error correction protects quantum search algorithms against decoherence
When quantum computing becomes a wide-spread commercial reality, Quantum Search Algorithms (QSA) and especially Grover’s QSA will inevitably be one of their main applications, constituting their cornerstone. Most of the literature assumes that the quantum circuits are free from decoherence. Practically, decoherence will remain unavoidable as is the Gaussian noise of classic circuits imposed by the Brownian motion of electrons, hence it may have to be mitigated. In this contribution, we investigate the effect of quantum noise on the performance of QSAs, in terms of their success probability as a function of the database size to be searched, when decoherence is modelled by depolarizing channels’ deleterious effects imposed on the quantum gates. Moreover, we employ quantum error correction codes for limiting the effects of quantum noise and for correcting quantum flips. More specifically, we demonstrate that, when we search for a single solution in a database having 4096 entries using Grover’s QSA at an aggressive depolarizing probability of 10-3, the success probability of the search is 0.22 when no quantum coding is used, which is improved to 0.96 when Steane’s quantum error correction code is employed. Finally, apart from Steane’s code, the employment of Quantum Bose-Chaudhuri-Hocquenghem (QBCH) codes is also considered
Studies Of A Quantum Scheduling Algorithm And On Quantum Error Correction
Quantum computation has been a rich field of study for decades because it promises possible spectacular advances, some of which may run counter to our classically rooted intuitions. At the same time, quantum computation is still in its infancy in both theoretical and practical areas. Efficient quantum algorithms are very limited in number and scope; no real breakthrough has yet been achieved in physical implementations. Grover\u27s search algorithm can be applied to a wide range of problems; even problems not generally regarded as searching problems can be reformulated to take advantage of quantum parallelism and entanglement leading to algorithms which show a square root speedup over their classical counterparts. This dissertation discusses a systematic way to formulate such problems and gives as an example a quantum scheduling algorithm for an R||C_max problem. This thesis shows that quantum solution to such problems is not only feasible but in some cases advantageous. The complexity of the error correction circuitry forces us to design quantum error correction codes capable of correcting only a single error per error correction cycle. Yet, time-correlated errors are common for physical implementations of quantum systems; an error corrected during a certain cycle may reoccur in a later cycle due to physical processes specific to each physical implementation of the qubits. This dissertation discusses quantum error correction for a restricted class of time-correlated errors in a spin-boson model. The algorithm proposed allows the correction of two errors per error correction cycle, provided that one of them is time-correlated. The algorithm can be applied to any stabilizer code, perfect or non-perfect, and simplified the circuit complexity significantly comparing to the classic quantum error correction codes
How Quantum Computers Fail: Quantum Codes, Correlations in Physical Systems, and Noise Accumulation
The feasibility of computationally superior quantum computers is one of the
most exciting and clear-cut scientific questions of our time. The question
touches on fundamental issues regarding probability, physics, and
computability, as well as on exciting problems in experimental physics,
engineering, computer science, and mathematics. We propose three related
directions towards a negative answer. The first is a conjecture about physical
realizations of quantum codes, the second has to do with correlations in
stochastic physical systems, and the third proposes a model for quantum
evolutions when noise accumulates. The paper is dedicated to the memory of
Itamar Pitowsky.Comment: 16 page
Effect of ancilla's structure on quantum error correction using the 7-qubit Calderbank-Shor-Steane code
In this work we discuss the ability of different types of ancillas to control
the decoherence of a qubit interacting with an environment. The error is
introduced into the numerical simulation via a depolarizing isotropic channel.
After the correction we calculate the fidelity as a quality criterion for the
qubit recovered. We observe that a recovery method with a three-qubit ancilla
provides reasonable good results bearing in mind its economy. If we want to go
further, we have to use fault-tolerant ancillas with a high degree of
parallelism, even if this condition implies introducing new ancilla
verification qubits.Comment: 24 pages, 10 Figures included. Accepted in Phys. Rev. A 200
Codeword stabilized quantum codes: algorithm and structure
The codeword stabilized ("CWS") quantum codes formalism presents a unifying
approach to both additive and nonadditive quantum error-correcting codes
(arXiv:0708.1021). This formalism reduces the problem of constructing such
quantum codes to finding a binary classical code correcting an error pattern
induced by a graph state. Finding such a classical code can be very difficult.
Here, we consider an algorithm which maps the search for CWS codes to a problem
of identifying maximum cliques in a graph. While solving this problem is in
general very hard, we prove three structure theorems which reduce the search
space, specifying certain admissible and optimal ((n,K,d)) additive codes. In
particular, we find there does not exist any ((7,3,3)) CWS code though the
linear programming bound does not rule it out. The complexity of the CWS search
algorithm is compared with the contrasting method introduced by Aggarwal and
Calderbank (arXiv:cs/0610159).Comment: 11 pages, 1 figur
- …