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General Qubit Errors Cannot Be Corrected
[article]
2002
arXiv
pre-print
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Error correction, in the standard meaning of the term, implies the ability to correct all small analog errors and some large errors. ...
Examining assumptions at the basis of the recently proposed quantum error-correcting codes, it is pointed out that these codes can correct only a subset of errors, and are unable to correct small phase ...
We cannot be hopeful for other methods of qubit error correction either, since the difficulty arises out of the analog nature of the error process. ...
arXiv:quant-ph/0206144v4
fatcat:f2vubpansraizdws7xbdo34sea
A Note on Quantum Errors and Their Correction
[article]
1998
arXiv
pre-print
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This note presents a few observations on the nonlocal nature of quantum errors and the expected performance of the recently proposed quantum error-correction codes that are based on the assumption that ...
the errors are either bit-flip or phase-flip or both. ...
The unitary matrix (1) represents an infinite number of cases of error. The error process is an analog process, and so, in general, such errors cannot be corrected. ...
arXiv:quant-ph/9811005v1
fatcat:62mwxgdb7fce5lzkz6r4fof5wy
Encoding one logical qubit into six physical qubits
2008
Physical Review A. Atomic, Molecular, and Optical Physics
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2008 pre-print arXiv:0803.1495v1 fatcat:4hi2jpouarejji6zddf2jqdh6eOther Versions
We then prove that a six-qubit code without entanglement assistance cannot simultaneously possess a Calderbank-Shor-Steane (CSS) stabilizer and correct an arbitrary single-qubit error. ...
Our first example is a degenerate six-qubit quantum error-correcting code. ...
All generators cannot be of the same type (X or Z). ...
doi:10.1103/physreva.78.012337
fatcat:zt6n7iajqbhktacnghqqn77rfi
The Initialization Problem in Quantum Computing
[article]
2002
arXiv
pre-print
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The paper also presents general observations on the nonlocal nature of quantum errors and the expected performance of the proposed quantum error-correction codes that are based on the assumption that the ...
It is argued that these codes cannot directly solve the initialization problem of quantum computing. ...
The unitary matrix (11) represents an infinite number of cases of error. The error process is an analog process, and so, in general, such errors cannot be corrected. ...
arXiv:quant-ph/9805002v2
fatcat:ysstiug7ezakpckielyt7nuvgi
A practical architecture for reliable quantum computers
2002
Computer
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Thus, errors can be continuous in nature, and minor shifts in the superposition of a qubit cannot be discriminated from the desired computation. ...
Quantum operations must be reversible, and we cannot perfectly clone qubitsthat is, we cannot copy their value. ...
The positions are at the Assistant Professor level, but exceptional candidates at the Associate or Full Professor level will also be considered. ...
doi:10.1109/2.976922
fatcat:happ5hbzrjezxhletq5qng7pci
Error correction and symmetrization in quantum computers
[article]
1996
arXiv
pre-print
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On the other hand, isolated errors can be corrected by quantum codewords that represent a logical qubit in a redundant way, by several physical qubits. ...
Errors in quantum computers are of two kinds: sudden perturbations to isolated qubits, and slow random drifts of all the qubits. ...
However, the codeword error correction procedure definitely requires four qubits to be correct, and it cannot cope with small drifts of all five qubits, or even two of them. ...
arXiv:quant-ph/9611046v1
fatcat:nvacuqzlhnc67hjtxvsi3kwjwa
Error symmetrization in quantum computers
[article]
1996
arXiv
pre-print
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It is possible to reduce some types of quantum computation errors by symmetrizing the quantum state of a redundant array. Various models are discussed. ...
However, the codeword error correction procedure definitely requires four qubits to be correct, and it cannot cope with small drifts of all five qubits. ...
In this theoretical model, an "error" means a state that is orthogonal to the correct one. This has to be generalized to the case of less radical errors. ...
arXiv:quant-ph/9605009v1
fatcat:2hv5vo74kvbrvaaelveo7m3eie
Quasi-Probabilistic Readout Correction of Mid-Circuit Measurements for Adaptive Feedback via Measurement Randomized Compiling
[article]
2024
arXiv
pre-print
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2023 pre-print arXiv:2312.14139v1 fatcat:6zueuoujtvgyppvjgji46naigeOther Versions
on an ancilla qubit used to detect and actively correct bit-flip errors on an entangled memory qubit. ...
Our approach enables the correction of readout errors on large numbers of qubits, and offers a strategy for correcting readout errors in adaptive circuits in which the results of mid-circuit measurements ...
In general, quantum measurement errors cannot be modeled by a confusion matrix because it ignores the effect of the measurement process on quantum superpositions. ...
arXiv:2312.14139v4
fatcat:7vf7elbonbgizgrwiwufujiwsm
Quantum error correction in the presence of spontaneous emission
1997
Physical Review A. Atomic, Molecular, and Optical Physics
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We present a quantum error correcting code that is invariant under the conditional time evolution between spontaneous emissions and which can correct for one general error. ...
The code presented here generalizes previous error correction codes in that not all errors lead to different error syndromes. This idea may lead to shorter codes than previously expected. ...
Steane for discussions about quantum error correction. ...
doi:10.1103/physreva.55.67
fatcat:3qr36t6u2zggdfypsfysn73x3y
An Introduction to Quantum Error Correction
[article]
2000
arXiv
pre-print
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Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. ...
The theory of quantum error-correcting codes has some close ties to and some striking differences from the theory of classical error-correcting codes. ...
Summary (Quantum Error Correction Sonnet) We cannot clone, perforce; instead, we split Coherence to protect it from that wrong That would destroy our valued quantum bit And make our computation take too ...
arXiv:quant-ph/0004072v1
fatcat:4bgdvb7bhvcqjeu2lfjgwsprea
5-qubit quantum error correction in a charge qubit quantum computer
[article]
2010
arXiv
pre-print
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We implement the DiVincenzo-Shor 5 qubit quantum error correcting code into a solid-state quantum register. ...
We evaluate the decay of the density matrix for this multi-qubit system and perform regular quantum error corrections. ...
In general, this leads to an error, which cannot be reduced to a single qubit error. In addition, this decoherence model does not take into account any relaxation the system might be subject to. ...
arXiv:1010.3242v1
fatcat:iwpaapcu6rah7jnftp2szbqnr4
Universal Fault-Tolerant Gates on Concatenated Stabilizer Codes
2016
Physical Review X
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In particular, we show how the limits of non-transversality can be overcome by performing rounds of intermediate error-correction to create logical gates on stabilizer codes that use no ancillas other ...
We detail such universal constructions for the smallest quantum codes, the 5-qubit and 7-qubit codes, and then proceed to generalize the approach. ...
In those cases, we must be extra careful to construct circuits that correct all errors we need to correct without introducing errors that cannot be corrected in the next round. ...
doi:10.1103/physrevx.6.031039
fatcat:ujuorrahrzfxnaxafhi7253e5e
Non-fault-tolerantTgates for the [7,1,3] quantum error-correction code
2013
Physical Review A. Atomic, Molecular, and Optical Physics
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2013 pre-print arXiv:1303.4291v1 fatcat:27rtwuohtbd3nfmsd6qf4h64ci
Meaning, any errors that may have occurred during implementation are 'correctable' and fault tolerance may still be achieved. ...
We simulate the implementation of a T-gate, or π/8-gate, for a [7,1,3] encoded logical qubit in a non-equiprobable error environment. ...
If even perfect error correction cannot (to first order) correct the errors in the T -gate then it is unlikely that this gate can be used for practical implementations of quantum computation. ...
doi:10.1103/physreva.87.032320
fatcat:feyuqq2taze7dlhbbhkujbt6r4
Unitary dynamics for quantum codewords
[article]
1996
arXiv
pre-print
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The recovery procedure may consist of the detection of an error syndrome, followed by the correction of the error, as in the classical case. ...
However, it can also be performed by means of unitary operations, without having to know the error syndrome. ...
This goal is much more difficult to achieve than classical error correction, because qubits cannot be read, or copied, or duplicated, without altering their quantum state in an unpredictable way [4] . ...
arXiv:quant-ph/9609015v1
fatcat:tu4oo7pecvhqritbrlpyai6eie
Fault-tolerant quantum computation with few qubits
2018
npj Quantum Information
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2017 pre-print arXiv:1705.05365v1 fatcat:aeop3bc6xvgzlb3xa7kirbdl6y
Reliable qubits are difficult to engineer, but standard fault-tolerance schemes use seven or more physical qubits to encode each logical qubit, with still more qubits required for error correction. ...
In particular, individual encoded qubits within the code block can be targeted. Fault-tolerant universal computation is possible with four extra qubits, 19 total. ...
The gadgets cannot prevent the gates from spreading single-qubit faults into problematic multi-qubit errors. ...
doi:10.1038/s41534-018-0085-z
fatcat:nqg6pitlg5bbpcub4eb5j7zt4e
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