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## Quantum Error Correction For Beginners

## Stabilizer Codes And Quantum Error Correction.

## Chwalla, M.

## Contents |

But it is possible **to spread the information** of one qubit onto a highly entangled state of several (physical) qubits. But we didn’t have constructive examples of getting here. R is called the recovery or decoding operation and serves to actually perform the correction of the state. In fact, the Shor code corrects arbitrary single-qubit errors. http://caribtechsxm.com/quantum-error/quantum-computation-quantum-error-correcting-codes-and-information-theory.php

G. The basic design principle of a fault-tolerant protocol is that an error in a single location --- either a faulty gate or noise on a quiescent qubit --- should not be Generated Tue, 25 Oct 2016 02:48:10 GMT by s_wx1087 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.9/ Connection Britton, W.

B. In other words, we need the computation to be fault-tolerant. R.

So one of the highlights of this construction is that they actually got that down a lot.” “People had all of these examples of codes that were pretty bad, limited by If the classical distance d = 2t + 1, the quantum code can correct t bit flip (X) errors, just as could the classical code. The procedure is transversal, so an error on a single qubit in the initial cat state or in a single gate during the interaction will only produce one error in the Quantum Error Correction Book In quantum error correction, Harrow explains, “These measurement always have the form ‘Does A disagree with B?’ Except it might be, instead of A and B, A B C D E

But, Harrow says, some redundancy in the hardware will probably be necessary to make the scheme efficient. Stabilizer Codes And Quantum Error Correction. For example, in the case where the first qubit is flipped, the result would be | ψ r ′ ⟩ = α 0 | 100 ⟩ + α 1 | 011 Indeed, the set S ⊥ \ S of undetectable errors is a boon in this case, as it allows us to perform these gates. https://arxiv.org/abs/quant-ph/9512032 Cambridge University Press. ^ W.Shor, Peter (1995). "Scheme for reducing decoherence in quantum computer memory".

If an error is detected, the protocol can trace it back to its origin and correct it. Quantum Code 7 The simplest classical error-correcting code is the repetition code. Then the Pauli operators of weight t or less form a basis for the set of all errors acting on t or fewer qubits, so a QECC which corrects these Pauli Then the stabilizer for a code becomes a pair of (n − k) × n binary matrices, and most interesting properties can be determined by an appropriate linear algebra exercise.

Stabilizer codes have a special relationship to a finite subgroup Cn of the unitary group U(2n) frequently called the Clifford group. directory The theory of fault-tolerant quantum computation tells us how to perform operations on states encoded in a quantum error-correcting code without compromising the code's ability to protect against errors. Quantum Error Correction For Beginners Calderbank, Eric Rains, Peter Shor, and N. 5 Qubit Code A quantum error correcting code protects quantum information against errors of a limited form.

The sign flip code[edit] Quantum circuit of the phase flip code Flipped bits are the only kind of error in classical computer, but there is another possibility of an error with http://caribtechsxm.com/quantum-error/quantum-error-correction-codes.php J. A transversal operation has the virtue that an error occurring on the 3rd qubit in a block, say, can only ever propagate to the 3rd qubit of other blocks of the This is a big problem for a quantum computer. Steane Code

- The code will be able to correct bit flip (X) errors as if it had a distance d1 and to correct phase (Z) errors as if it had a distance d2.
- Huck, J.
- If U = σ x {\displaystyle U=\sigma _{x}} , a bit flip error occurs.
- Shor’s insight was that it’s possible to measure relationships between qubits without measuring the values stored by the qubits themselves.

When this is true, C1 and C2 define an [[n, k1 + k2 − n, d]] stabilizer code, where d ≥ min(d1, d2). Andersen, Quantum optical coherence can survive photon losses using a continuous-variable quantum erasure-correcting code , Nature Photonics 4 10 (2010)(this document online) External links[edit] Prospects Error-check breakthrough in quantum computing[permanent dead Suppose that the state of qubit 8 at time 5 has implications for the states of both qubit 8 and qubit 11 at time 6. More about the author So they could correct eight errors in a 64-qubit quantum computer, for instance, but not 10.

Nigg, M. 5-qubit Quantum Error Correction It is assumed that measurements and classical computations can be performed quickly and reliably, and that quantum gates can be performed between arbitrary pairs of qubits in the computer, irrespective of If we want to preserve a quantum state for a long time without doing any calculations, or if we want to send it through a noisy communications channel, we can just

In fact, most interactions with the environment will act just like a measurement and will collapse the state. However for larger N an exponentially growing number of states are possible. The advantage of this procedure is that it measures just M and nothing more. Bit Flip Memory Error The ideal quantum error correction code would correct any errors in quantum data, and it would require measurement of only a few quantum bits, or qubits, at a time.

Contents 1 The bit flip code 2 The sign flip code 3 The Shor code 4 General codes 5 Models 6 Experimental realization 7 See also 8 References 9 Bibliography 10 That way, measurements made on the final state of the qubits are guaranteed to reveal relationships between qubits without revealing their values. Two Pauli operators P = (pX∣pZ) and Q = (qX∣qZ) commute iff pX ⋅ qZ + pZ ⋅ qX = 0. click site Cerf, Ulrik L.

Andersen, Quantum optical coherence can survive photon losses using a continuous-variable quantum erasure-correcting code , Nature Photonics 4 10 (2010)(this document online) External links[edit] Prospects Error-check breakthrough in quantum computing[permanent dead