Questions tagged [error-correction]

Quantum error correction (QEC) is a collection of techniques to protect quantum information from decoherence and other quantum noise, to realise fault-tolerant quantum computation. Quantum error correction is expected to be essential for practical quantum computation in the face of noise on stored quantum information, faulty quantum gates, faulty state preparations, and faulty measurements. (Wikipedia)

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154 views

How to create the logical $|0_L\rangle$ state for the Steane's 7-qubit code?

I don't know how to prepare using Qiskit the following state in order to implement a Steane's 7-qubit code circuit (I omit the normalization factor): \begin{align*} |0_L\rangle =&|0000000\rangle+|...
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143 views

Circuit for implementing Steane's code for Quantum Error Correction

I was reading about the Steane's code for QEC. However I could not find any implementation or circuit describing its creation. Can anyone share/explain how the Steane's code could be implemented. The ...
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89 views

A question about quantum noise model

Now, I try to understand some concept of Quantum Noise Model and Quantum Channel. The Quantum Noise can be represented as a quantum operator with their own probability. As far as I concerned,(I dont ...
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208 views

What is the pseudo threshold of a QECC using stabilizer formalism

Can someone explain what is the threshold and the pseudo threshold of a Quantum Error Correction Code , for instance the 9-qubit code, and how to calculate it using the stabilizer formalism simulation ...
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206 views

Find the Kraus operators of a combined amplitude and phase damping channel

I am going through the paper Surface code with decoherence: An analysis of three superconducting architectures and I have a doubt about how the authors get what they refer to as the combined channel ...
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50 views

Question regarding part of the proof for the typical subspace theorem

Part three (going by N&C page 544) states that $$tr(S(n)\rho^{\otimes n})=tr(S(n)\rho^{\otimes n}P(n,\epsilon))+tr(S(n)\rho^{\otimes n}(I-P(n,\epsilon))).$$ Now I understand how the term on the ...
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100 views

Quantum Error Correcting Codes and Graphs

Couple of weeks ago I asked this question on theory CS but I didn't get an answer. So trying it here. I was reading combinatorial approach towards quantum correction. A lot of work in this is on ...
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Qubit relaxation time dependencies

The qubit relaxation time $T_1$ is an important parameter in order to describe the coherence time that a qubit presents, that is, the time in which its coherence quantum state is not compromised by ...
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266 views

How to do error mitigation on the ibmq_16_melbourne?

I'm trying to make a calibration matrix using CompleteMeasFitter as in here on IBMQ Melbourne, but I need to use all 15 qubits, which mean it has to run 32768 calibration circuit, far exceeding the 75 ...
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194 views

Algorithm to find stabilizer states

I'm working on a project in which I have to find stabilizer states based on a few criteria, the main one being that it has to have a certain amount of coherence, I'm using the following equation to ...
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52 views

How to calculate destabilizer group of toric and other codes

Some papers use the "destabilizer group" for more efficient simulations; see for example (page 3): https://www.scottaaronson.com/showcase2/report/ted-yoder.pdf "In addition to ...
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106 views

Other than distance, what other metrics can be used to compare quantum error correcting codes?

Using classical error correction (or channel coding) as a reference, I'd like to be able to compare QECC's from different constructions. Distance is a reasonable measure and you can argue that an $[[...
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348 views

What are generators for a "real" Clifford group?

I work with stabilizer codes using the real version of Pauli matrices: $X=((0,1),(1,0))$, $Z=((1,0),(0,-1))$, $Y=XZ$ (not $\imath XZ$). I know the encoders for these codes lie in the Clifford group ...
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Quantum channels and error correction research groups

I am wondering which are the top universities or research groups through the world that are doing research in the topic of quantum error correction or quantum channels (decoherence noise models). I ...
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168 views

Quantum error correction on IBM devices?

I'm wondering if the gate errors on any of the IBM devices are low enough so that we could use some error correcting codes which do not require too many qubits? (such as 5- or 7-qubit codes). Even ...
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143 views

Can Shor's 9 Qubit Code Correct for a measurement on the first qubit?

Start with Shor's codeword for $|0 \rangle$: $|\psi\rangle = \frac{1}{\sqrt{8}}(|000\rangle + |111\rangle)\otimes(|000\rangle + |111\rangle)\otimes(|000\rangle + |111\rangle)$. Now, assume that ...
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Where can I find tutorials about correcting gate errors in the quantum circuit?

I just have a question about where can I find tutorials/examples about correcting gate errors (amplitude errors and phase errors) in a quantum circuit? Are there any resources I can learn from? Thanks!...
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What is a difference between error rates and qubit/gate fidelity?

What is a difference between error rates and qubit/gate fidelity? A bit of maths in the explanation is fine but I am an A Level student doing a research project so definitions would be preferred.
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What is the stabilizer group of a $|W\rangle$ state?

This question is related and complementary to this one: How to get the stabilizer group for a given state? What I want is to find the stabilizer group generators for the following state: $$|W\rangle ...
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256 views

How to get the stabilizer group for a given state?

Let's say we have the GHZ state with 3 qubits: $$ |\mathrm{GHZ}\rangle = \dfrac{1}{\sqrt{2}}\Big(|000\rangle + |111\rangle \Big)$$ I want to find the stabilizer group of this state, that is, the $...
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139 views

Smallest Distance-5 Quantum Error Correction Code?

Is it known/proven what the smallest quantum error correction code is that can correct arbitrary two-qubit Pauli errors? I can think of the nested/concatenated 5-qubit code or a 25-qubit version of ...
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217 views

Exponential Growth of Noise in Quantum Computers

I recently listened to a presentation for Introductory Quantum Computing. It was very general and meant to give the listeners an idea about the potential for Quantum Computing. The speaker ended the ...
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220 views

Physical Interpretation of Non-Trace Preserving Quantum Operations

In Chapter 8 of Nielsen and Chuang's Quantum Computation and Quantum Information, a mathematical framework is developed to describe the dynamics of open quantum systems. Suppose the initial state of ...
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How does the unitary encoding procedure in quantum secret sharing schemes or error correcting codes work?

In Cleve et al.'s paper "How to share a quantum secret", two encodings of quantum states are mentioned. The first one encodes one qutrit into three qutrits, $\alpha|0\rangle + \beta|1\rangle + \gamma|...
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113 views

Real-device error mitigation with qiskit

I'm trying to do error mitigation in IBM-Q quantum computers with qiskit. I followed the tutorial here. My thought was that in order to make sure that I'm correcting the qubits that I'm actually using ...
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80 views

Specifying qubits to achieve measurement error mitigation on Qiskit

I'm learning how to do error mitigation on Qiskit as my experiment result differs from the simulated result. I read the tutorial here, but I have some questions about it. If I have understood it ...
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Can a quantum error-correcting code really correct any linear combination of correctable errors?

It appears to me that in the survey by Gottesman (around Thm 2) as well as the book by Nielsen and Chuang (Thm 10.2) it is suggested that if a QEC code corrects errors $A$ and $B$ then it also ...
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134 views

Is there benefit to extra stabilizers in a rotated surface code?

I'm reading Horsman et al. "Surface code quantum computing by lattice surgery" and I'm wondering about the rotated surface code. Consider Figure 13: This is supposed to have distance 5. But in (c), ...
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How does Teleportation based Error Correction (TEC) detect and correct loss/erasure errors?

I'm looking at papers like Demonstration of teleportation-based error correction in the IBM quantum computer (page) 10 and Role of syndrome information on a one-way quantum repeater using ...
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Identity for linear codes and their duals: why do we have $\sum_y (-1)^{x\cdot y}=|C|\delta_{x\in C^\perp}$?

I've come across this exercise plenty of times and I still don't understand how to do it. (Here it is from N.C. Ex.10.25) Let $C$ be a linear code (Lets suppose its a binary code, i.e. a $k$-...
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Why should we measure in X/Z basis for Z/X errors in Steane syndrome extraction?

From the Steane syndrome extraction of quantum error correcting code, we use ancilla qubit prepared in logical X/Z basis to detect logical Z/X errors in the logical data state (The CNOT is transversal)...
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221 views

Different results between qasm_simulator and quantum computer: how to normalize for only few states

I recently started developing circuits with Qiskit. I made a 5 qubit circuit in which the fourth qubit at the end of execution must always have value 1: When I do the simulation with qasm everything ...
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82 views

Is there quantum error correction code package for python

I'm working on the development of a new quantum error correction protocol that tries to maximize the coherence of the qubit. Is there a package for python, similar to qutip, that could help me in this ...
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1answer
136 views

What does it mean to "measure a stabilizer"?

Say I have the stabilizer $XXI$, and a phase-flipped state $|\psi\rangle$. What does it mean to measure the stabilizer $XXI$? What is the math behind "measurement"?
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160 views

Different QFT results when using Simulator or Quantum Machine

I'm performing QFT using the following code: ...
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37 views

Obtaining low weight stabilizer generators

Suppose I know a set of stabilizer generators of a qubit quantum code. Is there a systematic (and possibly efficient) way to transform this set of generators to a different set (generating the same ...
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337 views

Mitigating the noise in a quantum circuit

I'm using Qiskit and I have a Quantum Circuit (say, circuit) that gives reasonable results when using the simulator, namely ...
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1answer
147 views

IBM Q calibration parameters

If I download calibration of a quantum processor on IBM Q website I see these parameters: T1 T2 frequency (GHz) readout error single qubit U2 error rate CNOT error rate T1 and T2 are relaxation and ...
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43 views

How is the theory of modular representation involved with error-correction?

Recently, I have heard that the theory of modular representation can be involved with error correction in quantum information theory. However, from a point of view of mathematician, I am still quite ...
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The behaviour of ebits in Entanglement-assisted Quantum Error Correction Codes?

I am reading about Entanglement-assisted Quantum Error Correction Codes from Quantum Information Processing and Quantum Error Correction: An Engineering Approach (Chapter 9) . It is a scheme that ...
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Quantum error correction - approximate vs exact

When one has a noisy quantum channel over which one wishes to send some quantum state, one usually comes up with an encoder and decoder. Then, the error between the input state and the output state is ...
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231 views

How to realize this quantum error correction circuit on real hardware?

I want to realize this error correction circuit. To do that, I created a circuit: However, I cannot execute on real hardware. How can I create a circuit to realize this correction on real hardware?
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51 views

Block codes with better parameters vs. surface codes, which need less ancilla qubits?

I'm learning quantum error correction by myself and I want to know the relation between block codes and surface codes. I find that many researchers in the field of coding theory are exploring quantum ...
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252 views

What kind of errors does the master equation in the Lindblad form describe, continuous errors or discrete errors?

I noticed that in page 427 in Nielsen & Chuang's book Quantum Computation and Quantum Information, quantum error correction is possible because errors can be discretized. In other hand, the ...
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How does Surface-17 tell apart Z errors on Db and Dc?

I'm looking into this paper from DiCarlo's group Scalable quantum circuit and control for a superconducting surface code. I don't understand how it's supposed to identify specific single-qubit errors, ...
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1answer
135 views

Understanding surface code diagrams

I originally posted this question on the Physics StackExchange site (see here), but I realized it would be better suited on this one. I'm trying to understand the diagrams used in the following paper....
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204 views

Logical qubit initialization for the surface code

I am reading Fowler et al's paper on the surface code.. I do not understand how to initialize a logical qubit in an arbitrary state with the surface code. I do understand how to initialize the qubit ...
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Why does quantum error correction work?

I read about some QEC codes such as Shor code. It encodes a logical qubit to 9 physical qubits, to correct the bit-flip and phase-flip error. To do this, it needs multiple $\mathrm{CNOT}$ and $\mathrm{...
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2k views

How to implement if statement based on measurement results in qiskit?

I tried to implement three qubit bit flip code in qiskit and need to get the result of measurements and then apply recovery quantum operations conditioned on the measurement results. The following is ...
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1answer
106 views

Syndrome extraction operator as matrix?

I am trying to understand how to achieve the syndrome extraction operator matrix in quantum repetition code (if it even exists). It is given that the syndrome is defined here (page 4) as: [perform]...