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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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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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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227 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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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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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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Different QFT results when using Simulator or Quantum Machine

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

Repetition code encoder circuit

The repetition code encodes $\vert \psi \rangle = \alpha \vert 0 \rangle + \beta \vert 1 \rangle \rightarrow \vert \psi \rangle = \alpha \vert 000 \rangle + \beta \vert 111 \rangle$ using the ...
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Quantum circuit for a three-qubit bit-flip code

I know a three-qubit bit-flip code has a common encoding circuit as follows, Further, as in page 35 in Gottesman's paper, the encoding circuit can also be constructed through stabilizer generators. ...
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Quantum error correction using bit-flip code for the amplitude damping channel

I do not understand the error correction process that uses quantum codes for amplitude damping channel. I will take three bit-flip code for example. The logical state of a three bit-flip code is $|0\...
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QISKit Connection

I ve beeen trying to use the qiskit package from spyder IDE inisde anaconda (Python version 3.7) but when i try to acces my account I get the following error: ...
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Where does error correction go in a quantum algorithm?

Where does QEC fit in the larger picture of the execution of a fault tolerant quantum algorithm? For QEC, there is an initial preparation of the qubit state and the ancillary qubits; then a "noisy ...
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Implications of commuting within the code space

The question: I have a Hilbert space $\mathcal{H}=\mathcal{H}_A\otimes \mathcal{H}_B$, and a codespace $\mathcal{H}_{code}\subset \mathcal{H}$, so that $\mathcal{H}=\mathcal{H}_{code}\oplus\mathcal{...
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The process behind constructing a Stabilizer Code?

I am really puzzled when it comes to the construction of a stabilizer code. By that, I mean how to come up with the subgroup $S$ and the matrix generators $M= \{M_1, M_2, \cdots, M_{n-k}\}$? In ...
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Renting quantum on the cloud: data privacy, adoption and error correction

If an individual or commercial enterprise resorts to renting quantum computing power on the cloud, wouldn't the company who owns and hosts the quantum computer be able to see/monitor/eavesdrop on the ...
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About a necessary condition for quantum error correcting codes

I'm John and I have a question which I have been thinking about. I'm studying quantum information, especially, quantum error-correcting codes. When I learned some types of quantum codes (e.g. 5 qubits ...
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Nielsen & Chuang Exercise Question on CSS code

I was reading the CSS ( Steane Code) from the Nielsen & Chuang book. It asked in Ex. 10.27 to prove that: suppose $C_1$ and $C_2$ are $[n,k_1]$ and $[n,k_2]$classical linear codes such that $C_2\...
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Can we conclude that errors on Sycamore are Poisson-distributed Pauli errors?

In Martinis' recent Caltech lecture on the Sycamore paper, he appears to make much of the fact that FIG. 4 of the paper show straight-line fidelity - that is, the fidelity decreases log-linearly with ...
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Matrix Index and multiplication rules for Hermitian Pauli group products

Given the Hermitian Pauli group products $$ \Omega_{a,b}=\{\pm 1,\pm i\}_{a,b}\cdot \{I,X,Y,Z\}_{a,b}^{\otimes n} $$ composed of $n$ 2x2 pauli matrices $(I,X,Y,Z)$ in tensor product, such that they ...
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Shor's Code: Understanding how it satisfies Knill Laflamme Theorem

I'm new to Quantum Error Correction, and I have a question on Shor's Code. If we have a protected subspace, $V \subset \mathbf{C}^2\otimes \cdots \otimes \mathbf{C}^2$ $V=\operatorname{span}\{|0_{...
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Is manual or automated error correction more practically promising in the near term?

I'm curious if there's any consensus on this question among actual practitioners, but please feel free to close it if it's hopelessly opinion-based (since we've only taken baby steps toward the ...
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Entanglement-assisted hashing bound for asymmetric depolarizing channels

I reading the paper EXIT-Chart Aided Quantum Code Design Improves the Normalised Throughput of Realistic Quantum Devices, which proposes the use of QTCs in order to do quantum error correction for ...
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Distance and number of corrected errors in quantum error correction [duplicate]

In Gottesman's introduction, it writes A code that corrects t errors is said to have distance 2t + 1, because it takes 2t + 1 single-qubit changes to get from one codeword to another. Other ...
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Link between distance of a stabilizer code and number of errors it is able to correct

I am confused by a property. In the N&Chuang it is said that an $[n,k,2t+1]$ stabilizer code is able to correct up to $t$ errors. But for me if the code has distance $d$ it should be able to ...
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The importance of length-4 cycles in Quantum LDPC codes

It is a proven and well-known fact that length-4 cycles are detrimental to the performance of classical LDPC codes. This is due to the fact that such short cycles impair the decoding algorithm (Sum ...
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Exercise 10.34 of Nielsen and Chuang : $-I$ not element of stabilizer group iff $g_j^2=I$ and $g_j \neq I$ where $g_j$ generators

I am stuck with this exercice of Nielsen and Chuang: Let $S = \langle g1,... ,gl \rangle $.Show that $−I$ is not an element of S if and only if $g^2_j = I$ for all $j$,and $g_j \neq − I$ for all $j$...
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What are the Main Classes of Quantum Error-Correcting Codes?

Classically, we have the Hamming Code, Turbo Code, Reed-Solomon Code, etc. I am interested in knowing the classes of quantum error-correcting codes. They don't have to be analogous to classical codes, ...
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Job execution issue while using IBMQ Experience

I am trying to run QSVM algorithm on the IBMQ backend devices using the API_TOKEN. Below is the snippet of the code that I am running. The code fails the validation test and throws an exception after ...
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How do I interpret the readout error for a quantum computer?

For example, the ibmqx2 computer has the most recent readout error of $4.40 \cdot 10^{-2}$. Does this mean per 1000 measurements, 44 faulty results exist?
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Intuition about Knill-Laflamme QEC conditions

The Knill Laflamme QEC conditions are stated this way: We consider a code space $C$ and its associated projector $P_C$. We consider a noise acting on our system: $E(\rho)=\sum_a E_a \rho E_a^{\...
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Questions about theorem and proof: "Quantum error correction condition", Thm 10.1 Nielsen & Chuang

I have some basic questions around the theorem giving quantum error correction conditions that give necessary & sufficient conditions to have an error correcting operation. The theorem is stated ...
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Knill-Laflamme condition and requirements for error correction

Suppose we have a stabilizer group $\mathcal{M}$, the Knill-Laflamme condition for error correction states An error with Kraus operators $\{E_k\}$ is correctable if either $$E^\dagger_kE_l\in\...