Stabilizing qubit coherence via tracking-control

2005 ◽  
Vol 5 (4&5) ◽  
pp. 350-363
Author(s):  
D.A. Lidar ◽  
S. Schneider
Keyword(s):  
Error Correction ◽  
Finite Time ◽  
Tracking Control ◽  
Quantum Error Correction ◽  
The State ◽  
Control Field ◽  
Dynamical Decoupling ◽  
Single Qubit ◽  
Quantum Error

We consider the problem of stabilizing the coherence of a single qubit subject to Markovian decoherence, via the application of a control Hamiltonian, without any additional resources. In this case neither quantum error correction/avoidance, nor dynamical decoupling applies. We show that using tracking-control, i.e., the conditioning of the control field on the state of the qubit, it is possible to maintain coherence for finite time durations, until the control field diverges.

Quantum Error Correction

2020 ◽  
Author(s):  
Todd A. Brun
Keyword(s):  
Error Correction ◽  
Quantum Computation ◽  
Single Photon ◽  
Error Correcting Code ◽  
Quantum Systems ◽  
Quantum Error Correction ◽  
The State ◽  
Quantum States ◽  
Quantum Code ◽  
Quantum Error

Quantum error correction is a set of methods to protect quantum information—that is, quantum states—from unwanted environmental interactions (decoherence) and other forms of noise. The information is stored in a quantum error-correcting code, which is a subspace in a larger Hilbert space. This code is designed so that the most common errors move the state into an error space orthogonal to the original code space while preserving the information in the state. It is possible to determine whether an error has occurred by a suitable measurement and to apply a unitary correction that returns the state to the code space without measuring (and hence disturbing) the protected state itself. In general, codewords of a quantum code are entangled states. No code that stores information can protect against all possible errors; instead, codes are designed to correct a specific error set, which should be chosen to match the most likely types of noise. An error set is represented by a set of operators that can multiply the codeword state. Most work on quantum error correction has focused on systems of quantum bits, or qubits, which are two-level quantum systems. These can be physically realized by the states of a spin-1/2 particle, the polarization of a single photon, two distinguished levels of a trapped atom or ion, the current states of a microscopic superconducting loop, or many other physical systems. The most widely used codes are the stabilizer codes, which are closely related to classical linear codes. The code space is the joint +1 eigenspace of a set of commuting Pauli operators on n qubits, called stabilizer generators; the error syndrome is determined by measuring these operators, which allows errors to be diagnosed and corrected. A stabilizer code is characterized by three parameters [[n,k,d]], where n is the number of physical qubits, k is the number of encoded logical qubits, and d is the minimum distance of the code (the smallest number of simultaneous qubit errors that can transform one valid codeword into another). Every useful code has n>k; this physical redundancy is necessary to detect and correct errors without disturbing the logical state. Quantum error correction is used to protect information in quantum communication (where quantum states pass through noisy channels) and quantum computation (where quantum states are transformed through a sequence of imperfect computational steps in the presence of environmental decoherence to solve a computational problem). In quantum computation, error correction is just one component of fault-tolerant design. Other approaches to error mitigation in quantum systems include decoherence-free subspaces, noiseless subsystems, and dynamical decoupling.

scholarly journals Experimental exploration of five-qubit quantum error correcting code with superconducting qubits

2021 ◽  
Author(s):  
Ming Gong ◽  
Xiao Yuan ◽  
Shiyu Wang ◽  
Yulin Wu ◽  
Youwei Zhao ◽  
...  
Keyword(s):  
Error Correction ◽  
Error Correcting Code ◽  
Error Correcting Codes ◽  
Quantum Error Correction ◽  
Superconducting Qubits ◽  
Perfect Code ◽  
Experimental Realization ◽  
Single Qubit ◽  
Universal Quantum ◽  
Quantum Error

Abstract Quantum error correction is an essential ingredient for universal quantum computing. Despite tremendous experimental efforts in the study of quantum error correction, to date, there has been no demonstration in the realisation of universal quantum error correcting code, with the subsequent verification of all key features including the identification of an arbitrary physical error, the capability for transversal manipulation of the logical state, and state decoding. To address this challenge, we experimentally realise the [[5, 1, 3]] code, the so-called smallest perfect code that permits corrections of generic single-qubit errors. In the experiment, having optimised the encoding circuit, we employ an array of superconducting qubits to realise the [[5, 1, 3]] code for several typical logical states including the magic state, an indispensable resource for realising non-Clifford gates. The encoded states are prepared with an average fidelity of $57.1(3)\%$ while with a high fidelity of $98.6(1)\%$ in the code space. Then, the arbitrary single-qubit errors introduced manually are identified by measuring the stabilizers. We further implement logical Pauli operations with a fidelity of $97.2(2)\%$ within the code space. Finally, we realise the decoding circuit and recover the input state with an overall fidelity of $74.5(6)\%$, in total with 92 gates. Our work demonstrates each key aspect of the [[5, 1, 3]] code and verifies the viability of experimental realization of quantum error correcting codes with superconducting qubits.

scholarly journals A Software Method For Mitigating Single Qubit Errors On Superconducting Quantum Devices

2020 ◽  
Author(s):  
Macauley Coggins ◽  
Devanshi Arora
Keyword(s):  
Error Correction ◽  
Quantum Error Correction ◽  
Superconducting Qubits ◽  
Quantum Decoherence ◽  
Small Scale ◽  
Quantum Devices ◽  
Single Qubit ◽  
Error Mitigation ◽  
Quantum Error

Quantum error correction schemes have gained a lot of attention in recent years. This is due to the emergence of small scale quantum devices that make use of superconducting qubits. However these devices are noisy and prone to quantum decoherence and thus errors. Along with quantum error correction there has been a push for new schemes in quantum error mitigation that take a more passive approach in eliminating readout errors. In this research we introduce a software method for quantum error mitigation that maps virtual qubits in a circuit to physical qubits with the least error. The method developed was tested on 9 IBM quantum devices. Results in the study have shown the method can reduce readout errors by up to 35.52%.

ROBUST DYNAMICAL DECOUPLING: FEEDBACK-FREE ERROR CORRECTION

2005 ◽  
Vol 03 (supp01) ◽  
pp. 41-52
Author(s):  
D. A. LIDAR ◽  
K. KHODJASTEH
Keyword(s):  
Error Correction ◽  
Efficiency Analysis ◽  
Error Correcting Codes ◽  
Quantum Error Correction ◽  
Dynamical Decoupling ◽  
Protection Scheme ◽  
Basic Concepts ◽  
Quantum Error

Dynamical decoupling is a feed-back free scheme for quantum error correction against noise and decoherence errors. An efficiency analysis of dynamical decoupling is performed. Furthermore we provide the basic concepts of dynamical decoupling and quantum error correcting codes, and give an example of a hybrid protection scheme. Some interesting extensions of dynamical decoupling are discussed at the end.

scholarly journals COMBATING ENTANGLEMENT SUDDEN DEATH WITH NON-LOCAL QUANTUM-ERROR CORRECTION

2009 ◽  
Vol 07 (supp01) ◽  
pp. 245-255 ◽  
Author(s):  
ISABEL SAINZ ◽  
GUNNAR BJÖRK
Keyword(s):  
Sudden Death ◽  
Error Correction ◽  
Finite Time ◽  
Quantum Error Correction ◽  
Entanglement Sudden Death ◽  
Local Quantum ◽  
Non Local ◽  
Quantum Error ◽  
Made In

We study the possibility of preventing finite-time disentanglement caused by dissipation by making use of non-local quantum error correction. This is made in comparison to previous results, where it was shown that local quantum error correction can delay disentanglement, but can also cause entanglement sudden death when it is not originally present.

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