scholarly journals Avoiding coherent errors with rotated concatenated stabilizer codes

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Yingkai Ouyang
Keyword(s):  
Fault Tolerant ◽  
Quantum Systems ◽  
Quantum Memory ◽  
Dominant Form ◽  
Amplitude Damping ◽  
Stabilizer Codes ◽  
Outer Code ◽  
Phase Errors ◽  
Stochastic Errors ◽  
Stabilizer Code

AbstractCoherent errors, which arise from collective couplings, are a dominant form of noise in many realistic quantum systems, and are more damaging than oft considered stochastic errors. Here, we propose integrating stabilizer codes with constant-excitation codes by code concatenation. Namely, by concatenating an [[n, k, d]] stabilizer outer code with dual-rail inner codes, we obtain a [[2n, k, d]] constant-excitation code immune from coherent phase errors and also equivalent to a Pauli-rotated stabilizer code. When the stabilizer outer code is fault-tolerant, the constant-excitation code has a positive fault-tolerant threshold against stochastic errors. Setting the outer code as a four-qubit amplitude damping code yields an eight-qubit constant-excitation code that corrects a single amplitude damping error, and we analyze this code’s potential as a quantum memory.

scholarly journals Fundamental limitations on distillation of quantum channel resources

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Bartosz Regula ◽  
Ryuji Takagi
Keyword(s):  
Lower Bounds ◽  
Quantum Channel ◽  
Quantum Communication ◽  
Fault Tolerant ◽  
State Of The Art ◽  
Quantum Systems ◽  
Noisy Channels ◽  
General Transformation ◽  
Fundamental Limitations ◽  
Strong Converse

AbstractQuantum channels underlie the dynamics of quantum systems, but in many practical settings it is the channels themselves that require processing. We establish universal limitations on the processing of both quantum states and channels, expressed in the form of no-go theorems and quantitative bounds for the manipulation of general quantum channel resources under the most general transformation protocols. Focusing on the class of distillation tasks — which can be understood either as the purification of noisy channels into unitary ones, or the extraction of state-based resources from channels — we develop fundamental restrictions on the error incurred in such transformations, and comprehensive lower bounds for the overhead of any distillation protocol. In the asymptotic setting, our results yield broadly applicable bounds for rates of distillation. We demonstrate our results through applications to fault-tolerant quantum computation, where we obtain state-of-the-art lower bounds for the overhead cost of magic state distillation, as well as to quantum communication, where we recover a number of strong converse bounds for quantum channel capacity.

Locality bounds on Hamiltonians for stabilizer codes

2009 ◽  
Vol 9 (5&6) ◽  
pp. 487-499
Author(s):  
S.S. Bullock ◽  
D.P. O'Leary
Keyword(s):  
Quantum Computing ◽  
Error Correction ◽  
Energy Gap ◽  
Stabilizer Codes ◽  
Adiabatic Quantum Computing ◽  
Group A ◽  
Stabilizer Code ◽  
Stabilizer Group ◽  
The Cost ◽  
Insight Into

In this paper, we study the complexity of Hamiltonians whose groundstate is a stabilizer code. We introduce various notions of $k$-locality of a stabilizer code, inherited from the associated stabilizer group. A choice of generators leads to a Hamiltonian with the code in its groundspace. We establish bounds on the locality of any other Hamiltonian whose groundspace contains such a code, whether or not its Pauli tensor summands commute. Our results provide insight into the cost of creating an energy gap for passive error correction and for adiabatic quantum computing. The results simplify in the cases of XZ-split codes such as Calderbank-Shor-Steane stabilizer codes and topologically-ordered stabilizer codes arising from surface cellulations.

scholarly journals Optical Quantum Memory and its Applications in Quantum Communication Systems

2020 ◽  
Vol 125 ◽  
Author(s):  
Lijun Ma ◽  
Oliver Slattery ◽  
Xiao Tang
Keyword(s):  
Communication Systems ◽  
Quantum Systems ◽  
Quantum Memory ◽  
Research Progress ◽  
Quantum Communications ◽  
Quantum Repeater ◽  
Quantum Networks ◽  
And Performance ◽  
The Impact ◽  
Photon Source

Optical quantum memory is a device that can store the quantum state of photons and retrieve it on demand and with high fidelity. It is emerging as an essential device to enhance security, speed, scalability, and performance of many quantum systems used in communications, computing, metrology, and more. In this paper, we will specifically consider the impact of optical quantum memory on quantum communications systems. Following a general overview of the theoretical and experimental research progress in optical quantum memory, we will outline its role in quantum communications, including as a photon source, photon interference, quantum key distribution (QKD), quantum teleportation, quantum repeater, and quantum networks.

scholarly journals Universal Fault-Tolerant Gates on Concatenated Stabilizer Codes

2016 ◽  
Vol 6 (3) ◽  
Author(s):  
Theodore J. Yoder ◽  
Ryuji Takagi ◽  
Isaac L. Chuang
Keyword(s):  
Fault Tolerant ◽  
Stabilizer Codes

scholarly journals Advanced exact synthesis of Clifford+T circuits

2020 ◽  
Vol 19 (9) ◽  
Author(s):  
Philipp Niemann ◽  
Robert Wille ◽  
Rolf Drechsler
Keyword(s):  
Large Scale ◽  
Fault Tolerant ◽  
Logic Synthesis ◽  
Research Problem ◽  
Quantum Systems ◽  
Quantum Circuits ◽  
Research Attention ◽  
Small Quantum ◽  
Significant Research ◽  
Important Research Problem

Abstract Quantum systems provide a new way of conducting computations based on the so-called qubits. Due to the potential for significant speed-ups, this field received significant research attention in recent years. The Clifford+T library is a very promising and popular gate library for these kinds of computations. Unlike other libraries considered so far, it consists of only a small number of gates for all of which robust, fault-tolerant realizations are known for many technologies that seem to be promising for large-scale quantum computing. As a consequence, (logic) synthesis of Clifford+T quantum circuits became an important research problem. However, previous work in this area has several drawbacks: Corresponding approaches are either only applicable to very small quantum systems or lead to circuits that are far from being optimal. The latter is mainly caused by the fact that current synthesis realizes the desired circuit by a local, i.e., column-wise, consideration of the underlying unitary transformation matrix to be synthesized. In this paper, we analyze the conceptual drawbacks of this approach and propose to overcome them by taking a global view of the matrices and perform a separation of concerns regarding individual synthesis steps. We precisely describe a corresponding algorithm as well as its efficient implementation on top of decision diagrams. Experimental results confirm the resulting benefits and show improvements of up to several orders of magnitudes in costs compared to previous work.

scholarly journals New Constructions of Quantum Stabilizer Codes Based on Difference Sets

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 655 ◽  
Author(s):  
Duc Nguyen ◽  
Sunghwan Kim
Keyword(s):  
Difference Sets ◽  
Combinatorial Design ◽  
Inner Product ◽  
Code Construction ◽  
Stabilizer Codes ◽  
Stabilizer Code ◽  
The Difference ◽  
Symplectic Inner Product ◽  
Quantum Stabilizer Code ◽  
Quantum Stabilizer Codes

In this paper, new conditions on parameters in difference sets are derived to satisfy symplectic inner product, and new constructions of quantum stabilizer codes are proposed from the conditions. The conversion of the difference sets into parity-check matrices is first explained. Then, the proposed code construction is composed of three steps, which are to choose the generators of quantum stabilizer code, to determine the quantum stabilizer groups, and to determine subspace codewords with large minimum distance. The quantum stabilizer codes with various length are also presented to explain the practicality of the code construction. The proposed design can be applied to quantum stabilizer code construction based on combinatorial design.

Scheme for fault-tolerant holonomic computation on stabilizer codes

2009 ◽  
Vol 80 (2) ◽  
Author(s):  
Ognyan Oreshkov ◽  
Todd A. Brun ◽  
Daniel A. Lidar
Keyword(s):  
Fault Tolerant ◽  
Stabilizer Codes

scholarly journals On subsystem codes beating the quantum Hamming or Singleton bound

2007 ◽  
Vol 463 (2087) ◽  
pp. 2887-2905 ◽  
Author(s):  
Andreas Klappenecker ◽  
Pradeep Kiran Sarvepalli
Keyword(s):  
The Other ◽  
Maximum Distance ◽  
Open Problems ◽  
Prime Field ◽  
Stabilizer Codes ◽  
Singleton Bound ◽  
Other Hand ◽  
Maximum Distance Separable ◽  
Linear Subsystem ◽  
Stabilizer Code

Subsystem codes are a generalization of noiseless subsystems, decoherence-free subspaces and stabilizer codes. We generalize the quantum Singleton bound to q -linear subsystem codes. It follows that no subsystem code over a prime field can beat the quantum Singleton bound. On the other hand, we show the remarkable fact that there exist impure subsystem codes beating the quantum Hamming bound. A number of open problems concern the comparison in the performance of stabilizer and subsystem codes. One of the open problems suggested by Poulin's work asks whether a subsystem code can use fewer syndrome measurements than an optimal q -linear maximum distance separable stabilizer code while encoding the same number of qudits and having the same distance. We prove that linear subsystem codes cannot offer such an improvement under complete decoding.

scholarly journals Optical Quantum Memory and its Applications in Quantum Communication Systems

2019 ◽  
Vol 124 ◽  
Author(s):  
Lijun Ma ◽  
Oliver Slattery ◽  
Xiao Tang
Keyword(s):  
Communication Systems ◽  
Quantum Systems ◽  
Quantum Memory ◽  
Research Progress ◽  
Quantum Communications ◽  
Quantum Repeater ◽  
Quantum Networks ◽  
And Performance ◽  
The Impact ◽  
Photon Source

Optical quantum memory is a device that can store the quantum state of photons and retrieve it on demand and with high fidelity. It is emerging as an essential device to enhance security, speed, scalability, and performance of many quantum systems used in communications, computing, metrology, and more. In this paper, we will specifically consider the impact of optical quantum memory on quantum communications systems. Following a general overview of the theoretical and experimental research progress in optical quantum memory, we will outline its role in quantum communications, including as a photon source, photon interference, quantum key distribution (QKD), quantum teleportation, quantum repeater, and quantum networks.

scholarly journals C_3, semi-Clifford and genralized semi-Clifford operations

2010 ◽  
Vol 10 (1&2) ◽  
pp. 41-59
Author(s):  
S. Beigi ◽  
P.W. Shor
Keyword(s):  
Quantum Computation ◽  
Basic Problem ◽  
Fault Tolerant ◽  
Quantum Codes ◽  
Stabilizer Codes

Fault-tolerant quantum computation is a basic problem in quantum computation, and teleportation is one of the main techniques in this theory. Using teleportation on stabilizer codes, the most well-known quantum codes, Pauli gates and Clifford operators can be applied fault-tolerantly. Indeed, this technique can be generalized for an extended set of gates, the so called ${\mathcal{C}}_k$ hierarchy gates, introduced by Gottesman and Chuang (Nature, 402, 390-392). ${\mathcal{C}}_k$ gates are a generalization of Clifford operators, but our knowledge of these sets is not as rich as our knowledge of Clifford gates. Zeng et al. in (Phys. Rev. A 77, 042313) raise the question of the relation between ${\mathcal{C}}_k$ hierarchy and the set of semi-Clifford and generalized semi-Clifford operators. They conjecture that any ${\mathcal{C}}_k$ gate is a generalized semi-Clifford operator. In this paper, we prove this conjecture for $k=3$. Using the techniques that we develop, we obtain more insight on how to characterize ${\mathcal{C}}_3$ gates. Indeed, the more we understand ${\mathcal{C}}_3$, the more intuition we have on ${\mathcal{C}}_k$, $k\geq 4$, and then we have a way of attacking the conjecture for larger $k$.

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