We present a quantum error correction code which protects three quantum bits (qubits) of quantum information against one erasure, i.e., a single-qubit arbitrary error at a known position. To accomplish this, we encode the original state by distributing quantum information over six qubits which is the minimal number for the present task (see reference [1]). The encoding and error recovery operations for such a code are presented. It is noted that the present code is also a three-qubit quantum hidded information code over each qubit. In addition, an encoding scheme for hiding $n$-qubit quantum information over each qubit is proposed.
We consider two bottlenecks in quantum computing: limited memory size and noise caused by heat dissipation. Trying to optimize both, we investigate "on-the-go erasure" of quantum registers that are no longer needed for a given algorithm: freeing up auxiliary qubits as they stop being useful would facilitate the parallelization of computations. We study the minimal thermodynamic cost of erasure in these scenarios, applying results on the Landauer erasure of entangled quantum registers. For the class of algorithms solving the Abelian hidden subgroup problem, we find optimal on-the-go erasure pro…
The quantum erasure channel (QEC) is considered. Codes for the QEC have to correct for erasures, i. e., arbitrary errors at known positions. We show that four qubits are necessary and sufficient to encode one qubit and correct one erasure, in contrast to five qubits for unknown positions. Moreover, a family of quantum codes for the QEC, the quantum BCH codes, that can be efficiently decoded is introduced.
We consider state changes in quantum theory due to "conditional action" and relate these to the discussion of entropy decrease due to interventions of "intelligent beings" and the principles of Szilard and Landauer/Bennett. The mathematical theory of conditional actions is a special case of the theory of "instruments" which describes changes of state due to general measurements and will therefore be briefly outlined in the present paper. As a detailed example we consider the imperfect erasure of a qubit that can also be viewed as a conditional action and will be realized by the coupling of a s…
Erasure surface code circuit without mid-circuit erasure checks
Yale Quantum Institute, Yale University（耶鲁量子研究所，耶鲁大学）；Department of Applied Physics, Yale University（耶鲁大学应用物理系）；Department of Physics, University of Massachusetts, Amherst（马萨诸塞大学阿默斯特分校物理系）；Department of Physics, University of Toronto（多伦多大学物理系）
Unitary-accessible coherence-erasure distance: Exact qubit solution and a tight qutrit bound
Changchun University of Technology（长春工业大学）；Yanbian University（延边大学）；Capital Normal University（首都师范大学）；Max-Planck-Institute for Mathematics in the Sciences（马克斯·普朗克科学促进部数理研究所）
Classical and quantum error correction are presented in the form of Maxwell's demon and their efficiency analyzed from the thermodynamic point of view. We explain how Landauer's principle of information erasure applies to both cases. By then extending this principle to entanglement manipulations we rederive upper bounds on purification procedures thereby linking the ''no local increase of entanglement'' principle to the Second Law of thermodynamics.
Given a suitably large and well connected (complex) graph state, any quantum algorithm can be implemented purely through local measurements on the individual qubits. Measurements can also be used to create the graph state: Path erasure techniques allow one to entangle multiple qubits by determining only global properties of the qubits. Here, this powerful approach is extended by demonstrating that even imperfect path erasure can produce the required graph states with high efficiency. By characterizing the degree of error in each path erasure attempt, one can subsume the resulting imperfect ent…
By exploiting a generalization of recent results on environment-assisted channel correction, we show that, whenever a quantum system undergoes a channel realized as an interaction with a probe, the more efficiently the information about the input state can be erased from the probe, the higher is the corresponding entanglement fidelity of the corrected channel, and vice-versa. The present analysis applies also to channels for which perfect quantum erasure is impossible, thus extending the original quantum eraser arrangement, and naturally embodies a general information-disturbance tradeoff.
In complete erasure any arbitrary pure quantum state is transformed to a fixed pure state by irreversible operation. Here we ask if the process of partial erasure of quantum information is possible by general quantum operations, where partial erasure refers to reducing the dimension of the parameter space that specifies the quantum state. Here we prove that quantum information stored in qubits and qudits cannot be partially erased, even by irreversible operations. The no-flipping theorem, which rules out the existence of a universal NOT gate for an arbitrary qubit, emerges as a corollary to th…
Dynamically protected erasure qubit via low-frequency charge driving
University of California at Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Chapman University（查普曼大学）；University of Rochester（罗切斯特大学）
Logical qubits with erasure conversion using metastable neutral atoms
Princeton University（普林斯顿大学）；Peking University（北京大学）；University of California, Berkeley（加州大学伯克利分校）；The Hong Kong University of Science and Technology（香港科技大学）；Yale University（耶鲁大学）
Executing quantum algorithms on error-corrected logical qubits is a critical step for scalable quantum computing, but the requisite numbers of qubits and physical error rates are demanding for current experimental hardware. Recently, the development of error correcting codes tailored to particular physical noise models has helped relax these requirements. In this work, we propose a qubit encoding and gate protocol for ${}^{171}$Yb neutral atom qubits that converts the dominant physical errors into erasures, that is, errors in known locations. The key idea is to encode qubits in a metastable el…
Losses in quantum communication lines severely affect the rates of reliable information transmission and are usually considered to be state-independent. However, the loss probability does depend on the system state in general, with the polarization dependent losses being a prominent example. Here we analyze biased trace decreasing quantum operations that assign different loss probabilities to states and introduce the concept of a generalized erasure channel. We find lower and upper bounds for the classical and quantum capacities of the generalized erasure channel as well as characterize its de…
In practical applications of quantum information science, quantum systems can have non-negligible interactions with the environment, and this generally degrades the power of quantum protocols as it introduces noise. Counteracting this by appropriately measuring the environment (and therefore projecting its state) would require access all the necessary degrees of freedom, which in practice can be far too hard to achieve. To better understand one's limitations, we calculate the upper bound of optimal quantum erasure (i.e. the highest recoverable visibility, or "coherence"), when erasure is reali…
In this work, we introduce a new concatenation scheme which aims at protecting information against the occurrence of both computational errors and quantum erasures. According to our scheme, the internal code must be a quantum loss-correcting code that does not perform measurements, while the external code must be a quantum error-correcting code. We illustrate the concatenation proposed with an example in which one qubit of information is protected against the occurrence of two erasures and one computational error.
Hardware-efficient erasure-error detection with an integer fluxonium
Massachusetts Institute of Technology（麻省理工学院）；Lincoln Laboratory, Massachusetts Institute of Technology（麻省理工学院林肯实验室）；IBM Quantum, IBM Research Cambridge（IBM剑桥量子计算与研究中心）
Using an error models motivated by the Knill, Laflamme, Milburn proposal for efficient linear optics quantum computing [Nature 409,46--52, 2001], error rate thresholds for erasure errors caused by imperfect photon detectors using a 7 qubit code are derived and verified through simulation. A novel method -- based on a Markov chain description of the erasure correction procedure -- is developed and used to calculate the recursion relation describing the error rate at different encoding levels from which the threshold is derived, matching threshold predictions by Knill, Laflamme and Milburn [quan…
We present a scheme able to protect k >= 3 qubits of information against the occurrence of multiple erasures, based on the code proposed by Yang et al. (2004 JETP Letters 79 236). In this scheme redundant blocks are used and we restrict to the case that each erasure must occur in distinct blocks. We explicitly characterize the encoding operation and the restoring operation required to implement this scheme. The operators used in these operations can be adjusted to construct different quantum erasure-correcting codes. A special feature of this scheme is that no measurement is required. To illus…
We investigate the usage of highly efficient error correcting codes of multilevel systems to protect encoded quantum information from erasure errors and implementation to repetitively correct these errors. Our scheme makes use of quantum polynomial codes to encode quantum information and generalizes teleportation based error correction for multilevel systems to correct photon losses and operation errors in a fault-tolerant manner. We discuss the application of quantum polynomial codes to one-way quantum repeaters. For various types of operation errors, we identify different parameter regions w…
Using the deterministic, on-demand generation of two entangled phonons, we demonstrate a quantum eraser protocol in a phononic interferometer where the which-path information can be heralded during the interference process. Omitting the heralding step yields a clear interference pattern in the interfering half-quanta pathways; including the heralding step suppresses this pattern. If we erase the heralded information after the interference has been measured, the interference pattern is recovered, thereby implementing a delayed-choice quantum erasure. The test is implemented using a closed surfa…
Erasure is fundamental for information processing. It is also key in connecting information theory and thermodynamics, as it is a logically irreversible task. We provide a new angle on this connection, noting that there may be an additional cost to erasure, that is not captured by standard results such as Landauer's principle. To make this point we use a model of irreversibility based on Constructor Theory - a recently proposed generalization of the quantum theory of computation. The model uses a machine called the "quantum homogenizer", which has the ability to approximately realise the trans…
Investigating principles for storage of quantum information at finite temperature with minimal need for active error correction is an active area of research. We bear upon this question in two-dimensional holographic conformal field theories via the quantum null energy condition (QNEC) that we have shown earlier to implement the restrictions imposed by quantum thermodynamics on such many-body systems. We study an explicit encoding of a logical qubit into two similar chirally propagating excitations of finite von-Neumann entropy on a finite temperature background whose erasure can be implemente…
