Measurement-free fault-tolerant quantum error correction in near-term devices

Logical qubits can be protected from decoherence by performing QEC cycles repeatedly. Algorithms for fault-tolerant QEC must be compiled to the specific hardware platform under consideration in order to practically realize a quantum memory that operates for in principle arbitrary long times. All circuit components must be assumed as noisy unless specific assumptions about the form of the noise are made. Modern QEC schemes are challenging to implement experimentally in physical architectures where in-sequence measurements and feed-forward of classical information cannot be reliably executed fast enough or even at all. Here we provide a novel scheme to perform QEC cycles without the need of measuring qubits that is fully fault-tolerant with respect to all components used in the circuit. Our scheme can be used for any low-distance CSS code since its only requirement towards the underlying code is a transversal CNOT gate. Similarly to Steane-type EC, we coherently copy errors to a logical auxiliary qubit but then apply a coherent feedback operation from the auxiliary system to the logical data qubit. The logical auxiliary qubit is prepared fault-tolerantly without measurements, too. We benchmark logical failure rates of the scheme in comparison to a flag-qubit based EC cycle. We map out a parameter region where our scheme is feasible and estimate physical error rates necessary to achieve the break-even point of beneficial QEC with our scheme. We outline how our scheme could be implemented in ion traps and with neutral atoms in a tweezer array. For recently demonstrated capabilities of atom shuttling and native multi-atom Rydberg gates, we achieve moderate circuit depths and beneficial performance of our scheme while not breaking fault tolerance. These results thereby enable practical fault-tolerant QEC in hardware architectures that do not support mid-circuit measurements.Comment: 24 pages, 19 figure

Dynamical subset sampling of quantum error correcting protocols

Quantum error correcting (QEC) stabilizer codes enable protection of quantum information against errors during storage and processing. Simulation of noisy QEC codes is used to identify the noise parameters necessary for advantageous operation of logical qubits in realistic quantum computing architectures. Typical quantum error correction techniques contain intermediate measurements and classical feedback that determine the actual noisy circuit sequence in an instance of performing the protocol. Dynamical subset sampling enables efficient simulation of such non-deterministic quantum error correcting protocols for any type of quantum circuit and incoherent noise of low strength. As an importance sampling technique, dynamical subset sampling allows one to effectively make use of computational resources to only sample the most relevant sequences of quantum circuits in order to estimate a protocol's logical failure rate with well-defined error bars. We demonstrate the capabilities of dynamical subset sampling with examples from fault-tolerant (FT) QEC. We show that, in a typical stabilizer simulation with incoherent Pauli noise of strength $p = 10^{-3}$, our method can reach a required sampling accuracy on the logical failure rate with two orders of magnitude fewer samples than direct Monte Carlo simulation. Furthermore, dynamical subset sampling naturally allows for efficient simulation of realistic multi-parameter noise models describing faulty quantum processors. It can be applied not only for QEC in the circuit model but any noisy quantum computing framework with incoherent fault operators including measurement-based quantum computation and quantum networks.Comment: 33 pages, 26 figure

Not Available

Not AvailableThe effect of different concentrations of GA (0, 10, 20 and 30 ppm) and ethephon (0, 1000, 2000 and 3000 ppm) combinations on vegetative growth, bulb size and yield of onion were studied. The results show that GaEo treatment combination (30 ppm GA + o ppm ethephon) produced maximum plant height (61.42 ern). number of leaves per plant (10.8); diameter of bulb at neck (1.62 cm) and the average of bolted plants (3.0), over all other treatment combinations. The same treatment combination significantly, increased the fresh weight of bulb (106.2g) cured weight (79.12g) diameter of bulb (5.52 cm) diameter of bulb at neck (0.91 cm) and yield 6.17 kg/plot (205.9 q/rta) over all other treatments. Whereas, ethephon separately or in combination with GA significantly reduced vegetative growth and yield characters.Not Availabl

Strategies for a practical advantage of fault-tolerant circuit design in noisy trapped-ion quantum computers

Fault-tolerant quantum error correction provides a strategy to protect information processed by aquantum computer against noise which would otherwise corrupt the data. A fault-tolerant universalquantum computer must implement a universal gate set on the logical level in order to perform arbi-trary calculations to in principle unlimited precision. In this manuscript, we characterize the recentdemonstration of a fault-tolerant universal gate set in a trapped-ion quantum computer [Postler etal. Nature 605.7911 (2022)] and identify aspects to improve the design of experimental setups toreach an advantage of logical over physical qubit operation. We show that various criteria to assessthe break-even point for fault-tolerant quantum operations are within reach for the ion trap quan-tum computing architecture under consideration. Furthermore, we analyze the influence of crosstalkin entangling gates for logical state preparation circuits. These circuits can be designed to respectfault tolerance for specific microscopic noise models. We find that an experimentally-informed de-polarizing noise model captures the essential noise dynamics of the fault-tolerant experiment thatwe consider, and crosstalk is negligible in the currently accessible regime of physical error rates. Fordeterministic Pauli state preparation, we provide a fault-tolerant unitary logical qubit initializationcircuit, which can be realized without in-sequence measurement and feed-forward of classical infor-mation. Additionally, we show that non-deterministic state preparation schemes, i.e. repeat untilsuccess, for logical Pauli and magic states perform with higher logical fidelity over their deterministiccounterparts for the current and anticipated future regime of physical error rates. Our results offerguidance on improvements of physical qubit operations and validate the experimentally-informednoise model as a tool to predict logical failure rates in quantum computing architectures based ontrapped ions

Demonstration of fault-tolerant universal quantum gate operations

Quantum computers can be protected from noise by encoding the logical quantum information redundantly into multiple qubits using error correcting codes. When manipulating the logical quantum states, it is imperative that errors caused by imperfect operations do not spread uncontrollably through the quantum register. This requires that all operations on the quantum register obey a fault-tolerant circuit design which, in general, increases the complexity of the implementation. Here, we demonstrate a fault-tolerant universal set of gates on two logical qubits in a trapped-ion quantum computer. In particular, we make use of the recently introduced paradigm of flag fault tolerance, where the absence or presence of dangerous errors is heralded by usage of few ancillary 'flag' qubits. We perform a logical two-qubit CNOT-gate between two instances of the seven qubit color code, and we also fault-tolerantly prepare a logical magic state. We then realize a fault-tolerant logical T-gate by injecting the magic state via teleportation from one logical qubit onto the other. We observe the hallmark feature of fault tolerance, a superior performance compared to a non-fault-tolerant implementation. In combination with recently demonstrated repeated quantum error correction cycles these results open the door to error-corrected universal quantum computation.Comment: v3 with updated acknowledgements, 14 pages, 7 figure