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Register a new userDistributed Quantum Computing Utilizing Multiple Codes on Imperfect Hardware
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Authors
Shota Nagayama
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Quantum bits have technological imperfections. Additionally, the capacity of a component that can be implemented feasibly is limited. Therefore, distributed quantum computation is required to scale up quantum computers. This dissertation presents a new quantum computer architecture which takes into account imperfections, aimed to realize distributed computation by connecting quantum computers each of which consists of multiple quantum CPUs and memories. Quantum CPUs employ a quantum error correcting code which has faster logical gates and quantum memories employ a code which is superior in space resource requirements. This dissertation focuses on quantum error correcting codes, giving a practical, concrete method for tolerating static losses such as faulty devices for the surface code. Numerical simulation with practical assumptions showed that a yield of functional qubits of 90% is marginally capable of building large-scale systems, by culling the poorer 50% of lattices during post-fabrication testing. Yield 80% is not usable even when culling 90% of generated lattices. For internal connections in a quantum computer and for connections between quantum computers, this dissertation gives a fault-tolerant method that bridges heterogeneous quantum error correcting codes. Numerical simulation showed that the scheme, which discards any quantum state in which any error is detected, always achieves an adequate logical error rate regardless of physical error rates in exchange for increased resource consumption. This dissertation gives a new extension of the surface code suitable for memories. This code is shown to require fewer physical qubits to encode a logical qubit than conventional codes. This code achieves the reduction of 50% physical qubits per a logical qubit. Collectively, the elements to propose the distributed quantum computer architecture are brought together.
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We describe the hardware, gateware, and software developed at Raytheon BBN Technologies for dynamic quantum information processing experiments on superconducting qubits. In dynamic experiments, real-time qubit state information is fedback or fedforward within a fraction of the qubits coherence time to dynamically change the implemented sequence. The hardware presented here covers both control and readout of superconducting qubits. For readout we created a custom signal processing gateware and software stack on commercial hardware to convert pulses in a heterodyne receiver into qubit state assignments with minimal latency, alongside data taking capability. For control, we developed custom hardware with gateware and software for pulse sequencing and steering information distribution that is capable of arbitrary control flow on a fraction superconducting qubit coherence times. Both readout and control platforms make extensive use of FPGAs to enable tailored qubit control systems in a reconfigurable fabric suitable for iterative development.
Bosonic rotation codes, introduced here, are a broad class of bosonic error-correcting codes based on phase-space rotation symmetry. We present a universal quantum computing scheme applicable to a subset of this class--number-phase codes--which includes the well-known cat and binomial codes, among many others. The entangling gate in our scheme is code-agnostic and can be used to interface different rotation-symmetric encodings. In addition to a universal set of operations, we propose a teleportation-based error correction scheme that allows recoveries to be tracked entirely in software. Focusing on cat and binomial codes as examples, we compute average gate fidelities for error correction under simultaneous loss and dephasing noise and show numerically that the error-correction scheme is close to optimal for error-free ancillae and ideal measurements. Finally, we present a scheme for fault-tolerant, universal quantum computing based on concatenation of number-phase codes and Bacon-Shor subsystem codes.
Extensive quantum error correction is necessary in order to scale quantum hardware to the regime of practical applications. As a result, a significant amount of decoding hardware is necessary to process the colossal amount of data required to constantly detect and correct errors occurring over the millions of physical qubits driving the computation. The implementation of a recent highly optimized version of Shors algorithm to factor a 2,048-bits integer would require more 7 TBit/s of bandwidth for the sole purpose of quantum error correction and up to 20,000 decoding units. To reduce the decoding hardware requirements, we propose a fault-tolerant quantum computing architecture based on surface codes with a cheap hard-decision decoder, the lazy decoder, combined with a sophisticated decoding unit that takes care of complex error configurations. Our design drops the decoding hardware requirements by several orders of magnitude assuming that good enough qubits are provided. Given qubits and quantum gates with a physical error rate $p=10^{-4}$, the lazy decoder drops both the bandwidth requirements and the number of decoding units by a factor 50x. Provided very good qubits with error rate $p=10^{-5}$, we obtain a 1,500x reduction in bandwidth and decoding hardware thanks to the lazy decoder. Finally, the lazy decoder can be used as a decoder accelerator. Our simulations show a 10x speed-up of the Union-Find decoder and a 50x speed-up of the Minimum Weight Perfect Matching decoder.
As a variety of quantum computing models and platforms become available, methods for assessing and comparing the performance of these devices are of increasing interest and importance. Despite being built of the same fundamental computational unit, radically different approaches have emerged for characterizing the performance of qubits in gate-based and quantum annealing computers, limiting and complicating consistent cross-platform comparisons. To fill this gap, this work proposes a single-qubit protocol (Q-RBPN) for measuring some basic performance characteristics of individual qubits in both models of quantum computation. The proposed protocol scales to large quantum computers with thousands of qubits and provides insights into the distribution of qubit properties within a particular hardware device and across families of devices. The efficacy of the Q-RBPN protocol is demonstrated through the analysis of more than 300 gate-based qubits spanning eighteen machines and 2000 annealing-based qubits from one machine, revealing some unexpected differences in qubit performance. Overall, the proposed Q-RBPN protocol provides a new platform-agnostic tool for assessing the performance of a wide range of emerging quantum computing devices.
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Angela Sara Cacciapuoti
, Marcello Caleffi
, Francesco Tafuri andn Francesco Saverio Cataliotti
2018
The Quantum Internet is envisioned as the final stage of the quantum revolution, opening fundamentally new communications and computing capabilities, including the distributed quantum computing. But the Quantum Internet is governed by the laws of quantum mechanics. Phenomena with no counterpart in classical networks, such as no-cloning, quantum measurement, entanglement and teleporting, impose very challenging constraints for the network design. Specifically, classical network functionalities, ranging from error-control mechanisms to overhead-control strategies, are based on the assumption that classical information can be safely read and copied. But this assumption does not hold in the Quantum Internet. As a consequence, the design of the Quantum Internet requires a major network-paradigm shift to harness the quantum mechanics specificities. The goal of this work is to shed light on the challenges and the open problems of the Quantum Internet design. To this aim, we first introduce some basic knowledge of quantum mechanics, needed to understand the differences between a classical and a quantum network. Then, we introduce quantum teleportation as the key strategy for transmitting quantum information without physically transferring the particle that stores the quantum information or violating the principles of the quantum mechanics. Finally, the key research challenges to design quantum communication networks are described.
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