Abstract In this theoretical study, we explore the use of quantum code-based memories to enhance the lifetime of qubits and exceed the break-even point, which is critical for the implementation of fault-tolerant quantum computing. Specifically, we investigate the quantum phase-flip repetition code as a quantum memory and theoretically demonstrate that it can preserve arbitrary quantum information longer than the lifetime of a single idle qubit in a dephasing-time-limited system, e.g. in semiconductor qubits. Our circuit-based analytical calculations show the efficiency of the phase-flip code as a quantum memory in the presence of relaxation, dephasing, and faulty quantum gates. Moreover, we identify the optimal repetition number of quantum error correction cycles required to reach the break-even point by considering the gate error probabilities of current platforms for quantum computing. Our results provide guidelines for developing quantum memories in semiconductor quantum devices.
ABSTRACT Q uantum mechanics can revolutionize the art of code-making by breaking standard encryption schemes and by making unbreakable codes. In this document, I survey the motivation, power and limitation of quantum code-making. * Keywords: Quantum computing, quantum information, quantum cryptography, security, key distribution,cryptography 1. INTRODUCTION Human desire to keep written messages secret is almost as old as writing itself. Indeed, cryptography—the artof code-making—dated back to the Babylonians. For thousands of years, code-makers and code-breakers have engaged in an escalating arms race with each other.' Cryptographers do not sleep well. Every innovation in code-making has so far been defeated by new innovation in code-breaking with disastrous consequence tothe unsuspecting users of those insecure codes. For instance, Queen Mary of Scotland was executed by QueenElizabeth following the decoding of encrypted communications between Queen Mary and her conspirators whichprovided the irrefutable proof of her quilt in plotting against Queen Elizabeth. In the Second World War, thebreaking of the legendary German Engima code by the Allied code-breakers contributed significantly to theoutcome of the war. In cryptography, one must expect the unexpected and even the unthinkable.Q uantum mechanics has made a recent entry in this life and death struggle between code-makers and code-23 In this document, I will address the following frequently asked questions:(1) What quantum code-breaking can do?(2) What quantum code-making can do?(3) What quantum code-making cannot do?
A fully fault-tolerant implementation of the quantum error-detecting Iceberg
[[2m,2m−2,2]] code applied to a Toffoli circuit achieved beyond-break-even error detection on a leading trapped-ion quantum computer, where the effect of encoding a circuit with a quantum error-detection code enables increased fidelity compared to an unencoded circuit. This code was also applied to Bell state preparation circuits, where a lean non-fault-tolerant implementation of the Iceberg code enables a fidelity gain as well. This highlights the important point that, at least for small-scale circuits with a substantial portion of error-free runs, it can be effective simply to use error detection to filter out the runs with errors. Furthermore, experiments performed in this work highlight the necessity for judicious compilation of circuits not only for a given hardware but also within a quantum error detection code.
Recent experimental progress in realizing surface code on hardware, including demonstrations of break-even logical memory on devices with up to hundreds of physical qubits, has materially advanced the prospects for fault-tolerant quantum computation. This progress creates urgency for the development of compilation workflows that directly target the forthcoming generation of devices with thousands of physical qubits, for which algorithm execution becomes practical. We develop a pipeline for compiling logical algorithms to physical circuits implementing lattice surgery on the surface code, and use this pipeline to identify the requirements for achieving algorithmic break-even -- where quantum error correction improves the performance of a quantum algorithm -- for two prominent quantum algorithms: the quantum approximate optimization algorithm (QAOA) and quantum phase estimation (QPE). Our pipeline integrates several open-source software tools, and leverages recent advances in error-aware unitary gate synthesis, high-fidelity magic state production, and the calculation of correlation surfaces in the surface code. We perform classical simulations of physical Clifford proxy circuits produced by our pipeline, and find that both 5-qubit QAOA and QPE can reach algorithmic break-even with 2517 physical qubits (surface code distance
d=11) at physical error rates of
p=10−3, or 1737 physical qubits (
d=9) at
p=5×10−4. Our work thereby identifies conditions for achieving algorithmic break-even with near-term quantum hardware and paves the way towards an end-to-end compiler for early-fault-tolerant surface code architectures.