Related papers: Towards Minimal Fault-tolerant Error-Correction Se…
Building reliable quantum computers requires protecting fragile quantum states from inevitable environmental noise and operational errors. While quantum error correction codes like the Steane $[\![7,1,3]\!]$ code provide elegant theoretical…
We prove a new version of the quantum threshold theorem that applies to concatenation of a quantum code that corrects only one error, and we use this theorem to derive a rigorous lower bound on the quantum accuracy threshold epsilon_0. Our…
Recent work has deployed linear combinations of unitaries techniques to reduce the cost of fault-tolerant quantum simulations of correlated electron models. Here, we show that one can sometimes improve upon those results with optimized…
One of the most promising paths towards large scale fault tolerant quantum computation is the use of quantum error correcting stabilizer codes. Just like every other quantum circuit, these codes must be compiled to hardware in a way to…
To build a fault-tolerant quantum computer, it is necessary to implement a quantum error correcting code. Such codes rely on the ability to extract information about the quantum error syndrome while not destroying the quantum information…
Collective coherent noise poses challenges for fault-tolerant quantum error correction (FTQEC), as it falls outside the usual stochastic noise models. While constant excitation (CE) codes can naturally avoid coherent noise, a complete…
Quantum simulation of fermionic systems is a leading application of quantum computers. One promising approach is to represent fermions with qubits via fermion-to-qubit mappings. In this work, we present high-distance fermion-to-qubit…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
We present a quantum circuit synthesis algorithm for implementing universal fault-tolerant quantum computing based on concatenated codes. To realize fault-tolerant quantum computing, the fault-tolerant quantum protocols should be…
Proving threshold theorems for fault-tolerant quantum computation is a burdensome endeavor with many moving parts that come together in relatively formulaic but lengthy ways. It is difficult and rare to combine elements from multiple papers…
The traditional approach to fault tolerant computing involves replicating computation units and applying a majority vote operation on individual result bits. This approach, however, has several limitations; the most severe is the resource…
The stabilization of a quantum computer by repeated error correction can be reduced almost entirely to repeated preparation of blocks of qubits in quantum codeword states. These are multi-particle entangled states with a high degree of…
Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance of topological quantum codes by rotating the four dimensional…
A central goal in quantum error correction is to reduce the overhead of fault-tolerant quantum computing by increasing noise thresholds and reducing the number of physical qubits required to sustain a logical qubit. We introduce a potential…
We propose a fault-tolerant quantum error correction architecture consisting of a linear array of emitters and delay lines. In our scheme, a resource state for fault-tolerant quantum computation is generated by letting the emitters interact…
Given that quantum error correction processes are unreliable, an efficient error syndrome extraction circuit should use fewer ancillary qubits, quantum gates, and measurements, while maintaining low circuit depth, to minimizing the circuit…
We investigate the performance of error mitigation via measurement of conserved symmetries on near-term devices. We present two protocols to measure conserved symmetries during the bulk of an experiment, and develop a zero-cost…
With gate error rates in multiple technologies now below the threshold required for fault-tolerant quantum computation, the major remaining obstacle to useful quantum computation is scaling, a challenge greatly amplified by the huge…
The distance of a stabilizer quantum code is a very important feature since it determines the number of errors that can be detected and corrected. We present three new fast algorithms and implementations for computing the symplectic…
The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…