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The strongly correlated systems we use to realise quantum error-correcting codes may give rise to high-weight, problematic errors. Encouragingly, we can expect local quantum error-correcting codes with no string-like logical operators $-$…
To implement fault-tolerant quantum computation (FTQC) with continuous variables, continuous variables need to be digitized using an appropriate code such as the Gottesman--Kitaev--Preskill (GKP) qubit. The scheme introduced in [K. Fukui…
We present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel. Our approach allows us to optimize the…
We construct a new error-suppression scheme that makes use of the adjoint of reversible quantum algorithms. For decoherence induced errors such as depolarization, it is presented that provided the depolarization error probability is less…
We demonstrate an improved concatenated encoded ancilla preparation procedure. Simulations show that this procedure significantly increases the error threshold beneath which arbitrarily long quantum computations are possible.
We analyze and study the effects of locality on the fault-tolerance threshold for quantum computation. We analytically estimate how the threshold will depend on a scale parameter r which estimates the scale-up in the size of the circuit due…
We show how to realize a general quantum circuit involving gates between arbitrary pairs of qubits by means of geometrically local quantum operations and efficient classical computation. We prove that circuit-level local stochastic noise…
Fault-tolerant quantum computation is a technique that is necessary to build a scalable quantum computer from noisy physical building blocks. Key for the implementation of fault-tolerant computations is the ability to perform a universal…
Quantum computational experiments exploiting Noisy Intermediate-Scale Quantum (NISQ) devices to demonstrate violation of a Bell inequality are proposed. They consist of running specified quantum algorithms on few-qubit computers. If such a…
We construct a pairwise measurement-based code on eight qubits that is error correcting for circuit noise, with fault distance 3. The code can be implemented on a subset of a rectangular array of qubits with nearest neighbor connectivity of…
Quantum error correction is an essential component for practical quantum computing on noisy quantum hardware. However, logical operations on error-corrected qubits require a significant resource overhead, especially for high-precision and…
A universal and fault tolerant scheme for quantum computation is proposed which utilizes a class of error correcting codes that is based on the detection of spontaneous emission (of, e.g., photons, phonons, and ripplons). The scheme is…
Fault tolerance is widely regarded as indispensable for achieving scalable and reliable quantum computing. However, the spacetime overhead required for fault-tolerant quantum computating remains prohibitively large. A critical challenge…
Quantum computing hardware is affected by quantum noise that undermine the quality of results of an executed quantum program. Amongst other quantum noises, coherent error that caused by parameter drifting and miscalibration, remains…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
Many current quantum error-correcting codes that achieve full fault tolerance suffer from having low ratios of logical to physical qubits and significant overhead. This makes them difficult to implement on current noisy intermediate-scale…
Current hardware for quantum computing suffers from high levels of noise, and so to achieve practical fault-tolerant quantum computing will require powerful and efficient methods to correct for errors in quantum circuits. Here, we explore…
As techniques for fault-tolerant quantum computation keep improving, it is natural to ask: what is the fundamental lower bound on redundancy? In this paper, we obtain a lower bound on the redundancy required for $\epsilon$-accurate…
We explore the feasibility of fault-tolerant quantum computation using the bit-flip repetition code in a biased noise channel where only the bit-flip error can occur. While several logic gates can potentially produce phase-flip errors even…
Quantum error detection can produce unbiased expectation values that exponentially converge to noiseless results as the code distance is increased. Despite this, its performance as an error mitigation technique is relatively understudied on…