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 in such a channel, we propose bias-preserving implementation of S , H , controlled- Z (CZ), and R z gates. We demonstrate that our scheme improves the computational precision in several tasks such as the time evolution of quantum systems and variational quantum eigensolver. Published by the American Physical Society 2024
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 in such a channel, we propose bias-preserving implementation of S , H , controlled- Z (CZ), and R z gates. We demonstrate that our scheme improves the computational precision in several tasks such as the time evolution of quantum systems and variational quantum eigensolver. Published by the American Physical Society 2024
Qubits with strongly biased noise, in which phase-flip errors are orders of magnitude more frequent than bit-flips, arise both naturally, as in electron and nuclear spins, and by engineering, as in stabilized cat qubits. This noise structure holds the promise of reducing the daunting hardware overhead of fault-tolerant quantum computing, but exploiting it requires physical operations that do not convert frequent phase-flips into rare bit-flips. In this review, we analyze the most prominent fault-tolerant protocols for biased-noise qubits, organized according to the available set of such bias-preserving operations. When this set is restricted to the CZ gate together with preparation and measurement in the X basis, we show that the complexity of the required syndrome extraction gadgets essentially cancels the benefit of the noise bias: at experimentally relevant error rates, one may as well ignore the bias and rely on standard error correction designed for depolarizing noise. The situation changes drastically when a bias-preserving CX gate is available: the hierarchy of errors can then be reflected in the structure of the code, with frequent phase-flips corrected by a dedicated high-threshold code and rare bit-flips by concatenation with a high-rate code. The same hierarchy also enables hardware-efficient preparation of magic states. Finally, as a bias-preserving CX is forbidden in naturally biased platforms and challenging in engineered ones, we present a measurement-based architecture in which a high-fidelity quantum non-demolition readout of multi-qubit Pauli Z operators takes its place, extending these overhead reductions to a much broader range of physical platforms.
Quantum sensors hold great promise for achieving better sensitivity in the measurement of physical quantities compared to their classical counterparts. However, the conditions under which quantum advantage in sensing can be achieved are rather restrictive, and most quantum enhancements in sensing are lost in the presence of noise, errors, or a poorly calibrated system. To overcome these limitations, we are motivated to import ideas from fault-tolerant quantum computing to quantum sensing. Specifically, we consider a qubit noise model where the probability of phase-flip errors is exponentially smaller (in qubit number) compared to the probability of bit-flip errors that occur with probability p. For this noise structure, we demonstrate that, given a total sensing time T, Heisenberg scaling can be attained for times up to T∝1/p(N+1)/2 for a N-qubit repetition code, in contrast with T∝1/p without using a fault-tolerant sensing protocol.
We construct a fault-tolerant quantum error-correcting protocol based on a qubit encoded in a large spin qudit using a spin-cat code, analogous to the continuous-variable cat encoding. With this, we can correct the dominant error sources, namely processes that can be expressed as error operators that are linear or quadratic in the components of angular momentum. Such codes tailored to dominant error sources can exhibit superior thresholds and lower resource overheads when compared to those designed for unstructured noise models. A key component is the gate that preserves the rank of spherical tensor operators. Categorizing the dominant errors as phase and amplitude errors, we demonstrate how phase errors, analogous to phase-flip errors for qubits, can be effectively corrected. Furthermore, we propose a measurement-free error-correction scheme to address amplitude errors without relying on syndrome measurements. Through an in-depth analysis of logical gate errors, we establish that the fault-tolerant threshold for error correction in the spin-cat encoding surpasses that of standard qubit-based encodings. We consider a specific implementation based on neutral-atom quantum computing, with qudits encoded in the nuclear spin of 87 Sr , and show how to generate the universal gate set, including the rank-preserving gate, using quantum control and the Rydberg blockade. These findings pave the way for encoding a qubit in a large spin with the potential to achieve fault tolerance, high threshold, and reduced resource overhead in quantum information processing. Published by the American Physical Society 2024
We present a 1D repetition code based on the so-called cat qubits as a viable approach toward hardwareefficient universal and fault-tolerant quantum computation.The cat qubits that are stabilized by a twophoton driven-dissipative process exhibit a tunable noise bias where the effective bit-flip errors are exponentially suppressed with the average number of photons.We propose a realization of a set of gates on the cat qubits that preserve such a noise bias.Combining these base qubit operations, we build, at the level of the repetition cat qubit, a universal set of fully protected logical gates.This set includes single-qubit preparations and measurements, NOT, controlled-NOT, and controlled-controlled-NOT (Toffoli) gates.Remarkably, this construction avoids the costly magic state preparation, distillation, and injection.Finally, all required operations on the cat qubits could be performed with slight modifications of existing experimental setups.
Quantum computing offers powerful new techniques for speeding up the calculation of many classically intractable problems. Quantum algorithms can allow for the efficient simulation of physical systems, with applications to basic research, chemical modeling, and drug discovery; other algorithms have important implications for cryptography and internet security. At the same time, building a quantum computer is a daunting task, requiring the coherent manipulation of systems with many quantum degrees of freedom while preventing environmental noise from interacting too strongly with the system. Fortunately, we know that, under reasonable assumptions, we can use the techniques of quantum error correction and fault tolerance to achieve an arbitrary reduction in the noise level. In this thesis, we look at how additional information about the structure of noise, or "noise bias," can improve or alter the performance of techniques in quantum error correction and fault tolerance. In Chapter 2, we explore the possibility of designing certain quantum gates to be extremely robust with respect to errors in their operation. This naturally leads to structured noise where certain gates can be implemented in a protected manner, allowing the user to focus their protection on the noisier unprotected operations. In Chapter 3, we examine how to tailor error-correcting codes and fault-tolerant quantum circuits in the presence of dephasing biased noise, where dephasing errors are far more common than bit-flip errors. By using an appropriately asymmetric code, we demonstrate the ability to improve the amount of error reduction and decrease the physical resources required for error correction. In Chapter 4, we analyze a variety of protocols for distilling magic states, which enable universal quantum computation, in the presence of faulty Clifford operations. Here again there is a hierarchy of noise levels, with a fixed error rate for faulty gates, and a second rate for errors in the distilled states which decreases as the states are distilled to better quality. The interplay of of these different rates sets limits on the achievable distillation and how quickly states converge to that limit.
Leveraging noise bias, where phase-flip errors dominate over bit-flips, can drastically reduce the hardware overhead of fault-tolerant quantum computation, but existing approaches require bias-preserving CNOT gates whose implementation remains experimentally challenging and is provably impossible for strictly two-dimensional systems. We show that high-fidelity quantum non-demolition (QND) multi-qubit Pauli Z measurements provide an equally powerful yet more accessible primitive. We demonstrate that such measurements can fully replace bias-preserving CNOT gates for compiling all operations required by bias-tailored error correction, including stabilizer measurements for repetition codes, XZZX surface codes, and LDPC codes. We propose concrete physical implementations of this primitive for two platforms: solid-state nuclear spins coupled to electron spin ancillas, and dissipatively stabilized superconducting cat qubits. Through circuit-level numerical simulations, we show that an asymmetric XZZX surface code implemented with weight-four QND Z measurements achieves a phase-flip threshold of ∼1.25% and provides a qubit overhead reduction of up to 6× compared to a bias-unaware surface code at noise bias η=104. In the regime of very large bias, a repetition code with QND Z measurements attains a threshold of ∼2.3% and achieves overhead comparable to that of a bias-preserving CNOT scheme, without requiring such a gate. Our results establish QND multi-Z measurements as a practical and hardware-efficient route to fault-tolerant quantum computation for a broad class of biased-noise platforms.