arXiv subjects

Diego Ruiz

Publications and source records attributed to Diego Ruiz.

9 recordsLinked to original sources

arXiv2026

Biased-noise qubits: a guide to efficient fault-tolerance using the hierarchy of errors

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.

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arXiv2026

Quantum non-demolition measurements as a practical primitive for fault-tolerant computation against biased noise

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 $\sim\!1.25\%$ and provides a qubit overhead reduction of up to $6\times$ compared to a bias-unaware surface code at noise bias $\eta = 10^4$. In the regime of very large bias, a repetition code with QND $Z$ measurements attains a threshold of $\sim\!2.3\%$ 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.

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arXiv2026

Elevator Codes: Concatenation for resource-efficient quantum memory under biased noise

Biased-noise qubits, in which one type of error (e.g. $X$- and $Y$-type errors) is significantly suppressed relative to the other (e.g. $Z$-type errors), can significantly reduce the overhead of quantum error correction. Codes such as the rectangular surface code or XZZX code substantially reduce the qubit overhead under biased noise, but they still face challenges. The rectangular surface code suffers from a relatively low threshold, while the XZZX code requires twice as many physical qubits to maintain the same code distance as the surface code. In this work, we introduce a 2D local code construction that outperforms these codes for noise biases $\eta \ge 7\times10^{4}$, reducing the qubit overhead by over 50% at $p_Z=10^{-3}$ and $\eta = 2 \times 10^6$ to achieve a logical error rate of $10^{-12}$. Our construction relies on the concatenation of two classical codes. The inner codes are repetition phase-flip codes while the outer codes are high-rate bit-flip codes enabled by their implementation at the logical level, which circumvents device connectivity constraints. These results indicate that under sufficiently biased noise, it is advantageous to address phase-flip and bit-flip errors at different layers of the coding scheme. The inner code should prioritize a high threshold for phase-flip errors, while the bit-flip outer code should optimize for encoding rate efficiency. In the strong biased-noise regime, high-rate outer codes keep the overhead for correcting residual bit-flip errors comparable to that of the repetition code itself, meaningfully lower than that required by earlier approaches.

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arXiv2025

Unfolded distillation: very low-cost magic state preparation for biased-noise qubits

Magic state distillation enables universal fault-tolerant quantum computation by implementing non-Clifford gates via the preparation of high-fidelity magic states. However, it comes at the cost of substantial logical-level overhead in both space and time. In this work, we propose a very low-cost magic state distillation scheme for biased-noise qubits. By leveraging the noise bias, our scheme enables the preparation of a magic state with a logical error rate of $3 \times 10^{-7}$, using only 53 qubits and 5.5 error correction rounds, under a noise bias of $\eta \gtrsim 5 \times 10^6$ and a phase-flip noise rate of $0.1\%$. This reduces the circuit volume by more than one order of magnitude relative to magic state cultivation for unbiased-noise qubits and by more than two orders of magnitude relative to standard magic state distillation. Moreover, our scheme provides three key advantages over previous proposals for biased-noise qubits. First, it only requires nearest-neighbor two-qubit gates on a 2D lattice. Second, the logical fidelity remains nearly identical even at a more modest noise bias of $\eta \gtrsim 80$, at the cost of a slightly increased circuit volume. Third, the scheme remains effective even at high physical phase-flip rates, in contrast to previously proposed approaches whose circuit volume grows exponentially with the error rate. Our construction is based on unfolding the $X$ stabilizer group of the Hadamard 3D quantum Reed-Muller code in 2D, enabling distillation at the physical level rather than the logical level, and is therefore referred to as $\textit{unfolded}$ distillation.

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arXiv2025

Enhancing dissipative cat qubit protection by squeezing

Dissipative cat-qubits are a promising architecture for quantum processors due to their built-in quantum error correction. By leveraging two-photon stabilization, they achieve an exponentially suppressed bit-flip error rate as the distance in phase-space between their basis states increases, incurring only a linear increase in phase-flip rate. This property substantially reduces the number of qubits required for fault-tolerant quantum computation. Here, we implement a squeezing deformation of the cat qubit basis states, further extending the bit-flip time while minimally affecting the phase-flip rate. We demonstrate a steep reduction in the bit-flip error rate with increasing mean photon number, characterized by a scaling exponent $γ=4.3$, rising by a factor of 74 per added photon. Specifically, we measure bit-flip times of 22 seconds for a phase-flip time of 1.3 $μ$s in a squeezed cat qubit with an average photon number $\bar{n}=4.1$, a 160-fold improvement in bit-flip time compared to a standard cat. Moreover, we demonstrate a two-fold reduction in $Z$-gate infidelity, with an estimated phase-flip probability of $ε_X = 0.085$ and a bit-flip probability of $ε_Z = 2.65 \cdot 10^{-9}$ which confirms the gate bias-preserving property. This simple yet effective technique enhances cat qubit performances without requiring design modification, moving multi-cat architectures closer to fault-tolerant quantum computation.

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arXiv2024

LDPC-cat codes for low-overhead quantum computing in 2D

Quantum low-density parity-check (qLDPC) codes are a promising construction for drastically reducing the overhead of fault-tolerant quantum computing (FTQC) architectures. However, all of the known hardware implementations of these codes require advanced technologies, such as long-range qubit connectivity, high-weight stabilizers, or multi-layered chip layouts. An alternative approach to reduce the hardware overhead of fault-tolerance is to use bosonic cat qubits where bit-flip errors are exponentially suppressed by design. In this work, we combine both approaches and propose an architecture based on cat qubits concatenated in classical LDPC codes correcting for phase-flips. We find that employing such phase-flip LDPC codes provides two major advantages. First, the hardware implementation of the code can be realised using short-range qubit interactions in 2D and low-weight stabilizers, which makes it readily compatible with current superconducting circuit technologies. Second, we demonstrate how to implement a fault-tolerant universal set of logical gates with a second layer of cat qubits while maintaining the local connectivity. We conduct a numerical brute force optimisation of these classical codes to find the ones with the best encoding rate for algorithmically relevant code distances. We discover that some of the best codes benefit from a cellular automaton structure. This allows us to define families of codes with high encoding rates and distances. Finally, we numerically assess the performance of our codes under circuit-level noise. Assuming a physical phase-flip error probability $ε\approx 0.1\%$, our $[165+8\ell, 34+2\ell, 22]$ code family allows to encode $100$ logical qubits with a total logical error probability (including both logical phase-flip and bit-flip) per cycle and per logical qubit $ε_L \leq 10^{-8}$ on a $758$ cat qubit chip.

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arXiv2023

Performance Analysis of a Repetition Cat Code Architecture: Computing 256-bit Elliptic Curve Logarithm in 9 Hours with 126133 Cat Qubits

Cat qubits provide appealing building blocks for quantum computing. They exhibit a tunable noise bias yielding an exponential suppression of bit flips with the average photon number and a protection against the remaining phase errors can be ensured by a simple repetition code. We here quantify the cost of a repetition code and provide valuable guidance for the choice of a large scale architecture using cat qubits by realizing a performance analysis based on the computation of discrete logarithms on an elliptic curve with Shor's algorithm. By focusing on a 2D grid of cat qubits with neighboring connectivity, we propose to implement 2-qubit gates via lattice surgery and Toffoli gates with off-line fault-tolerant preparation of magic states through projective measurements and subsequent gate teleportations. All-to-all connectivity between logical qubits is ensured by routing qubits. Assuming a ratio between single- and two-photon losses of 1e-5 and a cycle time of 500 ns, we show concretely that such an architecture can compute a 256-bit elliptic curve logarithm in 9 h with 126133 cat qubits and on average 19 photons by cat state. We give the details of the realization of Shor's algorithm so that the proposed performance analysis can be easily reused to guide the choice of architecture for others platforms.

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arXiv2023

Two-photon driven Kerr quantum oscillator with multiple spectral degeneracies

Kerr nonlinear oscillators driven by a two-photon process are promising systems to encode quantum information and to ensure a hardware-efficient scaling towards fault-tolerant quantum computation. In this paper, we show that an extra control parameter, the detuning of the two-photon drive with respect to the oscillator resonance, plays a crucial role in the properties of the defined qubit. At specific values of this detuning, we benefit from strong symmetries in the system, leading to multiple degeneracies in the spectrum of the effective confinement Hamiltonian. Overall, these degeneracies lead to a stronger suppression of bit-flip errors. We also study the combination of such Hamiltonian confinement with colored dissipation to suppress leakage outside of the bosonic code space. We show that the additional degeneracies allow us to perform fast and high-fidelity gates while preserving a strong suppression of bit-flip errors.

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arXiv2016

Construction of Bh[g] sets in product of groups

A subset A of an abelian group G is a Bh[g] set on G if every element of G can be written at most g ways as sum of h elements in A. In this work we present three constructions of Bh[g] sets on product of groups.

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