arXiv subjects

Theerapat Tansuwannont

Publications and source records attributed to Theerapat Tansuwannont.

13 recordsLinked to original sources

arXiv2026

Clifford gates with logical transversality for self-dual CSS codes

Quantum error-correcting codes with high encoding rate are good candidates for large-scale quantum computers as they use physical qubits more efficiently than codes of the same distance that encode only a few logical qubits. Some logical gate of a high-rate code can be fault-tolerantly implemented using transversal physical gates, but its logical operation may depend on the choice of a symplectic basis that defines logical Pauli operators of the code. In this work, we focus on $[\![n,k,d]\!]$ self-dual Calderbank-Shor-Steane (CSS) codes with $k \geq 1$ and prove necessary and sufficient conditions for the code to have a symplectic basis such that (1) transversal logical Hadamard gates $\bigotimes_{j=1}^{k} \bar{H}_j$ can be implemented by transversal physical Hadamard gates $\bigotimes_{i=1}^{n} H_i$, and (2) for any $(a_1,\dots,a_k)\in\{-1,1\}^k$, transversal logical phase gates $\bigotimes_{j=1}^{k} \bar{S}_j^{a_j}$ can be implemented by transversal physical phase gates $\bigotimes_{i=1}^{n} S_i^{b_i}$ for some $(b_1,\dots,b_n)\in\{-1,1\}^n$. Self-dual CSS codes satisfying the conditions include any codes with odd $n$. We also generalize the idea to concatenated self-dual CSS codes and show that certain logical Clifford gates have multiple transversal implementations, each by logical gates at a different level of concatenation. Several applications of our results for fault-tolerant quantum computation with low overhead are also provided.

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arXiv2026

Construction of the full logical Clifford group for high-rate quantum Reed-Muller codes using only transversal and fold-transversal gates

To build large-scale quantum computers while minimizing resource requirements, one may want to use high-rate quantum error-correcting codes that can efficiently encode information. However, realizing an addressable gate$\unicode{x2014}$a logical gate on a subset of logical qubits within a high-rate code$\unicode{x2014}$in a fault-tolerant manner can be challenging and may require ancilla qubits. Transversal and fold-transversal gates could provide a means to fault-tolerantly implement logical gates using a constant-depth circuit without ancilla qubits, but available gates of these types could be limited depending on the code and might not be addressable. In this work, we study a family of $[\![n=2^m,k={m \choose m/2}\approx n/\sqrt{π\log_2(n)/2},d=2^{m/2}=\sqrt{n}]\!]$ self-dual quantum Reed$\unicode{x2013}$Muller codes, where $m$ is a positive even number. For any code in this family, we construct a generating set of the full logical Clifford group comprising only transversal and fold-transversal gates, thus enabling the implementation of any addressable Clifford gate. To our knowledge, this is the first known construction of the full logical Clifford group using only transversal and fold-transversal gates without requiring ancilla qubits for a family of codes in which $k$ grows near-linearly in $n$.

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arXiv2024

Synchronizable hybrid subsystem codes

Quantum synchronizable codes are quantum error correcting codes that can correct not only Pauli errors but also errors in block synchronization. The code can be constructed from two classical cyclic codes $\mathcal{C}$, $\mathcal{D}$ satisfying $\mathcal{C}^{\perp} \subset \mathcal{C} \subset \mathcal{D}$ through the Calderbank-Shor-Steane (CSS) code construction. In this work, we establish connections between quantum synchronizable codes, subsystem codes, and hybrid codes constructed from the same pair of classical cyclic codes. We also propose a method to construct a synchronizable hybrid subsystem code which can correct both Pauli and synchronization errors, is resilient to gauge errors by virtue of the subsystem structure, and can transmit both classical and quantum information, all at the same time. The trade-offs between the number of synchronization errors that the code can correct, the number of gauge qubits, and the number of logical classical bits of the code are also established. In addition, we propose general methods to construct hybrid and hybrid subsystem codes of CSS type from classical codes, which cover relevant codes from our main construction.

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arXiv2024

Concatenated Steane code with single-flag syndrome checks

A fault-tolerant error correction (FTEC) protocol with a high error suppression rate and low overhead is very desirable for the near-term implementation of quantum computers. In this work, we develop a distance-preserving flag FTEC protocol for the [[49,1,9]] concatenated Steane code, which requires only two ancilla qubits per generator and can be implemented on a planar layout. We generalize the weight-parity error correction (WPEC) technique from [Phys. Rev. A 104, 042410 (2021)] and find a gate ordering of flag circuits for the concatenated Steane code which makes syndrome extraction with two ancilla qubits per generator possible. The FTEC protocol is constructed using the optimization tools for flag FTEC developed in [PRX Quantum 5, 020336 (2024)] and is simulated under the circuit-level noise model without idling noise. Our simulations give a pseudothreshold of $1.64 \times 10^{-3}$ for the [[49,1,9]] concatenated Steane code, which is better than a pseudothreshold of $1.43 \times 10^{-3}$ for the [[61,1,9]] 6.6.6 color code simulated under the same settings. This is in contrast to the code capacity model where the [[61,1,9]] code performs better.

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arXiv2024

Boosting end-to-end entanglement fidelity in quantum repeater networks via hybridized strategies

Quantum networks are expected to enhance distributed quantum computing and quantum communication over long distances while providing security dependent upon physical effects rather than mathematical assumptions. Through simulation, we show that a quantum network utilizing only entanglement purification or only quantum error correction as error management strategies cannot create Bell pairs with fidelity that exceeds the requirement for a secured quantum key distribution protocol for a broad range of hardware parameters. We propose hybrid strategies utilizing quantum error correction on top of purification and show that they can produce Bell pairs of sufficiently high fidelity. We identify the error parameter regime for gate and measurement errors in which these hybrid strategies are applicable.

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arXiv2024

Optimization tools for distance-preserving flag fault-tolerant error correction

Lookup table decoding is fast and distance-preserving, making it attractive for near-term quantum computer architectures with small-distance quantum error-correcting codes. In this work, we develop several optimization tools that can potentially reduce the space and time overhead required for flag fault-tolerant quantum error correction (FTQEC) with lookup table decoding on Calderbank-Shor-Steane (CSS) codes. Our techniques include the compact lookup table construction, the Meet-in-the-Middle technique, the adaptive time decoding for flag FTQEC, the classical processing technique for flag information, and the separated $X$ and $Z$ counting technique. We evaluate the performance of our tools using numerical simulation of hexagonal color codes of distances 3, 5, 7, and 9 under circuit-level noise. Combining all tools can result in more than an order of magnitude increase in pseudothreshold for the hexagonal color code of distance 9, from $(1.34 \pm 0.01) \times 10^{-4}$ to $(1.42 \pm 0.12) \times 10^{-3}$.

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arXiv2023

Adaptive syndrome measurements for Shor-style error correction

The Shor fault-tolerant error correction (FTEC) scheme uses transversal gates and ancilla qubits prepared in the cat state in syndrome extraction circuits to prevent propagation of errors caused by gate faults. For a stabilizer code of distance $d$ that can correct up to $t=\lfloor(d-1)/2\rfloor$ errors, the traditional Shor scheme handles ancilla preparation and measurement faults by performing syndrome measurements until the syndromes are repeated $t+1$ times in a row; in the worst-case scenario, $(t+1)^2$ rounds of measurements are required. In this work, we improve the Shor FTEC scheme using an adaptive syndrome measurement technique. The syndrome for error correction is determined based on information from the differences of syndromes obtained from consecutive rounds. Our protocols that satisfy the strong and the weak FTEC conditions require no more than $(t+3)^2/4-1$ rounds and $(t+3)^2/4-2$ rounds, respectively, and are applicable to any stabilizer code. Our simulations of FTEC protocols with the adaptive schemes on hexagonal color codes of small distances verify that our protocols preserve the code distance, can increase the pseudothreshold, and can decrease the average number of rounds compared to the traditional Shor scheme. We also find that for the code of distance $d$, our FTEC protocols with the adaptive schemes require no more than $d$ rounds on average.

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arXiv2023

A Hamming-Like Bound for Degenerate Stabilizer Codes

The quantum Hamming bound was originally put forward as an upper bound on the parameters of nondegenerate quantum codes, but over the past few decades much work has been done to show that many degenerate quantum codes must also obey this bound. In this paper, we show that there is a Hamming-like bound stricter than the quantum Hamming bound that applies to degenerate $t$-error-correcting stabilizer codes of length greater than some positive integer $N(t)$. We show that this bound holds for all single-error-correcting degenerate stabilizer codes, forcing all but a handful of optimal distance-3 stabilizer codes to be nondegenerate.

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arXiv2023

Hybrid Error-Management Strategies in Quantum Repeater Networks

A quantum network is expected to enhance distributed quantum computing and quantum communication over a long distance while providing unconditional security. As quantum entanglement is essential for a quantum network, major issues from various types of noise and decoherence prevent it from being realized, and research has been intensively active to obtain optimal configurations for a quantum network. In this work, we address the performance of a quantum network capable of quantum error correction and entanglement purification. Our results show that one should distribute Bell pairs as fast as possible while balancing the deployment of fidelity enhancement. We also show suitable hybrid strategies in quantum cryptography tasks under some noise regimes that need to use purification and quantum error correction together. Our results suggest that using purification to distribute high fidelity Bell pairs and preserving them for application using quantum error correction is a promising way to achieve a near-term quantum network for secure communication.

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arXiv2022

Achieving fault tolerance on capped color codes with few ancillas

Attaining fault tolerance while maintaining low overhead is one of the main challenges in a practical implementation of quantum circuits. One major technique that can overcome this problem is the flag technique, in which high-weight errors arising from a few faults can be detected by a few ancillas and distinguished using subsequent syndrome measurements. The technique can be further improved using the fact that for some families of codes, errors of any weight are logically equivalent if they have the same syndrome and weight parity, as previously shown in [Phys. Rev. A 104, 042410 (2021)]. In this work, we develop a notion of distinguishable fault set which captures both concepts of flags and weight parities, and extend the use of weight parities in error correction from [Phys. Rev. A 104, 042410 (2021)] to families of capped and recursive capped color codes. We also develop fault-tolerant protocols for error correction, measurement, state preparation, and logical T gate implementation via code switching, which are sufficient for performing fault-tolerant Clifford computation on a capped color code, and performing fault-tolerant universal quantum computation on a recursive capped color code. Our protocols for a capped or a recursive capped color code of any distance require only 2 ancillas, assuming that the ancillas can be reused. The concept of distinguishable fault set also leads to a generalization of the definitions of fault-tolerant gadgets proposed by Aliferis, Gottesman, and Preskill.

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arXiv2021

Fault-tolerant quantum error correction using error weight parities

In quantum error correction using imperfect primitives, errors of high weight arising from a few faults are major concerns since they might not be correctable by the quantum error correcting code. Fortunately, some errors of different weights are logically equivalent and the same correction procedure is applicable to all equivalent errors, thus correcting high-weight errors is sometimes possible. In this work, we introduce a technique called weight parity error correction (WPEC) which can correct Pauli error of any weight in some stabilizer codes provided that the parity of the weight of the error is known. We show that the technique is applicable to concatenated codes constructed from the [[7,1,3]] Steane code or the [[23,1,7]] Golay code. We also provide a fault-tolerant error correction protocol using WPEC for the [[49,1,9]] concatenated Steane code which can correct up to 3 faults and requires only 2 ancillas.

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arXiv2019

Flag fault-tolerant error correction, measurement, and quantum computation for cyclic CSS codes

Flag qubits have recently been proposed in syndrome extraction circuits to detect high-weight errors arising from fewer faults. The use of flag qubits allows the construction of fault-tolerant protocols with the fewest number of ancillas known to-date. In this work, we prove some critical properties of CSS codes constructed from classical cyclic codes that enable the construction of a flag fault-tolerant error correction scheme. We then develop fault-tolerant protocols as well as a family of circuits for flag fault-tolerant error correction and operator measurement, requiring only four ancilla qubits and applicable to cyclic CSS codes of distance 3. The measurement protocol can be further used for logical Clifford gate implementation via quantum gate teleportation. We also provide examples of cyclic CSS codes with large encoding rates.

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arXiv2015

Quantum Phase Estimation Algorithm for Finding Polynomial Roots

Quantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum algorithm for finding the roots of nth degree polynomials where n is any positive integer. In classical algorithm, the resources required for solving this problem increase drastically when n increases and it would be impossible to practically solve the problem when n is large. It was found that any polynomial can be rearranged into a corresponding companion matrix, whose eigenvalues are roots of the polynomial. This leads to a possibility to perform a quantum algorithm where the number of computational resources increase as a polynomial of n. In this study, we construct a quantum circuit representing the companion matrix and use eigenvalue estimation technique to find roots of polynomial.

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