Learning unknown stabilizer codes using product measurements
Heather Leitch, Sri. S. Tirukkovalluri, Yingkai Ouyang
arXiv:2609.04997 [quant-ph]
Efficiently characterizing quantum error correcting codes is a key challenge on the path to fault-tolerant quantum computation. Stabilizer codes, a central class of such codes, are defined by a set of stabilizer generators. Here, we present an algorithm that uses random single-qubit measurements to learn the stabilizer generators of any stabilizer code from N copies of stabilizer states in its codespace, requiring no prior knowledge of the code's structure. This also enables verification that a device implements its intended code. We derive a lower bound on N needed to recover the stabilizer generators with high probability, together with a bound on the algorithm's overall probability of success. When applied to quantum low-density parity-check (qLDPC) codes, a leading candidate for practical fault-tolerant architectures, our approach requires a number of states that scales polylogarithmically with n, the number of qubits.
Recovery Algorithm for Correlated Errors in Permutation-Invariant Quantum Codes
Omprakash Chandra, Yingkai Ouyang, Gopikrishnan Muraleedharan, Gavin Brennen
arXiv:2607.02346 [quant-ph]
Quantum Error Recovery (QER) uses knowledge of the error channel acting on a quantum system to find optimal recovery maps. We use a generic coherent QER map implemented with a quantum circuit acting on the system together with ancillary qubits to recover quantum information stored in permutation invariant (PI) codes. We showcase the method by modeling QER in PI codes after collective and local symmetric correlated amplitude-damping (AD) noise, and propose a new PI code family called CAD codes with explicit examples on 4 and 9 qubits.
Magic state distillation with permutation-invariant codes and a two-qubit example
Heather Leitch, Yingkai Ouyang
arXiv:2603.04310 [quant-ph]
We present a distillation protocol based on permutation-invariant gnu codes, as small as two qubits. The two-qubit protocol achieves a 0.5 error threshold and 1/2 distillation rate, surpassing prior schemes for comparable codes. Our protocol furthermore distils magic states with arbitrary magic by varying the position of the ideal input states on the Bloch sphere by allowing the use of non-Clifford gates in the distillation protocol.
A theory of quantum error correction for permutation-invariant codes
Yingkai Ouyang, Gavin K. Brennen
arXiv:2602.13638 [quant-ph]
We present for the first time a general theory of error correction for permutation invariant (PI) codes. Using representation theory of the symmetric group we construct efficient algorithms that can correct any correctible error on any PI code. These algorithms involve measurements of total angular momentum, quantum Schur transforms or logical state teleportations, and geometric phase gates.
The equivalence of quantum deletion and insertion errors on permutation-invariant codes
Lewis Bulled, Yingkai Ouyang
arXiv:2602.08780 [quant-ph]
Quantum synchronisation errors change the number of qubits in a quantum system. We address the longstanding problem of a quantum insertion-deletion equivalence on permutation-invariant codes, detailing the conditions under which such codes are t-insertion error-correctable. We extend these conditions to quantum insdel errors, formulating a more restrictive set of conditions under which permutation-invariant codes are (t,s)-insdel error-correctable.
An angular momentum approach to quantum insertion errors
Lewis Bulled, Yingkai Ouyang
arXiv:2509.03413 [quant-ph]
We detail a quantum error correction protocol that can correct single insertion errors on a class of gapped permutation-invariant codes. We provide a simple two-stage syndrome extraction protocol that yields a two-bit syndrome, by measuring the total angular momentum and its projection along the z-axis (modulo the code gap) of the post-insertion state.
Fault-Tolerant Quantum Error Correction for Constant-Excitation Stabilizer Codes under Coherent Noise
Ching-Yi Lai, Pei-Hao Liou, Yingkai Ouyang
arXiv:2507.10395 [quant-ph, cs.IT]
Collective coherent noise poses challenges for fault-tolerant quantum error correction (FTQEC). Here, we introduce a complete fault-tolerant architecture for CE CSS codes based on dual-rail concatenation. We introduce CE-preserving logical CNOT gates and modified Shor- and Steane-type syndrome extraction schemes using zero-controlled NOT gates and CE-compatible ancilla.
The Quantum Internet (Technical Version)
Peter P. Rohde, Zixin Huang, Yingkai Ouyang, He-Liang Huang, Zu-En Su, Simon Devitt, Rohit Ramakrishnan, Atul Mantri, Si-Hui Tan, Nana Liu, Scott Harrison, Chandrashekar Radhakrishnan, Gavin K. Brennen, Ben Q. Baragiola, Jonathan P. Dowling, Tim Byrnes, William J. Munro
arXiv:2501.12107 [quant-ph]
Following the emergence of quantum computing, the subsequent quantum revolution will be that of interconnecting individual quantum computers at global level. This work examines in detail how the quantum internet would evolve in practice, focusing not only on the technology itself but also on the implications it will have economically and politically.
Degenerate quantum erasure decoding
Kao-Yueh Kuo, Yingkai Ouyang
Erasures are the primary type of errors in physical systems dominated by leakage errors. We propose belief propagation (BP) decoders that run in linear time and exploit error degeneracy in stabilizer codes, achieving capacity or near-capacity performance for a broad class of codes, including bicycle codes, product codes, and topological codes.
Measurement-free code-switching for low overhead quantum computation using permutation invariant codes
Yingkai Ouyang, Yumang Jing, Gavin K. Brennen
We present a measurement-free code-switching protocol for universal quantum computation, switching between a stabiliser code for transversal Cliffords and a permutation-invariant (PI) code for transversal non-Cliffords that are logical Z rotations for any rational multiple of pi. We present a protocol for performing controlled-NOTs between the codes using near-term quantum control operations that employ a catalytic bosonic mode.
The Cramér-Rao approach and global quantum estimation of bosonic states
Masahito Hayashi, Yingkai Ouyang
In general, it is unclear whether the Cramér-Rao approach is applicable for global estimation instead of local estimation. In this paper, we find situations where the Cramér-Rao approach does and does not work for quantum state estimation problems involving a family of bosonic states in a non-IID setting, where we only use one copy of the bosonic quantum state in the large number of bosons setting.
Robust projective measurements through measuring code-inspired observables
Yingkai Ouyang
We present a scheme that implements a robust projective measurement through measuring code-inspired observables. Given a projective POVM, a classical code and a constraint on the number of measurement outcomes each observable can have, we construct commuting observables whose measurement is equivalent to the projective measurement in the noiseless setting.
Finding the optimal probe state for multiparameter quantum metrology using conic programming
Masahito Hayashi, Yingkai Ouyang
Determining the optimal input probe state and the corresponding precision bounds in estimation is a non-trivial problem, particularly in the multi-parameter setting. In this paper, we present a conic programming framework that allows us to determine the optimal probe state for the corresponding multi-parameter precision bounds.
Approximate reconstructability of quantum states and noisy quantum secret sharing schemes
Yingkai Ouyang, Kaumudibikash Goswami, Jacquiline Romero, Barry C. Sanders, Min-Hsiu Hsieh, Marco Tomamichel
We introduce and analyse approximate quantum secret sharing in a formal cryptographic setting. In particular, viewing the map encoding the quantum secret to shares for players in an authorized structure as a quantum channel, we show that approximate reconstructability of the quantum secret by these players is possible if and only if the information leakage is small.
Finite-round quantum error correction on symmetric quantum sensors
Yingkai Ouyang, Gavin K. Brennen
arXiv:2212.06285 [quant-ph]
We introduce a quantum sensing protocol ECSense based on permutation-invariant quantum error correction (QEC) codes that support tunable code parameters to suit the physical noise model. We prove using a non-Markovian QEC strategy, that even for a linear number of deletion errors, a variance approaching the Heisenberg limit is still achievable.
Tight Cramér-Rao type bounds for multiparameter quantum metrology through conic programming
Masahito Hayashi, Yingkai Ouyang
We solve the fundamental problem of finding uncorrelated measurement strategies with optimal precisions by introducing a framework of conic programming that unifies the theory of precision bounds for multiparameter estimates for uncorrelated and correlated measurement strategies under a common umbrella.
Privacy and correctness trade-offs for information-theoretically secure quantum homomorphic encryption
Yanglin Hu, Yingkai Ouyang, Marco Tomamichel
We establish a definition of circuit privacy for quantum homomorphic encryption with information-theoretic security. Furthermore, we reduce quantum oblivious transfer to quantum homomorphic encryption to unravel fundamental trade-offs between circuit privacy, data privacy and correctness.
Learning quantum graph states with product measurements
Yingkai Ouyang, Marco Tomamichel
We consider the problem of learning N identical copies of an unknown n-qubit quantum graph state with product measurements. We detail an explicit algorithm that uses product measurements on multiple identical copies of such graph states to learn them, and supply bounds when every graph state encounters independent depolarizing errors.
Permutational-key quantum homomorphic encryption with homomorphic quantum error-correction
Yingkai Ouyang, Peter P. Rohde
arXiv:2204.10471 [quant-ph, cs.CR]
We revisit a permutational-key quantum homomorphic encryption protocol with information-theoretic security. We explain how to integrate this protocol with quantum error correction that has the error correction encoding as a homomorphism, enabling client and server to apply encoding and decoding steps without the encrypting permutation-key.
Imaging stars with quantum error correction
Zixin Huang, Gavin K. Brennen, Yingkai Ouyang
We show how to overcome physical limitations of optical interferometers using quantum communication techniques. We present a general framework for using quantum error correction codes for protecting and imaging starlight received at distant telescope sites, showing even small codes offer significant protection against noise.
Linear programming bounds for quantum channels acting on quantum error-correcting codes
Yingkai Ouyang, Ching-Yi Lai
For any Kraus decomposition of any given quantum channel, we introduce corresponding quantum weight enumerators that naturally generalize the Shor-Laflamme weight enumerators. We establish an indirect linear relationship and construct a general framework for constructing a linear program to check approximate quantum error correction bounds.
Quantum key distribution with non-ideal heterodyne detection: composable security of discrete-modulation continuous-variable protocols
Cosmo Lupo, Yingkai Ouyang
We present a theory to rigorously account for the experimental limitations of realistic heterodyne detection. We establish for the first time the composable security of discrete-modulation continuous-variable quantum key distribution in the finite-size regime. Tight bounds on the key rates are obtained through semi-definite programming.
The equivalence between correctability of deletions and insertions of separable states in quantum codes
Taro Shibayama, Yingkai Ouyang
In this paper, we prove the equivalence of inserting separable quantum states and deletions. Hence any quantum code that corrects deletions automatically corrects separable insertions. We prove this using developed algebra for commuting Kraus operators and the Knill-Laflamme conditions.
Permutation-invariant quantum coding for quantum deletion channels
Yingkai Ouyang
We note that any permutation-invariant quantum code that has a distance of t+1 can correct t quantum deletions for any positive integer t in both the qubit and the qudit setting. We focus attention on a specific family of shifted gnu codes, showing that their encoding and decoding algorithms run efficiently.
Constructing quantum codes from any classical code and their embedding in ground space of local Hamiltonians
Ramis Movassagh, Yingkai Ouyang
We introduce a framework that takes any classical code and explicitly constructs the corresponding QEC code. Our framework generalizes CSS codes and goes beyond the stabilizer formalism. We then introduce a local quantum spin-chain Hamiltonian whose ground space contains explicit quantum codes with linear distance, side-stepping the Bravyi-Terhal no-go theorem.
Avoiding coherent errors with rotated concatenated stabilizer codes
Yingkai Ouyang
We propose integrating stabilizer codes with constant-excitation codes by code concatenation. By concatenating an [[n,k,d]] stabilizer outer code with dual-rail inner codes, we obtain a [[2n,k,d]] constant-excitation code immune from coherent phase errors and equivalent to a Pauli-rotated stabilizer code.
Trade-offs on number and phase shift resilience in bosonic quantum codes
Yingkai Ouyang, Earl T. Campbell
We obtain results pertaining to the non-existence of approximate quantum error correcting g-gapped single-mode bosonic codes with respect to Gaussian dephasing errors. We show that by using artificially many modes, g-gapped multi-mode codes can yield good approximate quantum error correction codes for any finite magnitude of dephasing.
Describing quantum metrology with erasure errors using weight distributions of classical codes
Yingkai Ouyang, Narayanan Rengaswamy
We consider using quantum probe states with a structure that corresponds to classical [n,k,d] binary block codes. We show that the quantum Fisher information is proportional to the variances of the weight distributions of the corresponding shortened codes, enabling asymptotically optimal field-sensing that passively tolerates erasure errors.
Quantifying quantum speedups: improved classical simulation from tighter magic monotones
James R. Seddon, Bartosz Regula, Hakop Pashayan, Yingkai Ouyang, Earl T. Campbell
We propose three different classical algorithms for simulating universal quantum circuits and characterize them using magic monotones. Our first simulator introduces a new class of quasiprobability distributions and significantly improves exponential scaling compared to all prior quasiprobability simulators for qubits.
Linear programming bounds for quantum amplitude damping codes
Yingkai Ouyang, Ching-Yi Lai
We introduce quantum weight enumerators for amplitude damping (AD) errors and work within the framework of approximate quantum error correction. We introduce an auxiliary exact weight enumerator intrinsic to a code space, establishing a linear relationship to implement a linear program for bounding AQEC code capabilities.
Tight bounds on the simultaneous estimation of incompatible parameters
Jasminder S. Sidhu, Yingkai Ouyang, Earl T. Campbell, Pieter Kok
The Holevo Cramer-Rao bound (HCRB) provides the most fundamental, simultaneously attainable bound for multi-parameter estimation problems. In this work, we develop an analytic approach to solving the HCRB for two parameters, greatly reducing the complexity of determining the HCRB to solving a set of linear equations.
Compilation by stochastic Hamiltonian sparsification
Yingkai Ouyang, David R. White, Earl T. Campbell
We introduce a new scheme that approximates a complicated Hamiltonian with a sparser Hamiltonian containing fewer terms. By stochastically sparsifying weaker Hamiltonian terms, we benefit from a quadratic suppression of errors relative to deterministic approaches, combining the strengths of randomized Trotterisation with qDRIFT.
Robust quantum metrology with explicit symmetric states
Yingkai Ouyang, Nathan Shettell, Damian Markham
We prove that, for a set of carefully chosen symmetric probe states that lie within certain quantum error correction codes, quantum metrology exhibits an advantage over classical metrology even after the probe states are corrupted by a constant number of erasure and dephasing errors.
Quantum storage in quantum ferromagnets
Yingkai Ouyang
Since Heisenberg ferromagnets are readily available, we investigate their potential for robust quantum storage. We propose to use permutation-invariant quantum codes to store quantum data because the ground space of any Heisenberg ferromagnet must be symmetric under any permutation of the underlying qubits.
Homomorphic encryption of linear optics quantum computation on almost arbitrary states of light with asymptotically perfect security
Yingkai Ouyang, Si-Hui Tan, Joseph Fitzsimons, Peter P. Rohde
We present a scheme for the homomorphic encryption of arbitrary quantum states of light with no more than a fixed number of photons, under the evolution of both passive and adaptive linear optics. The scheme uses random coherent displacements in phase-space to obfuscate client data with high information-theoretic secrecy.
Faster quantum computation with permutations and resonant couplings
Yingkai Ouyang, Yi Shen, Lin Chen
We consider quantum computation in a decoherence-free subspace and optimize its speed. To achieve this, we perform certain single-qubit quantum computations by simply permuting the underlying qubits. Together with exchange-interactions or resonant couplings, we present a scheme that optimizes computation speed.
Permutation-invariant constant-excitation quantum codes for amplitude damping
Yingkai Ouyang, Rui Chao
The purpose of this paper is to give constant-excitation quantum codes that not only correct amplitude damping errors, but are also immune against permutations of their underlying modes. To construct such quantum codes, we use the nullspace of a specially constructed matrix based on integer partitions.
Causal limit on quantum communication
Robert Pisarczyk, Zhikuan Zhao, Yingkai Ouyang, Vlatko Vedral, Joseph F. Fitzsimons
We uncover a connection between quantum causality and channel capacity. We show the amount of temporal correlations between two ends of a noisy quantum channel, as quantified by a causality measure, implies a general upper bound on its channel capacity. The expression is simple to evaluate compared to prior bounds.
Practical quantum somewhat-homomorphic encryption with coherent states
Si-Hui Tan, Yingkai Ouyang, Peter P. Rohde
We present a scheme for implementing homomorphic encryption on coherent states encoded using phase-shift keys. The encryption operations require only rotations in phase space, which commute with computations in the codespace performed via passive linear optics. We quantify security via ciphertext indistinguishability.
Computing spectral bounds of the Heisenberg ferromagnet from geometric considerations
Yingkai Ouyang
We give a polynomial-time algorithm for computing upper bounds on some of the smaller energy eigenvalues in a spin-1/2 ferromagnetic Heisenberg model with any graph G for the underlying interactions. The algorithm relies on connections between Heisenberg models and the symmetric products of graphs.
Computing on quantum shared secrets
Yingkai Ouyang, Si-Hui Tan, Liming Zhao, Joseph F. Fitzsimons
We propose a method of performing computation on quantum shared secrets. We introduce an (n,n)-quantum secret sharing scheme together with a set of protocols that allow quantum circuits to be evaluated on the shared secret without the need to decode the secret.
Edge-isoperimetric inequalities for the symmetric product of graphs
Yingkai Ouyang
arXiv:1612.08259 [math.CO, cs.DM]
Withdrawn / Merged into arXiv:1707.02446
The k-th symmetric product of a graph G is a graph with vertices as k-sets of V. Using the isoperimetric properties of the vertex-induced subgraphs of G and Sobolev inequalities on graphs, we obtain various edge-isoperimetric inequalities pertaining to the symmetric product of finite and infinite graphs.
Classical verification of quantum circuits containing few basis changes
Tommaso F. Demarie, Yingkai Ouyang, Joseph F. Fitzsimons
We consider the task of verifying the correctness of quantum computation for a restricted class of circuits which contain at most two basis changes. We show that when the circuit has an outcome with high enough probability, the outcome can be checked in polynomial time by a completely classical verifier.
Permutation-invariant qudit codes from polynomials
Yingkai Ouyang
We give an algebraic construction of new families of d-dimensional permutation-invariant codes on qudits that can correct t errors. The construction relies on a real polynomial with multiple roots at the roots of unity, and a sequence of real polynomials satisfying combinatorial constraints.
Permutation-invariant codes encoding more than one qubit
Yingkai Ouyang, Joseph Fitzsimons
A permutation-invariant code on m qubits is a subspace of the symmetric subspace of the m qubits. We derive permutation-invariant codes that can encode an increasing amount of quantum information while suppressing leading order spontaneous decay errors using elementary number theory.
Quantum homomorphic encryption from quantum codes
Yingkai Ouyang, Si-Hui Tan, Joseph Fitzsimons
We present a quantum encryption scheme which is homomorphic for arbitrary classical and quantum circuits which have at most some constant number of non-Clifford gates. Unlike classical schemes, the security of this scheme is information-theoretic and independent of adversarial computational power.
A quantum approach to homomorphic encryption
Si-Hui Tan, Joshua A. Kettlewell, Yingkai Ouyang, Lin Chen, Joseph F. Fitzsimons
Inspired by group theoretic tools, we use the centralizer of a subgroup of operations to present a private-key quantum homomorphic encryption scheme that enables a broad class of quantum computation on encrypted data, hiding up to a constant fraction of the encrypted information.
Permutation-invariant quantum codes
Yingkai Ouyang
Ideally, a quantum code lies within the ground space of a physical system. When the model is the Heisenberg ferromagnet, the ground-space contains all permutation-invariant states. We use techniques from combinatorics and operator theory to construct families of permutation-invariant quantum codes.
Truncated channel representations for coupled harmonic oscillators
Yingkai Ouyang, Wee Hao Ng
We explicitly study a pair of initially decoupled quantum harmonic oscillators interacting with a spring-like coupling. We treat the map on the system as a quantum channel, derive the truncated transition amplitudes, and demonstrate explicitly that substantial leakage errors can be mitigated via QEC.
Channel covariance, twirling, contraction, and some upper bounds on the quantum capacity
Yingkai Ouyang
We restrict our attention to obtaining upper bounds on the quantum capacity using a generalization of Smith and Smolin's degradable extension technique. As an application of our main result, we supply new upper bounds on the quantum capacity of some unital and non-unital channels.
Concatenated quantum codes can attain the quantum Gilbert-Varshamov bound
Yingkai Ouyang
We demonstrate the existence of concatenated quantum codes that can asymptotically attain the quantum Gilbert-Varshamov bound. The outer codes are quantum generalized Reed-Solomon codes, and the inner codes are random independently chosen stabilizer codes.