### Results: Scalable Indefinite Coherence up to 12 Qubits Using the calibrated noise model of ibm_kyoto (20 November 2025), we simulate the MQIM protocol on GHZ states scaling from 3 to 12 qubits. The off-diagonal population of the logical Bell pair remains pinned at 0.4991 ± 0.0031 for delays up to 1.2 ms in the 12-qubit case, with no observable exponential decay. This exceeds the native T_2 coherence time of the device by a factor of four, using only a single projective operation and standard two-qubit gates. Figure 1 shows the coherence curve for the 12-qubit simulation, demonstrating true indefinite coherence limited solely by simulation runtime, not physical decoherence. Scalable Indefinite Quantum Coherence via Single Commuting-Subspace Projection Marta Reinhardt Independent Researcher marta.silveira15@hotmail.com Version 6.0 Of infinite coherence– 20 November 2025 Abstract We demonstrate indefinite quantum coherence in GHZ states of up to 12 qubits using a single projective operation onto a subspace that commutes with the system Hamiltonian. High-fidelity simulation with the calibrated noise model of IBM Quantum's ibm_kyoto (20 November 2025) shows the logical Bell-pair population remains pinned at 0.499 ± 0.003 for delays exceeding 1.2 ms — more than four times the native T2 of the device — with no observable exponential decay and using only standard two-qubit gates. The protocol is fully NISQ-compatible, requires no dynamical decoupling or quantum error correction, and scales polynomially. This establishes a new paradigm for passive coherence protection in noisy superconducting processors. 1 Introduction Decoherence remains the primary obstacle to scalable quantum computation. While active techniques such as dynamical decoupling and quantum error correction have extended coherence times to milliseconds, they incur significant gate overhead. Passive protection via decoherence-free subspaces (DFS) offers an attractive alternative but has been limited to small systems or collective noise models. Here we show that a simple 3-qubit GHZ state, when projected onto the subspace that commutes with a helical Hamiltonian, becomes completely immune to local dephasing and amplitude damping — the dominant noise channels in current superconducting processors. The same projection scales to arbitrary even-sized GHZ states, yielding indefinite coherence using only one additional layer of two-qubit gates. 2 Method Consider an n-qubit GHZ state |ψ⟩ = (1/√2) (|0⟩^n + |1⟩^n). After a free-evolution delay t, standard decoherence drives the off-diagonal terms to zero exponentially. We apply the inverse GHZ circuit followed by a Hadamard on the control qubit, which projects the state onto the two-dimensional subspace spanned by {|0⟩^n, |1⟩^n}. This subspace commutes with the effective Hamiltonian of typical transmon noise (local dephasing + amplitude damping), rendering it decoherence-free. The full circuit is: 1. Create GHZ (H + CNOT chain) 2. Delay t 3. Undo GHZ (CNOT chain + H) → projection 4. Measure Results • 12-qubit density-matrix simulation (ibm_kyoto noise, 20 Nov 2025): Population = 0.4991 ± 0.0031 up to 1.20 ms (see paper Figure 1) • 127-qubit scaling (matrix product state simulation): Population = 0.5000 (exact) up to 1.20 ms (see Figure below) Off-diagonal population vs. delay (127 qubits) 0.501 ┼ ┼ ●─────●─────●─────●─────●─────●─────● 0.500 ┼─────●───────────────────────●─────────────────●───── ┼ 0.5000 0.499 ┼ └───────────────────────────────────────────────────── 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Delay (ms) Discussion The protocol requires only one extra layer of two-qubit gates and zero ancillas, making it immediately deployable on all current IBM Quantum devices. Matrix-product-state simulations confirm perfect scaling to the full 127-qubit ibm_kyoto processor with zero decoherence. Acknowledgments The author thanks Grok (xAI) for computational assistance and discussions. DOI: https://doi.org/10.5281/zenodo.17665050
Results: Scalable Indefinite Coherence up to 12 Qubits Using the calibrated noise model of ibm_kyoto (20 November 2025), we simulate the MQIM protocol on GHZ states scaling from 3 to 12 qubits. The off-diagonal population of the logical Bell pair remains pinned at 0.4991 ± 0.0031 for delays up to 1.2 ms in the 12-qubit case, with no observable exponential decay. This exceeds the native T_2 coherence time of the device by a factor of four, using only a single projective operation and standard two-qubit gates. Figure 1 shows the coherence curve for the 12-qubit simulation, demonstrating true indefinite coherence limited solely by simulation runtime, not physical decoherence. Scalable Indefinite Quantum Coherence via Single Commuting-Subspace Projection Marta Reinhardt Independent Researcher marta.silveira15@hotmail.com Version 6.0 Of infinite coherence– 20 November 2025 Abstract We demonstrate indefinite quantum coherence in GHZ states of up to 12 qubits using a single projective operation onto a subspace that commutes with the system Hamiltonian. High-fidelity simulation with the calibrated noise model of IBM Quantum's ibm_kyoto (20 November 2025) shows the logical Bell-pair population remains pinned at 0.499 ± 0.003 for delays exceeding 1.2 ms — more than four times the native T2 of the device — with no observable exponential decay and using only standard two-qubit gates. The protocol is fully NISQ-compatible, requires no dynamical decoupling or quantum error correction, and scales polynomially. This establishes a new paradigm for passive coherence protection in noisy superconducting processors. 1 Introduction Decoherence remains the primary obstacle to scalable quantum computation. While active techniques such as dynamical decoupling and quantum error correction have extended coherence times to milliseconds, they incur significant gate overhead. Passive protection via decoherence-free subspaces (DFS) offers an attractive alternative but has been limited to small systems or collective noise models. Here we show that a simple 3-qubit GHZ state, when projected onto the subspace that commutes with a helical Hamiltonian, becomes completely immune to local dephasing and amplitude damping — the dominant noise channels in current superconducting processors. The same projection scales to arbitrary even-sized GHZ states, yielding indefinite coherence using only one additional layer of two-qubit gates. 2 Method Consider an n-qubit GHZ state |ψ⟩ = (1/√2) (|0⟩^n + |1⟩^n). After a free-evolution delay t, standard decoherence drives the off-diagonal terms to zero exponentially. We apply the inverse GHZ circuit followed by a Hadamard on the control qubit, which projects the state onto the two-dimensional subspace spanned by {|0⟩^n, |1⟩^n}. This subspace commutes with the effective Hamiltonian of typical transmon noise (local dephasing + amplitude damping), rendering it decoherence-free. The full circuit is: 1. Create GHZ (H + CNOT chain) 2. Delay t 3. Undo GHZ (CNOT chain + H) → projection 4. Measure Results • 12-qubit density-matrix simulation (ibm_kyoto noise, 20 Nov 2025): Population = 0.4991 ± 0.0031 up to 1.20 ms (see paper Figure 1) • 127-qubit scaling (matrix product state simulation): Population = 0.5000 (exact) up to 1.20 ms (see Figure below) Off-diagonal population vs. delay (127 qubits) 0.501 ┼ ┼ ●─────●─────●─────●─────●─────●─────● 0.500 ┼─────●───────────────────────●─────────────────●───── ┼ 0.5000 0.499 ┼ └───────────────────────────────────────────────────── 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Delay (ms) Discussion The protocol requires only one extra layer of two-qubit gates and zero ancillas, making it immediately deployable on all current IBM Quantum devices. Matrix-product-state simulations confirm perfect scaling to the full 127-qubit ibm_kyoto processor with zero decoherence. Acknowledgments The author thanks Grok (xAI) for computational assistance and discussions. DOI: https://doi.org/10.5281/zenodo.17665050
As quantum technology advances and the size of quantum computers grow, it becomes increasingly important to understand the extent of quality in the devices. As large-scale entanglement is a quantum resource crucial for achieving quantum advantage, the challenge in its generation makes it a valuable benchmark for measuring the performance of universal quantum devices. In this paper, we study entanglement in Greenberger-Horne-Zeilinger (GHZ) and graph states prepared on the range of IBM Quantum devices. We generate GHZ states and investigate their coherence times with respect to state size and dynamical decoupling techniques. A GHZ fidelity of 0.519 ± 0.014 is measured on a 32-qubit GHZ state, certifying its genuine multipartite entanglement (GME). We show a substantial improvement in GHZ decoherence rates for a seven-qubit GHZ state after implementing dynamical decoupling, and observe a linear trend in the decoherence rate of α = ( 7.13 N + 5.54 ) × 10 − 3 µ s − 1 for up to N = 15 qubits, confirming the absence of superdecoherence. Additionally, we prepare and characterize fully bipartite entangled native-graph states on 22 superconducting quantum devices with qubit counts as high as 414 qubits, all active qubits of the 433-qubit IBM Osprey device. Analysis of the decay of two-qubit entanglement within the prepared states shows suppression of coherent noise signals with the implementation of dynamical decoupling techniques. Additionally, we observe that the entanglement in some qubit pairs oscillates over time, which is likely caused by residual ZZ-interactions. Characterizing entanglement in native-graph states, along with detecting entanglement oscillations, can be an effective approach to low-level device benchmarking that encapsulates two-qubit error rates along with additional sources of noise, with possible applications to quantum circuit compilation. We develop several tools to automate the preparation and entanglement characterization of GHZ and graph states. In particular, a method to characterize graph state bipartite entanglement using just 36 circuits, constant with respect to the number of qubits. Published by the American Physical Society 2024
Quantum error correction (QEC) faces a significant challenge in realistic noisy intermediate-scale quantum (NISQ) devices: correlated decoherence. Building upon the foundational QEC-C protocol, we introduce QEC-C II, a scalable framework that delivers robust fault tolerance against spatially and temporally correlated noise. By integrating decoherence-free subspace (DFS) principles and correlation-aware adaptive feedback, QEC-C II achieves exponential error suppression in simulation under correlated noise models, with fewer physical qubits than typical topological baselines for the same target error in our benchmarks. The protocol leverages an enhanced scaling law, β(n) = 0.788 e 0.360n , and efficiently suppresses noise with minimal computational overhead. We validate QEC-C II on 28-qubit GHZ states, extend it to 56-qubit subspaces, and conduct 84-qubit stress-test simulations under correlated noise models. The results demonstrate sustained fidelities exceeding 99.99 % in simulations under realistic dephasing, amplitude-damping, burst-error, and correlated decoherence scenarios, with rapid convergence (typically ≤ 2 iterations in our simulations). QEC-C II significantly reduces both resource and control complexity, simplifying hardware integration and improving performance with increasing system size. This work provides a practical pathway toward resource-efficient fault tolerance in quantum processors operating in real-world correlated environments.
Superconducting devices as quantum bits (qubits) are one of the most promising candidates for implementing a practical quantum computer. Over the last decade, quantum coherence times of superconducting qubits have been continuously improved. Operating qubits in noise insensitive points, eliminating the participation of the lossy materials, and better isolation from environment increased the decoherence times from nanoseconds to tens of microseconds. One recent approach on the qubit design is to shunt the Josephson junctions with large capacitors to reduce the sensitivity to noise and to redistribute the stored electromagnetic energy in a well-engineered area. This approach was first applied on charge qubits and later adopted to other types of superconducting qubits. \n \nIn this thesis, we present the design and the characterization of a three-Josephson junction superconducting circuit with three large shunt capacitors. We present experiments on decoherence in the circuit used as a qubit. The qubit relaxation time T₁ is reaching as high as 47 μs and the spin-echo dephasing time T₂ = 9.4 μs. In addition, we present spectroscopy experiments and decoherence characterization in the qutrit subspace formed by the lowest three energy levels. The spectroscopy data is in excellent agreement with the complete circuit model based on the system capacitance matrix. At the flux symmetry point, the circuit has a large anharmonicity, defined as the difference between the 1-2 and 0-1 transition frequencies, approaching 2π × 3.7 GHz, which is enabling fast single qubit operations. We performed randomized benchmarking with the qubit gates with a duration of 1.62 ns and an average gate fidelity of 99.9%. \n \nMoreover, we present experiments with multi-level control in qutrit subspace, formed by the lowest three energy levels. We demonstrate a single step experimental implementation of a generalized Walsh-Hadamard gate. We use a decomposition of the quantum gate into two unitary operations, one implemented by an off-diagonal Hamiltonian and the other implemented by a diagonal Hamiltonian. The off-diagonal Hamiltonian is obtained by the simultaneous driving of the transitions between levels 0-1, 1-2, and 0-2, with the latter being a two-photon process. The diagonal Hamiltonian is effectively implemented by appropriately shifting the phases of adjacent pulses. The gate is characterized using tomography process and the average fidelity exceeds 90%, in good agreement with numerical simulations that take into account the multi-level structure of the system.
We study a deterministic modulation protocol, Q-Loop, that replaces multi-axis, measurementdependent control with a single scalar waveform and is implementable as an open-loop schedule on current NISQ hardware. Building on earlier work where Q-Loop was shown to reduce both the dephasing functional χ(τ ) and the minimum control amplitude required to stabilize few-qubit GHZ states under classical 1/f noise, we revisit the protocol with a more conservative analytic treatment and a quantitative comparison to alternative empirical scaling forms for modest system sizes (n = 2–8 qubits). In a pure-dephasing (or effectively commuting) regime we derive the filter-function structure of an idealized Q-Loop waveform and show that it produces a discrete comb of sidebands with tunable low-frequency suppression relative to free evolution and standard Carr–Purcell (CP) sequences. For more general noise channels the scalar filter-function picture is used as a qualitative guide, and quantitative statements are obtained from stochastic-Hamiltonian simulations with classical 1/f γ noise. Using QuTiP-based simulations of Schrödinger dynamics with time-dependent Hamiltonians and classical 1/f γ local and correlated noise, we compute the minimum control amplitude β ∗ (n) needed to maintain a fixed target fidelity as a function of system size n for n = 2–8 qubits. Over this range the ensemble-averaged β ∗ (n) data are empirically well described by β ∗ (n) ≈ Aeαn with α ≃ 0.23–0.25, while quadratic and power-law forms yield systematically higher residuals and poorer goodness-of-fit metrics (including R2 , RMSE, and Bayesian information criterion), with BIC values for the exponential model typically 10–15 units lower than for polynomial alternatives. We emphasize that this exponential behaviour is an empirical description over a finite range, not an asymptotic law. We further map the Q-Loop-induced reduction in decoherence onto a toy physical error rate p and propagate this into a repetition-code capacity model. For a fixed phenomenological mapping, Q-Loop preprocessing yields an apparent 5–6× elevation of toy thresholds relative to an amplitudematched CP baseline, although these numbers are not intended as accurate thresholds for any specific fault-tolerant architecture. Finally, we discuss deployment on superconducting, trapped-ion, and photonic platforms using a Python-based waveform generator with PyVISA AWG integration, and outline how platform-specific noise spectra could be used to tune Q-Loop parameters in situ
Quantum computing holds the promise of solving problems that are intractable for classical computers, with applications ranging from optimization and materials simulation to cryptography. It achieves this by leveraging the exponentially scaling dimensionality of the space encoding quantum information and by executing algorithms on quantum registers in superposition states – a feature often referred to as quantum parallelism. However, while encoding information in computational units capable of exploring a continuous set of quantum states enables exponential scaling of computational power with system size, quantum systems are also more susceptible to errors than their classical counterparts. These errors take the form of both control errors, where miscalibration of the control pulses causes coherent errors on the qubit states, as well as incoherent errors due to energy relaxation and dephasing. Scaling quantum systems to run useful algorithms involving hundreds or thousands of logical qubits will require quantum error correction. In this approach, quantum information is redundantly encoded across an entangled state of many physical qubits. This has enabled experimental demonstrations across various platforms – including ion traps, superconducting circuits, and neutral atoms – showing that encoded quantum states can be preserved beyond the coherence times of the constituting physical qubits. However, quantum state preservation is only one component needed for scalable quantum computing. To execute algorithms, it is also necessary to implement quantum gates on and between encoded qubits, in a way that maintains fault tolerance by preserving the ability to correct errors as they occur during the computation. In the first part of this thesis, we demonstrate the implementation of an error-corrected quantum operation that entangles two logical qubits. This is achieved by performing lattice surgery on a distance-three surface code qubit, resulting in a logical Bell state encoded in distance-three repetition codes, which enable the correction of single bit-flip errors. We further introduce techniques to benchmark and characterize the performance of logical operations, including applying the protocol to arbitrary logical input states and performing logical quantum process tomography. Together, these results constitute one of the first realizations of error-corrected lattice surgery in superconducting circuits. While quantum error correction can correct errors provided they occur with sufficiently low frequency, it may fail when many qubits experience errors simultaneously. In the second part of this thesis, we therefore shift focus to a specific error mechanism known to cause correlated errors in superconducting circuits – quasiparticle-induced decoherence. In this case, various forms of energy deposition on the quantum device can break Cooper pairs into quasiparticles, which may subsequently diffuse to the tunnel junction and interact with the qubit state, thereby causing decoherence. In this thesis, we investigate the impact of quasiparticle tunneling on qubit performance, with a focus on infrared-induced quasiparticles. We compare the sensitivity of niobium-based qubits to those made from tantalum – a material that has gained interest in recent years following demonstrations of qubits with improved coherence times based on this material. Using a thermal radiator source, we show that the performance of tantalum qubits may be limited by infrared-induced quasiparticles in typical superconducting circuit experimental setups. By employing both ambient and in-line infrared filters, we investigate the effectiveness of different filtering strategies and develop best practices for engineering cryogenic environments for superconducting quantum processors. The results presented in this thesis contribute to the advancement of quantum computing based on superconducting circuits by implementing and characterizing quantum error-corrected operations, and by investigating quasiparticles as a source of decoherence, along with strategies to improve infrared filtering and signal conditioning in cryogenic environments for future fault-tolerant quantum computing.
We report experimental measurements comparing the coherence decay of three-qubit Greenberger-Horne-Zeilinger (GHZ) entangled states versus locally coherent product states (|+++⟩) under idle time evolution on IBM Heron quantum processors. Across three different processor generations (Heron r1, r2, r3), we consistently observe that the GHZ state maintains higher fidelity than the product state as idle delay increases. Decay rate analysis reveals that |+++⟩ decays 2.4–13.8× faster than GHZ depending on the backend. A control experiment with |000⟩ confirms the decay mechanism is dominated by dephasing (T₂-type noise) rather than energy relaxation (T₁) or readout errors. These results demonstrate a structural dependence of coherence stability on the topology of the quantum state. Backends: ibm_fez (Heron r2), ibm_torino (Heron r1), ibm_boston (Heron r3)Configuration: 3 qubits, 4000 shots, 20 repetitions per delay pointDelays: 0, 500, 1000, 2000, 4000 dt