This paper addresses high-fidelity Bell state preparation under depolarizing noise. A split-qubit approach is proposed: dynamic decoupling for the control qubit and error correction for the target qubit. Qiskit simulations show fidelity maintained at 1.0000, with error rates reduced from ~24% to 0.4%, requiring only four X gates. The method achieves low-complexity, high-fidelity entanglement preparation.
This paper addresses high-fidelity Bell state preparation under depolarizing noise. A split-qubit approach is proposed: dynamic decoupling for the control qubit and error correction for the target qubit. Qiskit simulations show fidelity maintained at 1.0000, with error rates reduced from ~24% to 0.4%, requiring only four X gates. The method achieves low-complexity, high-fidelity entanglement preparation.
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.
This study focuses on achieving high-fidelity preparation of Bell states in depolarization noise environments. Based on Qiskit simulations, we propose a quantum-bit-by-quantum-bit noise-resistant strategy: applying dynamic decoupling to control qubits and implementing quantum error correction for target qubits. Experimental results demonstrate that this strategy maintains fidelity at 1. 0000 while significantly reducing the error rate from approximately 24% to 0. 4%, requiring only four additional quantum gate operations. The method achieves high-fidelity quantum entanglement with low complexity, showcasing significant practical value. As the standard form. of two-qubit maximum entanglement state, the Bell states are widely applied in critical tasks such as quantum teleportation, superdense coding, and quantum key distribution. However, real quantum systems inevitably interact with their environment, leading to quantum state decoherence and a significant decrease in the fidelity of the Bell state. Existing anti-jamming schemes mainly fall into two categories: dynamic decoupling through periodic pulse application to cancel noise, and quantum error correction through redundant encoding to fix errors. However, dynamic decoupling requires extremely high synchronization for multi-qubit systems, while quantum error correction necessitates additional auxiliary qubits, resulting in an exponential growth in circuit complexity.
Realistic quantum computing is subject to noise. Therefore, an important frontier in quantum computing is to implement noise-resilient quantum control over qubits. At the same time, dynamical decoupling can protect the coherence of qubits. Here we demonstrate non-trivial quantum evolution steered by dynamical decoupling control, which simultaneously suppresses noise effects. We design and implement a self-protected controlled-NOT gate on the electron spin of a nitrogen-vacancy centre and a nearby carbon-13 nuclear spin in diamond at room temperature, by employing an engineered dynamical decoupling control on the electron spin. Final state fidelity of 0.91(1) is observed in preparation of a Bell state using the gate. At the same time, the qubit coherence time is elongated at least 30 fold. The design scheme does not require the dynamical decoupling control to commute with the qubit interaction and therefore works for general qubit systems. This work marks a step towards implementing realistic quantum computing systems. Realistic quantum computers require a high degree of qubit control and must also be resilient to noise. Using dynamical decoupling control techniques, Liuet al.implement a self-protected controlled-NOT gate for electron and nuclear spins that retains a high final state fidelity.
Any quantum computation begins with some process of state preparation where the prepared state functions as the input value for the computation. For most states, preparation becomes exceedingly more demanding as the number of qubits increases. Moreover, the noise present in the gate operations further complicates the process by contributing to the decoherence of the state. This thesis studies possible approaches to address these problems. For a reader not familiar with the basic principles of quantum computing, Chapter 2 should provide a sufficient summary in order to follow through the rest of the thesis. In Chapter 3 a standard method of state preparation is presented in detail for 2 and 4-qubit cases and then generalized for an arbitrary number of qubits. However in order to present a comprehensive coverage, the necessary gate decompositions for state preparation are first presented and proved. The number of required quantum gates for the preparation of a general state increases exponentially in the number of qubits. Each gate introduces a small error in the computation, the cumulative effect of which can make the decoherence in the final state very severe. Therefore it is perhaps more suitable to prepare a less complex approximation of the target state with fewer gates to obtain better fidelity in the presence of noise. For this purpose, two methods are presented: low-rank state preparation algorithm (LRSP) and a genetic algorithm. LRSP provides a systematic way to generate circuits for approximate state preparation; however, for any given state LRSP can make only very specific approximations, giving us a very limited range of circuits to work with. For this reason our work introduces a genetic algorithm to iterate over the LRSP circuits and to provide a wider range of candidate circuits for approximate state preparation. Using this approach we prepared a range of approximate state preparation circuits for 1000 different Haar-random states and ran them with simulated noise on IBM Qiskit FakeVigo backend. We found that the numerical results matched closely with our theoretical prediction and showed that when run on a noisy quantum computer, the highest fidelity is obtained not for the exact state preparation circuit but for a shorter approximate circuit.
Preparing smooth real-amplitude quantum states is a key subroutine in quantum solvers for dissipative PDEs, such as LCHS, where discretized positive weights must be encoded into amplitudes. Exact state-preparation decompositions can reach unit fidelity ideally, but their two-qubit depth grows quickly and causes severe fidelity loss on NISQ hardware. We propose a low-depth, hardware-aware variational ansatz tailored to smooth, weakly entangled, near-real target distributions typical of damped PDE dynamics. The circuit uses one layer of local Ry rotations to generate real amplitudes, a nearest-neighbor CZ entangling layer to introduce limited entanglement, and additional Rz rotations implemented virtually as frame updates. Virtual Rz operations add no physical pulses and do not increase circuit duration, providing extra degrees of freedom without enlarging the gate footprint; in simulation they are treated as ideal to isolate their benefit. From a tensor-network viewpoint, the alternating structure restricts the state to a low-bond-dimension MPS, matching the target smoothness (for 3 qubits, bond dimension <= 2). We optimize parameters with COBYLA to minimize infidelity and benchmark against exact state preparation (Qiskit) and a RealAmplitudes (CZ) baseline. Under depolarizing noise representative of NISQ and early fault-tolerant regimes, the proposed single-layer circuit achieves high ideal fidelity with O(n) depth and substantially higher noisy fidelity than deeper exact constructions. In coherent-noise sweeps, virtual Rz parameters absorb systematic phase errors and axis mismatch, maintaining near-unity fidelity over a wide error range. These results indicate that virtual-Rz-enabled, low-depth circuits provide a practical, noise-resilient state-preparation primitive for PDE solvers on NISQ and early FTQC hardware.