Abstract A controlled-NOT gate acting on a coherent control qubit converts single-qubit coherence into two-qubit entanglement, ideally only if the gate is perfect and the entangled state is used at once. We analyze how this conversion degrades when the gate carries a fault and the output then idles in a finite-temperature environment of relaxation, thermal excitation, and dephasing. Four representative fault classes are treated: coherent under- or over-rotation, a coherent control-phase error, a stochastic phase flip, and a stochastic bit flip. The gate faults and the idle environment are matched in a limited but explicit sense, referred to a common set of device parameters; a commutation argument identifies when an intra-gate noise process reduces exactly to one of the four classes, with the residual error quantified in the borderline cases. Within this deliberately minimal model we obtain closed-form expressions for the conversion efficiency of each fault class, for the entanglement surviving the idle period, and for the boundary at which entanglement disappears abruptly, recovering the known amplitude-damping threshold for sudden death as a special case. The classes leave distinct signatures: coherent calibration errors are insensitive to leading order and therefore mild, stochastic faults degrade the conversion in proportion to their probability, and the bit-flip class alone carries an angle-dependent signature separating it from a phase flip. Control-phase errors leave the entanglement measure unchanged and are invisible to this benchmark, a limitation we state plainly rather than present as a strength. All analytic results are verified against independent numerical simulation, and a diagnostic inferring the dominant fault class from angle-resolved measurements identifies strong stochastic faults reliably but cannot separate weak coherent errors from an ideal gate. The results are intended as transparent analytic benchmarks for a specific resource-conversion task, not as general device characterization.
Abstract A controlled-NOT gate acting on a coherent control qubit converts single-qubit coherence into two-qubit entanglement, ideally only if the gate is perfect and the entangled state is used at once. We analyze how this conversion degrades when the gate carries a fault and the output then idles in a finite-temperature environment of relaxation, thermal excitation, and dephasing. Four representative fault classes are treated: coherent under- or over-rotation, a coherent control-phase error, a stochastic phase flip, and a stochastic bit flip. The gate faults and the idle environment are matched in a limited but explicit sense, referred to a common set of device parameters; a commutation argument identifies when an intra-gate noise process reduces exactly to one of the four classes, with the residual error quantified in the borderline cases. Within this deliberately minimal model we obtain closed-form expressions for the conversion efficiency of each fault class, for the entanglement surviving the idle period, and for the boundary at which entanglement disappears abruptly, recovering the known amplitude-damping threshold for sudden death as a special case. The classes leave distinct signatures: coherent calibration errors are insensitive to leading order and therefore mild, stochastic faults degrade the conversion in proportion to their probability, and the bit-flip class alone carries an angle-dependent signature separating it from a phase flip. Control-phase errors leave the entanglement measure unchanged and are invisible to this benchmark, a limitation we state plainly rather than present as a strength. All analytic results are verified against independent numerical simulation, and a diagnostic inferring the dominant fault class from angle-resolved measurements identifies strong stochastic faults reliably but cannot separate weak coherent errors from an ideal gate. The results are intended as transparent analytic benchmarks for a specific resource-conversion task, not as general device characterization.
An ideal CNOT maps the phase of a coherent qubit onto the coherence between ∣00⟩ and ∣11⟩ of a two-qubit state, producing an output that carries both entanglement and estimable phase information. We ask how post-gate noise degrades these two quantities, and find that they are not lost together. For the phase-encoded X states generated by the protocol, the negativity is a thresholded difference of the surviving coherence z=fκ and a population penalty g, vanishing once fκ≤g, while the phase quantum Fisher information (QFI) is the smooth ratio Fφ=4z2/(a+b), which stays positive for any nonzero coherence. As a result there is an exact region of state space in which the output is separable but still phase-sensitive. We characterize this region, give the residual QFI Fφ⋆=4g⋆2/(1−2g⋆) at entanglement death, and show that channels reaching death at the same coordinate share this residual, with global and independent local depolarization forming one such class and Fφ⋆=1/6 at maximal input coherence. Four standard channels appear as trajectories through this common geometry, and asymmetric population transfer adds a third coordinate that changes the entanglement but leaves the QFI unchanged, which marks where the two-coordinate description applies. We identify a measurement that attains the bound and compare with a direct single-qubit probe, which is more precise under matched exposure; the results are therefore reference benchmarks for phase-information retention, not a claim of metrological advantage.
Coherence-to-entanglement conversion transforms single-qubit superposition into a practical two-qubit resource, but noise limits this process in near-term quantum hardware. We derive closed-form benchmarks for a minimal CNOT primitive in which a coherent qubit and an incoherent ancilla generate entanglement before undergoing phase damping, global depolarizing, amplitude damping, or independent local depolarizing noise. Using the ℓ1-norm of coherence and negativity, we prove the noiseless law N0=Cℓ1/2, valid for arbitrary mixed inputs, and obtain exact negativities, survival fractions, and entanglement-sudden-death thresholds. For all X-state-preserving channels, a master relation shows that entanglement loss results from the competition between coherence suppression and partial-transpose spectral shifts. Phase damping yields η=1−p without finite-noise sudden death; global depolarization gives coherence-dependent sudden death; amplitude damping adds an excited-population penalty and sudden death only for θ>π/4; while local depolarization is most destructive at equal depolarizing strength. The initial survival slopes, −1, −3/2, −2, and −3, act as compact noise fingerprints. Since concurrence satisfies C=2N for the generated states, all robustness rankings remain unchanged. Mapping channel parameters to T1, Tφ, and average gate fidelity connects the theory to hardware-level performance.
We develop an analytical framework for coherence-to-entanglement conversion in bipartite high-dimensional quantum systems, so-called qunits. An arbitrary coherent input qunit is coupled to an incoherent ancilla through a generalized controlled-shift operation, producing a maximally correlated bipartite state. By analyzing the partial transpose of the output state, we establish an exact dimension-independent connection between the input coherence and the generated entanglement. We then study how this conversion is affected by three standard noise processes applied after the conversion step: phase damping, global depolarizing noise, and independent amplitude damping. The resulting expressions show that these channels degrade entanglement in qualitatively different ways. Phase damping leads to a uniform attenuation of the entanglement generated from coherence, depolarizing noise introduces pairwise thresholds associated with entanglement sudden death, and amplitude damping produces an asymmetric decay governed by relaxation toward the ground state. For maximally coherent inputs, the general results reduce to simple closed-form behavior, allowing direct comparison of the three noise mechanisms as the system dimension increases. In particular, global depolarizing noise exhibits a dimension-dependent sudden-death threshold, while amplitude damping leads to a smooth suppression in the maximally coherent case. These results provide useful analytical benchmarks for high-dimensional resource conversion and for assessing noisy entanglement generation in qudit-based quantum-information settings.
ABSTRACT Coherence‐to‐entanglement conversion transforms single‐qubit superposition into a practical two‐qubit resource, but noise limits this process in near‐term quantum hardware. We derive closed‐form benchmarks for a minimal CNOT primitive in which a coherent qubit and an incoherent ancilla generate entanglement before undergoing phase damping, global depolarizing, amplitude damping, or independent local depolarizing noise. Using the ‐norm of coherence and negativity, we prove the noiseless law , valid for arbitrary mixed inputs, and obtain exact negativities, survival fractions, and entanglement‐sudden‐death thresholds. For all ‐state‐preserving channels, a master relation shows that entanglement loss results from the competition between coherence suppression and partial‐transpose spectral shifts. Phase damping yields without finite‐noise sudden death; global depolarization gives coherence‐dependent sudden death; amplitude damping adds an excited‐population penalty and sudden death only for ; while local depolarization is most destructive at equal depolarizing strength. The initial survival slopes, , , , and , act as compact noise fingerprints. Since concurrence satisfies for the generated states, all robustness rankings remain unchanged. Mapping channel parameters to , , and average gate fidelity connects the theory to hardware‐level performance.
Present-day quantum processors are open systems in which dissipation and decoherence degrade the information carried by a quantum state as it propagates through a circuit. We study this degradation in dissipative random quantum circuits, modeling each two-qubit gate as a diluted unitary that interpolates between the intended unitary operation and a random dissipative quantum channel. Using the fidelity between the ideal and noisy output states as a diagnostic, we show that sufficiently random unitary gates or dissipative Kraus operators lead to a universal decay of the average fidelity. This decay is determined only by the dissipation strength, system size, and circuit depth, while microscopic details of the gates and noise, including the Kraus rank, appear only in subleading corrections to higher moments. We derive a closed-form expression for the average fidelity in terms of three physically meaningful error parameters, dissipation strength, coherent two-qubit gate-error strength, and connectivity-error probability. Finally, we identify the cases when dissipative effects can be reproduced by an unitary-noise model and when dissipation-induced decoherence remains distinguishable from coherent noise at the level of the average fidelity.
Abstract Because of their long coherence time and compatibility with industrial foundry processes, electron spin qubits are a promising platform for scalable quantum processors. A full-fledged quantum computer will need quantum error correction, which requires high-fidelity quantum gates. Analyzing and mitigating gate errors are useful to improve gate fidelity. Here, we demonstrate a simple yet reliable calibration procedure for a high-fidelity controlled-rotation gate in an exchange-always-on Silicon quantum processor, allowing operation above the fault-tolerance threshold of quantum error correction. We find that the fidelity of our uncalibrated controlled-rotation gate is limited by coherent errors in the form of controlled phases and present a method to measure and correct these phase errors. We then verify the improvement in our gate fidelities by randomized benchmark and gate-set tomography protocols. Finally, we use our phase correction protocol to implement a virtual, high-fidelity, controlled-phase gate.