We propose a scheme for realizing quantum gates [controlled-NOT (CNOT) and Toffoli] using a two-level quantum system by means of a pulsed bias. We show how to realize a CNOT gate using a two-qubit, two-level coupled system and a Toffoli gate using a three-qubit, two-level coupled system. For the CNOT gate, we show how to reduce the $4\ifmmode\times\else\texttimes\fi{}4$ Hamiltonian of the coupled system to a $2\ifmmode\times\else\texttimes\fi{}2$ Hamiltonian in order to solve for parameter values of the system. When these values are substituted into the coupled system equations for the two-qubit system, the simulation results confirm the CNOT gate operation. We further demonstrate our proposed scheme for a CNOT gate operation using a multilevel system of two coupled superconducting quantum interference devices as a particular example. We next use the same approach to implement a Toffoli gate using a three-qubit system.
Leveraging noise bias, where phase-flip errors dominate over bit-flips, can drastically reduce the hardware overhead of fault-tolerant quantum computation, but existing approaches require bias-preserving CNOT gates whose implementation remains experimentally challenging and is provably impossible for strictly two-dimensional systems. We show that high-fidelity quantum non-demolition (QND) multi-qubit Pauli
Z measurements provide an equally powerful yet more accessible primitive. We demonstrate that such measurements can fully replace bias-preserving CNOT gates for compiling all operations required by bias-tailored error correction, including stabilizer measurements for repetition codes, XZZX surface codes, and LDPC codes. We propose concrete physical implementations of this primitive for two platforms: solid-state nuclear spins coupled to electron spin ancillas, and dissipatively stabilized superconducting cat qubits. Through circuit-level numerical simulations, we show that an asymmetric XZZX surface code implemented with weight-four QND
Z measurements achieves a phase-flip threshold of
∼1.25% and provides a qubit overhead reduction of up to
6× compared to a bias-unaware surface code at noise bias
η=104. In the regime of very large bias, a repetition code with QND
Z measurements attains a threshold of
∼2.3% and achieves overhead comparable to that of a bias-preserving CNOT scheme, without requiring such a gate. Our results establish QND multi-
Z measurements as a practical and hardware-efficient route to fault-tolerant quantum computation for a broad class of biased-noise platforms.
We present a universal scheme of pulsed operations suitable for the IBM oscillator-stabilized flux qubit comprising the controlled-σ z (cphase) gate, single-qubit preparations and measurements. Based on numerical simulations, we argue that the error rates for these operations can be as low as about 0.5% and that noise is highly biased, with phase errors being stronger than all other types of errors by a factor of nearly 10 3 . In contrast, the design of a controlled-σ x (cnot) gate for this system with an error rate of less than about 1.2% seems extremely challenging. We propose a special encoding that exploits the noise bias allowing us to implement a logical cnot gate where phase errors and all other types of errors have nearly balanced rates of about 0.4%. Our results illustrate how the design of an encoding scheme can be adjusted and optimized according to the available physical operations and the particular noise characteristics of experimental devices.
We study the coupled-qubit oscillation driven by an oscillating field. When the period of the non-resonant mode is commensurate with that of the resonant mode of the Rabi oscillation, we show that the controlled-NOT (CNOT) gate operation can be demonstrated. For a weak coupling the CNOT gate operation is achievable by the commensurate oscillations, while for a sufficiently strong coupling it can be done for arbitrary parameter values. By finely tuning the amplitude of oscillating field it is shown that the high fidelity of the CNOT gate can be obtained for any fixed coupling strength and qubit energy gap in experiments.