Controlled-NOT (CNOT) gates are commonly included in the standard gate set of quantum processors and provide an important way to entangle qubits. For fixed-frequency qubits using the cross-resonance entangling technique, using the higher-frequency qubit to control the lower-frequency qubit enables much shorter entangling times than using the lower-frequency qubit as the control. Consequently, when implementing a CNOT gate where logical control by the lower-frequency qubit is needed, compilers may implement this functionality by using an equivalent circuit such as placing Hadamard gates on both qubits before and after a CNOT gate controlled by the higher-frequency qubit. However, since the implementation is different depending on which qubit is the control, a natural question arises regarding the relative performance of the implementations. We have explored this using quantum processors on the IBM Q network. The basic circuit used consisted of operations to create a Bell State, followed by the inverse operations so as to return the qubits to their initial state in the absence of errors (Hadamard + CNOT + barrier + CNOT + Hadamard). The circuit depth was varied using multiples of this basic circuit. An asymmetry in the error of the final state was observed that increased with the circuit depth. The strength and direction of the asymmetry was unique but repeatable for each pair of coupled qubits tested. This observation suggests that the asymmetry in CNOT implementation should be characterized for the qubits of interest and incorporated into circuit transpilation to obtain the best accuracy for a particular computation.
Controlled-NOT (CNOT) gates are commonly included in the standard gate set of quantum processors and provide an important way to entangle qubits. For fixed-frequency qubits using the cross-resonance entangling technique, using the higher-frequency qubit to control the lower-frequency qubit enables much shorter entangling times than using the lower-frequency qubit as the control. Consequently, when implementing a CNOT gate where logical control by the lower-frequency qubit is needed, compilers may implement this functionality by using an equivalent circuit such as placing Hadamard gates on both qubits before and after a CNOT gate controlled by the higher-frequency qubit. However, since the implementation is different depending on which qubit is the control, a natural question arises regarding the relative performance of the implementations. We have explored this using quantum processors on the IBM Q network. The basic circuit used consisted of operations to create a Bell State, followed by the inverse operations so as to return the qubits to their initial state in the absence of errors (Hadamard + CNOT + barrier + CNOT + Hadamard). The circuit depth was varied using multiples of this basic circuit. An asymmetry in the error of the final state was observed that increased with the circuit depth. The strength and direction of the asymmetry was unique but repeatable for each pair of coupled qubits tested. This observation suggests that the asymmetry in CNOT implementation should be characterized for the qubits of interest and incorporated into circuit transpilation to obtain the best accuracy for a particular computation.
We present a theoretical analysis of the selective darkening method for implementing quantum controlled-NOT (CNOT) gates. This method, which we have recently proposed and demonstrated, consists of driving two transversely coupled quantum bits (qubits) with a driving field that is resonant with one of the two qubits. For specific relative amplitudes and phases of the driving field felt by the two qubits, one of the two transitions in the degenerate pair is darkened or, in other words, becomes forbidden by effective selection rules. In these driving conditions, the evolution of the two-qubit state realizes a CNOT gate. The gate speed is found to be limited only by the coupling energy J , which is the fundamental speed limit for any entangling gate. Numerical simulations show that at gate speeds corresponding to 0.48 J and 0.07 J , the gate fidelity is 99% and 99.99%, respectively, and increases further for lower gate speeds. In addition, the effect of higher-lying energy levels and weak anharmonicity is studied, as well as the scalability of the method to systems of multiple qubits. We conclude that in all these respects this method is competitive with existing schemes for creating entanglement, with the added advantages of being applicable for qubits operating at fixed frequencies (either by design or for the exploitation of coherence sweet-spots) and having the simplicity of microwave-only operation.
Engineering high-fidelity two-qubit gates is an indispensable step toward practical quantum computing. For superconducting quantum platforms, one important setback is the stray interaction between qubits, which causes significant coherent errors. For transmon qubits, protocols for mitigating such errors usually involve fine-tuning the hardware parameters or introducing usually noisy flux-tunable couplers. In this work, we propose a simple scheme to cancel these stray interactions. The coupler used for such cancelation is a driven high-coherence resonator, where the amplitude and frequency of the drive serve as control knobs. Through the resonator-induced-phase interaction, the static ZZ coupling can be entirely neutralized. We numerically show that such a scheme can enable short and high-fidelity entangling gates, including cross-resonance controlled-not (cnot) gates within 40 ns and adiabatic controlled-Z gates within 140 ns. Our architecture is not only ZZ-free, but also contains no extra noisy components, such that it preserves the coherence times of fixed-frequency transmon qubits. With the state-of-the-art coherence times, the error of our cross-resonance cnot gate can be reduced to below ${10}^{\ensuremath{-}4}$.
Abstract The utility of a quantum computer is highly dependent on the ability to reliably perform accurate quantum logic operations. For finding optimal control solutions, it is of particular interest to explore model-free approaches, since their quality is not constrained by the limited accuracy of theoretical models for the quantum processor—in contrast to many established gate implementation strategies. In this work, we utilize a continuous control reinforcement learning algorithm to design entangling two-qubit gates for superconducting qubits; specifically, our agent constructs cross-resonance and CNOT gates without any prior information about the physical system. Using a simulated environment of fixed-frequency fixed-coupling transmon qubits, we demonstrate the capability to generate novel pulse sequences that outperform the standard cross-resonance gates in both fidelity and gate duration, while maintaining a comparable susceptibility to stochastic unitary noise. We further showcase an augmentation in training and input information that allows our agent to adapt its pulse design abilities to drifting hardware characteristics, importantly, with little to no additional optimization. Our results exhibit clearly the advantages of unbiased adaptive-feedback learning-based optimization methods for transmon gate design.
Entangling gates between qubits are a crucial component for performing algorithms in quantum computers. However, any quantum algorithm must ultimately operate on error-protected logical qubits encoded in high-dimensional systems. Typically, logical qubits are encoded in multiple two-level systems, but entangling gates operating on such qubits are highly complex and have not yet been demonstrated. Here we realize a controlled NOT (CNOT) gate between two multiphoton qubits in two microwave cavities. In this approach, we encode a qubit in the high-dimensional space of a single cavity mode, rather than in multiple two-level systems. We couple two such encoded qubits together through a transmon, which is driven by an RF pump to apply the gate within 190 ns. This is two orders of magnitude shorter than the decoherence time of the transmon, enabling a high-fidelity gate operation. These results are an important step towards universal algorithms on error-corrected logical qubits.
A scalable and programmable quantum computer holds the potential to solve computationally intensive tasks that classical computers cannot accomplish within a reasonable time frame, achieving quantum advantage. However, the vulnerability of the current generation of quantum processors to errors poses a significant challenge towards executing complex and deep quantum circuits required for practical problems. Quantum error-correction codes such as stabilizer codes offer a promising path forward for fault-tolerant quantum computing; however, their realization on quantum hardware is an on-going area of research. In particular, fault-tolerant quantum processing must employ logical gates on logical qubits with error suppression with realistically large size codes. This work has implemented a transversal controlled-not (cnot) gate between two logical qubits constructed using the repetition code with flag qubits, and demonstrated error suppression with increasing code size under multiple rounds of error detection and correction. Our results conducted on IBM quantum devices through cloud access show that despite the potential for error propagation among logical qubits during the transversal cnot gate operation, scaling the code distance as we increase the number of physical qubits from 21 to 39 and 57 can suppress errors, which persists over ten rounds of error detection and correction. Our work establishes the feasibility of employing logical cnot gates alongside error detection on a superconductor-based processor using current generation quantum hardware.
Abstract Entangling gates between qubits are a crucial component for performing algorithms in quantum computers. However, any quantum algorithm must ultimately operate on error-protected logical qubits encoded in high-dimensional systems. Typically, logical qubits are encoded in multiple two-level systems, but entangling gates operating on such qubits are highly complex and have not yet been demonstrated. Here we realize a controlled NOT (CNOT) gate between two multiphoton qubits in two microwave cavities. In this approach, we encode a qubit in the high-dimensional space of a single cavity mode, rather than in multiple two-level systems. We couple two such encoded qubits together through a transmon, which is driven by an RF pump to apply the gate within 190 ns. This is two orders of magnitude shorter than the decoherence time of the transmon, enabling a high-fidelity gate operation. These results are an important step towards universal algorithms on error-corrected logical qubits.