One-way quantum computing is a promising candidate for fault-tolerant quantum computing. Here, we propose protocols to realize a deterministic one-way controlled-not (cnot) gate and one-way $X$ rotations on current quantum-computing platforms. By applying a delayed-choice scheme, we overcome a limit of most currently available quantum computers, which are unable to implement further operations on measured qubits or operations conditioned on measurement results from other qubits. Moreover, we decrease the error rate of the one-way logic gates, compared to the original protocol using local operations and classical communication. In addition, we apply our deterministic one-way cnot gate in the Deutsch-Jozsa algorithm to show the feasibility of our proposal. We demonstrate all these one-way gates and algorithms by running experiments on the cloud quantum-computing platform IBM Quantum Experience.
One-way quantum computing is a promising candidate for fault-tolerant quantum computing. Here, we propose protocols to realize a deterministic one-way controlled-not (cnot) gate and one-way X rotations on current quantum-computing platforms. By applying a delayed-choice scheme, we overcome a limit of most currently available quantum computers, which are unable to implement further operations on measured qubits or operations conditioned on measurement results from other qubits. Moreover, we decrease the error rate of the one-way logic gates, compared to the original protocol using local operations and classical communication. In addition, we apply our deterministic one-way cnot gate in the Deutsch-Jozsa algorithm to show the feasibility of our proposal. We demonstrate all these one-way gates and algorithms by running experiments on the cloud quantum-computing platform IBM Quantum Experience.
Abstract One-way quantum computation focuses on initially generating an entangled cluster state followed by a sequence of measurements with classical communication of their individual outcomes. Recently, a delayed-measurement approach has been applied to replace classical communication of individual measurement outcomes. In this work, by considering the delayed-measurement approach, we demonstrate a modified one-way CNOT gate using the on-cloud superconducting quantum computing platform: Quafu. The modified protocol for one-way quantum computing requires only three qubits rather than the four used in the standard protocol. Since this modified cluster state decreases the number of physical qubits required to implement one-way computation, both the scalability and complexity of the computing process are improved. Compared to previous work, this modified one-way CNOT gate is superior to the standard one in both fidelity and resource requirements. We have also numerically compared the behavior of standard and modified methods in large-scale one-way quantum computing. Our results suggest that in a noisy intermediate-scale quantum (NISQ) era, the modified method shows a significant advantage for one-way quantum computation.
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.
Quantum computers promise to solve computational problems that are inaccessible to classical machines. The reliable execution of large-scale quantum algorithms requires robust operations in the presence of noise. Quantum error correction addresses this challenge by encoding quantum information redundantly across several physical qubits, such that errors can be detected and corrected during a computation. However, no single error-correcting code intrinsically supports an inherently robust, fault-tolerant implementation of all gates needed for universal quantum computing. Moreover, most modern approaches to both quantum error correction and the implementation of universal logical operations on encoded qubits rely on mid-circuit measurements and feed-forward control. These types of operations are technologically demanding, often slow, and prone to high error rates, and they limit the overall success probability of quantum algorithms. In this thesis, we develop fault-tolerant protocols and circuits for quantum error correction and universal logical computation, with an emphasis on implementations compatible with current hardware systems. We first focus on fault-tolerant quantum error correction on small codes. By comparing different protocols, we identify trade-offs between compact circuit constructions and their robustness to noise. We then assess their practical performance by comparing numerical simulations of noisy circuits with experimental data. Beyond the preservation of encoded information, we study how universal logic can be implemented in a fault-tolerant manner on encoded qubits. A central approach considered in this thesis is code switching, in which logical information is transferred between two distinct error-correcting codes that support complementary sets of inherently fault-tolerant logical gates. In combination, these codes give access to a complete universal fault-tolerant logical gate set. In this thesis, we determine conditions that allow us to construct fault-tolerant protocols for code switching. We adapt these protocols to the capabilities of current hardware, thereby enabling the first experimental realization of universal fault-tolerant logic by means of code switching. However, the overall performance of these schemes is limited by slow and noisy mid-circuit measurements. To address this bottleneck, we construct a suite of measurement-free fault-tolerant universal operations that do not require any measurements during the execution of an algorithm. In this framework, error correction and logical operations are implemented coherently as part of the quantum circuit, without mid-circuit measurements or in-sequence classical control. We introduce measurement-free code-switching schemes that can be scaled to arbitrary code distances through concatenation, and which thereby provide, in principle, arbitrarily strong error suppression. We further tailor our approach to the capabilities of current trapped-ion quantum processors. New circuit constructions support the first experimental implementation of a logical quantum algorithm without mid-circuit measurements, demonstrated through Grover's search on three encoded qubits. Together, the results of this thesis expand the toolbox for early fault-tolerant quantum computation. They show how protocols for quantum error correction and universal logical gates can be designed without mid-circuit measurements with realistic hardware constraints in mind, opening new pathways towards universal quantum logic.
The promise of tremendous computational power, coupled with the development of robust error-correcting schemes, has fuelled extensive efforts to build a quantum computer. The requirements for realizing such a device are confounding: scalable quantum bits (two-level quantum systems, or qubits) that can be well isolated from the environment, but also initialized, measured and made to undergo controllable interactions to implement a universal set of quantum logic gates. The usual set consists of single qubit rotations and a controlled-NOT (CNOT) gate, which flips the state of a target qubit conditional on the control qubit being in the state 1. Here we report an unambiguous experimental demonstration and comprehensive characterization of quantum CNOT operation in an optical system. We produce all four entangled Bell states as a function of only the input qubits' logical values, for a single operating condition of the gate. The gate is probabilistic (the qubits are destroyed upon failure), but with the addition of linear optical quantum non-demolition measurements, it is equivalent to the CNOT gate required for scalable all-optical quantum computation.
Topological color codes are widely acknowledged as promising candidates for fault-tolerant quantum computing. Neither a two-dimensional nor a three-dimensional topology, however, can provide a universal gate set {H, T, CNOT}, with the T-gate missing in the two-dimensional and the H-gate in the three-dimensional case. These complementary shortcomings of the isolated topologies may be overcome in a combined approach, by switching between a two- and a three-dimensional code while maintaining the logical state. In this work, we construct resource-optimized deterministic and non-deterministic code switching protocols for two- and three-dimensional distance-three color codes using fault-tolerant quantum circuits based on flag-qubits. Deterministic protocols allow for the fault-tolerant implementation of logical gates on an encoded quantum state, while non-deterministic protocols may be used for the fault-tolerant preparation of magic states. Taking the error rates of state-of-the-art trapped-ion quantum processors as a reference, we find a logical failure probability of 3% for deterministic logical gates, which cannot be realized transversally in the respective code. By replacing the three-dimensional distance-three color code in the protocol for magic state preparation with the morphed code introduced in [1], we reduce the logical failure rates by two orders of magnitude, thus rendering it a viable method for magic state preparation on near-term quantum processors. Our results demonstrate that code switching enables the fault-tolerant and deterministic implementation of a universal gate set under realistic conditions, and thereby provide a practical avenue to advance universal, fault-tolerant quantum computing and enable quantum algorithms on first, error-corrected logical qubits.
Quantum gate teleportation provides an approach to introduce nonlinear interactions between long-distance qubits, facilitating distributed quantum computation. We present two alternative protocols for deterministically teleporting controlled-not (cnot) and controlled-phase-flip (cpf) gates, using minimal resources---one entangled qubit (ebit) and two classical bits (cbits). Our protocols eliminate the need for local cnot gates at each party, which are typically required in the standard quantum circuit model [Eisert et al. Phys. Rev. A 62, 052317 (2000)]. Instead, by using a superposition of single-qubit gate orders, our approach makes quantum gate teleportation more experimentally feasible and flexible. Remarkably, the teleportation of the cpf gate and other two-qubit controlled unitary gates can be achieved by adjusting inherent single-qubit operations, reducing the need for single-qubit gates in cnot-based constructions. Additionally, we develop two optical architectures for the teleportation of these gates. The polarization-based and transverse spatial-based setups show that this approach is more feasible and practical, and pave a way for a distributed quantum computing network.