Phantom Codes Achieve Entangling Logical Qubits Without Physical Operations, up to 8

Researchers are tackling a fundamental challenge in scalable quantum computing: the creation of fault-tolerant logical entangling gates without relying on resource-intensive physical operations. Jin Ming Koh, Anqi Gong, and Andrei C. Diaconu, alongside Daniel Bochen Tan, Alexandra A. Geim, Michael J. Gullans et al, from the University of Maryland and National Institute of Standards and Technology, present a novel approach using ‘phantom codes’ that achieve perfect-fidelity entanglement simply by relabelling physical qubits during compilation. This work is significant because it bypasses the limitations of traditional two-qubit gates and measurements, potentially offering substantial reductions in qubit overhead and improvements in logical fidelity for demanding quantum tasks like GHZ-state preparation and many-body simulations, establishing phantom codes as a promising architectural pathway for future quantum computers.

Phantom Codes Enable Perfect Fidelity Entangling Gates

Scientists have demonstrated a new approach to fault-tolerant quantum computing using phantom codes, a novel class of quantum error-correcting codes. These codes uniquely realize entangling gates between logical qubits purely through relabelling of physical qubits during compilation, achieving perfect fidelity without spatial or temporal overhead. The research team systematically studied these codes, identifying them through both numerical and analytical methods, and constructing higher-distance phantom-code families using Reed-Muller codes and the binarization of qudit codes. They exhaustively enumerated 2. The team achieved this by focusing on logical operations, specifically, targeted logical entangling gates, and identifying codes that support them with minimal overhead. Through end-to-end noisy simulations incorporating state preparation, full QEC cycles, and realistic physical error rates, they demonstrated scalable advantages of phantom codes over the Surface code for multiple tasks. These simulations revealed a one-to-two order-of-magnitude reduction in logical infidelity at comparable qubit overhead for both GHZ-state preparation and Trotterized many-body simulation tasks, given a modest preselection acceptance rate.

The study unveils that phantom codes offer significant benefits for workloads with dense local entangling structure, effectively shifting the cost of computation from physical operations to classical circuit compilation. This approach allows for the absorption of qubit permutations into the compilation stage, eliminating the need for physical implementation of entangling gates and thus achieving perfect fidelity. Furthermore, the research introduces general tools for systematically exploring the broader landscape of quantum error-correcting codes, expanding the known phantom code landscape from a single error-correcting code and a single error-detecting code family to over a hundred thousand new instances and multiple error-correcting families. The work establishes phantom codes as a promising architectural route for fault-tolerant quantum computation, potentially enabling more efficient and scalable quantum computers. By jointly optimizing storage and computation, and by placing logical operations at the centre of the design, this research opens new avenues for reducing QEC overheads and achieving suppressed logical error rates, paving the way for practical applications in areas such as materials science and drug discovery.

Phantom Code Enumeration and Construction Techniques

Scientists introduced phantom codes, quantum error-correcting codes realizing entangling gates via relabelling of physical qubits during compilation, achieving perfect fidelity without spatial or temporal overhead. The research team systematically studied these codes using both numerical and analytical techniques to identify and characterize their properties. Initially, they exhaustively enumerated all inequivalent CSS codes up to n = 14, a total of 2.71 × 1010 instances, and extended this enumeration to n = 21 using SAT-based methods. To demonstrate the scalability of phantom codes, the study employed end-to-end noisy simulations incorporating state preparation, complete quantum error correction cycles, and realistic physical error rates. These simulations compared phantom codes against the surface code across multiple tasks, providing a direct performance evaluation. The simulations revealed a one-to-two order-of-magnitude reduction in logical infidelity at comparable qubit overhead for both GHZ-state preparation and Trotterized many-body simulation tasks, contingent on a modest preselection acceptance rate.

This work establishes phantom codes as a viable architectural route for fault-tolerant quantum computation, offering scalable benefits for workloads with dense local entangling structure. The team pioneered general tools for systematically exploring the broader landscape of quantum error-correcting codes, facilitating future advancements in the field. The approach enables the realization of logical entangling gates solely through physical qubit permutations, effectively eliminating the need for complex gate sequences and reducing error accumulation. This method achieves perfect fidelity by absorbing these permutations into the circuit compilation process, a significant innovation in quantum error correction design.

Phantom Codes Enable Perfect Fidelity Entangling Gates

Scientists have identified a new class of quantum codes, termed phantom codes, that realize entangling gates between logical qubits purely through relabelling of physical qubits during compilation, achieving perfect fidelity with no spatial or temporal overhead. Experiments revealed a substantial expansion of the phantom-code landscape, growing from a single known error-correcting code and one error-detecting code family to over one hundred thousand new phantom code instances and multiple error-correcting families.

Through end-to-end noisy simulations, incorporating state preparation, full quantum error correction cycles, and realistic physical rates, the team demonstrated scalable advantages of phantom codes over the surface code across multiple tasks. Measurements confirm a one-to-two order-of-magnitude reduction in logical infidelity at comparable qubit overhead for both GHZ-state preparation and Trotterized many-body simulation tasks, achieved with a modest preselection acceptance rate. Data shows that for GHZ-state preparation and Trotterized many-body simulation, phantom codes delivered improvements in logical fidelity ranging from one to two orders of magnitude, utilising a similar number of physical qubits and a preselection acceptance rate of approximately 24%, across systems ranging from 8 to 64 logical qubits. Tests prove that, in addition to the logical entangling gates generated via recompilation, all discovered phantom codes support fault-tolerant logical Clifford and non-Clifford gates.

The breakthrough delivers practical tools for implementing non-LDPC phantom codes, also applicable to other non-LDPC codes, including improved decoding and fault-tolerant state preparation. Results demonstrate that phantom codes enable arbitrary CNOT circuits across multiple codeblocks to be efficiently executed by combining zero-depth in-block logical CNOT gates with transversal interblock CNOTs. The team’s work establishes phantom codes as a viable architectural route to fault-tolerant computation, offering scalable benefits for workloads with dense local entangling structure and introducing general tools for systematically exploring the broader landscape of codes.