Mikhail Lukin

Performing large-scale, accurate quantum simulations of many-fermion systems is a central challenge in quantum science, with applications in chemistry, materials, and high-energy physics. Despite significant progress, realizing generic fermionic algorithms with qubit systems incurs significant space-time overhead, scaling as $O(N)$ for $N$ fermionic modes. Here we present a method for faster fermionic simulation with asymptotic space-time overhead of $O(\log(N))$ in the worst case, and $O(1)$ for circuits with additional structure, including important subroutines like the fermionic fast Fourier transform. This exponential reduction is achieved by using reconfigurable quantum systems with non-local connectivity, mid-circuit measurement, and classical feedforward, to generate dynamical fermion-to-qubit mappings. We apply this technique to achieve efficient compilation for key simulation tasks, including Hamiltonian simulation of the sparse Sachdev–Ye–Kitaev model and periodic materials, as well as free-fermion state-preparation. Moreover, we show that the algorithms themselves can be adapted to use only the $O(1)$-overhead structures to further reduce resource overhead. These techniques can lower gate counts by orders of magnitude for practical system sizes and are natively compatible with error corrected computation, making them ideal for early fault-tolerant quantum devices. Our results tightly bound the computational gap between fermionic and qubit models and open new directions in quantum simulation algorithm design and implementation.

High-rate quantum LDPC (qLDPC) codes reduce space overhead by densely packing many logical qubits into a single block of physical qubits. Here we extend such savings to computation by constructing batched fault-tolerant operations that apply the same logical gate across many code blocks in parallel. By leveraging shared physical resources to execute many logical operations in parallel, these operations realize high rates in space-time and significantly reduce computational costs. For arbitrary CSS qLDPC codes, we build batched gadgets with constant space-time overhead for (i) single-shot error correction and state preparation, (ii) code switching, and (iii) addressable Clifford gates. Using these batched gadgets we also construct parallel non-Clifford gates with low space-time cost. We outline principles for designing parallel quantum algorithms optimized for a batched architecture, and show in particular how lattice Hamiltonian dynamical simulations can be compiled efficiently. We also propose a near-term–friendly implementation using new self-dual Bivariate-Bicycle codes with high encoding rates (∼ 1/10), transversal Clifford gates, and global T gates, enabling Hamiltonian simulations with a lower space-time cost than analogous surface-code protocols and low-rate qLDPC protocols. These results open new paths toward scalable quantum computation via co-design of parallel quantum algorithms and high-rate fault-tolerant protocols.

We present a low-overhead architecture that supports the layout and resource estimation of large-scale fault-tolerant quantum algorithms. Utilizing recent advances in fault tolerance with transversal gate operations, this architecture achieves a run time speed-up on the order of the code distance d, which we find directly translates to run time improvements of large-scale quantum algorithms. Our architecture consists of functional building blocks of key algorithmic subroutines, including magic state factories, quantum arithmetic units, and quantum look-up tables. These building blocks are implemented using efficient transversal operations, and we design space-time-efficient versions of them that minimize interaction distance, thereby reducing atom move times and minimizing the volume for correlated decoding. We further propose models to estimate their logical error performance. We perform resource estimation for a large-scale implementation of Shor's factoring algorithm, one of the prototypical benchmarks for large-scale quantum algorithms, on dynamically reconfigurable neutral atom arrays, finding that 2048-bit RSA factoring can be executed with 19 million qubits in 5.6 days, for 1 ms QEC cycle times. This represents close to 50x speed-up of the run-time compared to existing estimates with similar assumptions, with no increase in space footprint, achieving a genuine reduction of the space-time volume required for error-corrected quantum computation, and bringing the runtime of large-scale algorithms on emerging platforms into a practical regime.

The preparation of high-fidelity non-Clifford (magic) states is an essential subroutine for universal quantum computation, but imposes substantial space-time overhead. Magic state factories based on high rate and distance quantum low-density parity check (LDPC) codes equipped with transversal non-Clifford gates can potentially reduce these overheads significantly, by circumventing the need for multiple rounds of distillation and by producing a large number of magic states in a single code-block. As a step towards realizing efficient, fault-tolerant magic state production, we introduce a class of finite block-length quantum LDPC codes which we name tricycle codes, generalizing the well-known bicycle codes to three homological dimensions. These codes can support constant-depth physical circuits that implement logical $CCZ$ gates between three code blocks. To construct these constant-depth $CCZ$ circuits, we develop new analytical and numerical techniques that apply to a broad class of three-dimensional homological and balanced product codes. We further show that tricycle codes enable single-shot state-preparation and error correction, leading to a highly efficient magic-state generation protocol. Numerical simulations of specific codes confirm robust performance under circuit-level noise, demonstrating a high circuit-noise threshold of $>0.5\%$. With modest post-selection, certain tricycle codes of block-lengths of only $50-100$ qubits are shown to achieve logical error-rates of $6\times 10^{-10}$ or lower. Finally, we construct optimal depth syndrome extraction circuits for tricycle codes and present a protocol for implementing them efficiently on a reconfigurable neutral atom platform.

Fault-tolerant logical entangling gates are essential for scalable quantum computing, but are limited by the error rates and overheads of physical two-qubit gates and measurements. To address this limitation we introduce phantom codes---quantum error-correcting codes that realize entangling gates between all logical qubits in a codeblock purely through relabelling of physical qubits during compilation, yielding perfect fidelity with no spatial or temporal overhead. We present a systematic study of such codes. First, we identify phantom codes using complementary numerical and analytical approaches. We exhaustively enumerate all 2.71 x 10^{10} inequivalent CSS codes up to n=14 and identify additional instances up to n=21 via SAT-based methods. We then construct higher-distance phantom-code families using quantum Reed--Muller codes and the binarization of qudit codes. Across all identified codes, we characterize other supported fault-tolerant logical Clifford and non-Clifford operations. Second, through end-to-end noisy simulations with state preparation, full QEC cycles, and realistic physical error rates, we demonstrate scalable advantages of phantom codes over the surface code across multiple tasks. We observe one–to–two–order-of-magnitude reduction in logical infidelity at comparable qubit overhead for GHZ-state preparation and Trotterized many-body simulation tasks, given a modest preselection acceptance rate. Our work establishes phantom codes as a viable architectural route to fault-tolerant quantum computation with scalable benefits for workloads with dense local entangling structure, and introduces general tools for systematically exploring the broader landscape of quantum error-correcting codes.

Quantum error correction (QEC) is required for large-scale computation, but incurs a significant resource overhead. Recent advances have shown that by jointly decoding logical qubits in algorithms composed of transversal gates, the number of syndrome extraction rounds can be reduced by a factor of the code distance d, at the cost of increased classical decoding complexity. Here, we reformulate the problem of decoding transversal circuits by directly decoding relevant logical operator products as they propagate through the circuit. This procedure transforms the decoding task into one closely resembling that of a single-qubit memory propagating through time. The resulting approach leads to fast decoding and reduced problem size while maintaining high performance. Focusing on the surface code, we prove that this method enables fault-tolerant decoding with minimum-weight perfect matching, and benchmark its performance on example circuits including magic state distillation. We find that the threshold is comparable to that of a single-qubit memory, and that the total decoding run time can be, in fact, less than that of conventional lattice surgery. Our approach enables fast correlated decoding, providing a pathway to directly extend single-qubit QEC techniques to transversal algorithms.

We demonstrate that in quantum many-body systems, local arrows of time can differ from the global time $t$ induced by Hamiltonian evolution. That is, within a quantum many-body system, the flow of time can be relative to each observer or by proxy each local subsystem. We provide a definition of local arrows of time in quantum many-body systems, and explain their relation to spacetime quantum entropies. Then we give a variety of numerical and analytical examples which explore different ways in which local arrows of time can manifest in quantum many-body dynamics, including exotic arrows of time arising from quantum thermalization and quantum error correction. We find that even in standard Hamiltonian dynamics, the arrow of time is not strictly temporal; it develops spatial components that deviate from the local entropy gradient.