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1. Extending the Frontier of Quantum Computers with Qutrits

   https://doi.org/10.1109/MM.2020.2985976  

   Gokhale, Pranav; Baker, Jonathan M.; Duckering, Casey; Brown, Natalie C.; Brown, Kenneth R.; Chong, Fred (April 2020, IEEE Micro)

   We advocate for a fundamentally different way to perform quantum computation by using three-level qutrits instead of qubits. In particular, we substantially reduce the resource requirements of quantum computations by exploiting a third state for temporary variables (ancilla) in quantum circuits. Past work with qutrits has demonstrated only constant factor improvements, owing to the lg(3) binary-to-ternary compression factor. We present a novel technique using qutrits to achieve a logarithmic runtime decomposition of the Generalized Toffoli gate using no ancilla - an exponential improvement over the best qubit-only equivalent. Our approach features a 70× improvement in total two-qudit gate count over the qubit-only decomposition. This results in improvements for important algorithms for arithmetic and QRAM. Simulation results under realistic noise models indicate over 90% mean reliability (fidelity) for our circuit, versus under 30% for the qubit-only baseline. These results suggest that qutrits offer a promising path toward extending the frontier of quantum computers. 

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2. Spacetime-Efficient Low-Depth Quantum State Preparation with Applications

   https://doi.org/10.22331/q-2024-02-15-1257  

   Gui, Kaiwen; Dalzell, Alexander M.; Achille, Alessandro; Suchara, Martin; Chong, Frederic T. (February 2024, Quantum)

   We propose a novel deterministic method for preparing arbitrary quantum states. When our protocol is compiled into CNOT and arbitrary single-qubit gates, it prepares an $N$-dimensional state in depth $O(\log (N\left)\right)$and $\text{spacetime allocation}$(a metric that accounts for the fact that oftentimes some ancilla qubits need not be active for the entire circuit) $O\left(N\right)$, which are both optimal. When compiled into the $\left\{\mathrm{H},\mathrm{S},\mathrm{T},\mathrm{C}\mathrm{N}\mathrm{O}\mathrm{T}\right\}$gate set, we show that it requires asymptotically fewer quantum resources than previous methods. Specifically, it prepares an arbitrary state up to error $ϵ$with optimal depth of $O(\log (N)+\log (1/ϵ\left)\right)$and spacetime allocation $O(N\log (\log \left(N\right)/ϵ\left)\right)$, improving over $O(\log (N)\log (\log \left(N\right)/ϵ\left)\right)$and $O(N\log (N/ϵ\left)\right)$, respectively. We illustrate how the reduced spacetime allocation of our protocol enables rapid preparation of many disjoint states with only constant-factor ancilla overhead – $O\left(N\right)$ancilla qubits are reused efficiently to prepare a product state of $w$ $N$-dimensional states in depth $O(w+\log (N\left)\right)$rather than $O(w\log (N\left)\right)$, achieving effectively constant depth per state. We highlight several applications where this ability would be useful, including quantum machine learning, Hamiltonian simulation, and solving linear systems of equations. We provide quantum circuit descriptions of our protocol, detailed pseudocode, and gate-level implementation examples using Braket. 

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3. Fast and Parallelizable Logical Computation with Homological Product Codes

   https://doi.org/10.1103/PhysRevX.15.021065  

   Xu, Qian; Zhou, Hengyun; Zheng, Guo; Bluvstein, Dolev; Ataides, J_Pablo Bonilla; Lukin, Mikhail D; Jiang, Liang (May 2025, Physical Review X)

   Quantum error correction is necessary to perform large-scale quantum computation but requires extremely large overheads in both space and time. High-rate quantum low-density-parity-check (qLDPC) codes promise a route to reduce qubit numbers, but performing computation while maintaining low space cost has required serialization of operations and extra time costs. In this work, we design fast and parallelizable logical gates for qLDPC codes and demonstrate their utility for key algorithmic subroutines such as the quantum adder. Our gate gadgets utilize transversal logical s between a data qLDPC code and a suitably constructed ancilla code to perform parallel Pauli product measurements (PPMs) on the data logical qubits. For hypergraph product codes, we show that the ancilla can be constructed by simply modifying the base classical codes of the data code, achieving parallel PPMs on a subgrid of the logical qubits with a lower space-time cost than existing schemes for an important class of circuits. Generalizations to 3D and 4D homological product codes further feature fast PPMs in constant depth. While prior work on qLDPC codes has focused on individual logical gates, we initiate the study of fault-tolerant compilation with our expanded set of native qLDPC code operations, constructing algorithmic primitives for preparing $k$-qubit Greenberger-Horne-Zeilinger states and distilling or teleporting $k$magic states with $O\left(1\right)$space overhead in $O\left(1\right)$and $O\left(\sqrt{k}\log k\right)$logical cycles, respectively. We further generalize this to key algorithmic subroutines, demonstrating the efficient implementation of quantum adders using parallel operations. Our constructions are naturally compatible with reconfigurable architectures such as neutral atom arrays, paving the way to large-scale quantum computation with low space and time overheads. Published by the American Physical Society2025 

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4. Asymptotic improvements to quantum circuits via qutrits

   https://doi.org/10.1145/3307650.3322253  

   Gokhale, Pranav; Baker, Jonathan M.; Duckering, Casey; Brown, Natalie C.; Brown, Kenneth R.; Chong, Frederic T. (June 2019, ISCA '19 Proceedings of the 46th International Symposium on Computer Architecture)

   Quantum computation is traditionally expressed in terms of quantum bits, or qubits. In this work, we instead consider three-level qutrits. Past work with qutrits has demonstrated only constant factor improvements, owing to the log2(3) binary-to-ternary compression factor. We present a novel technique using qutrits to achieve a logarithmic depth (runtime) decomposition of the Generalized Toffoli gate using no ancilla-a significant improvement over linear depth for the best qubit-only equivalent. Our circuit construction also features a 70x improvement in two-qudit gate count over the qubit-only equivalent decomposition. This results in circuit cost reductions for important algorithms like quantum neurons and Grover search. We develop an open-source circuit simulator for qutrits, along with realistic near-term noise models which account for the cost of operating qutrits. Simulation results for these noise models indicate over 90% mean reliability (fidelity) for our circuit construction, versus under 30% for the qubit-only baseline. These results suggest that qutrits offer a promising path towards scaling quantum computation. 

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5. A quantum hamiltonian simulation benchmark

   https://doi.org/10.1038/s41534-022-00636-x  

   Dong, Yulong; Whaley, K. Birgitta; Lin, Lin (December 2022, npj Quantum Information)

   Abstract Hamiltonian simulation is one of the most important problems in quantum computation, and quantum singular value transformation (QSVT) is an efficient way to simulate a general class of Hamiltonians. However, the QSVT circuit typically involves multiple ancilla qubits and multi-qubit control gates. In order to simulate a certain class of n -qubit random Hamiltonians, we propose a drastically simplified quantum circuit that we refer to as the minimal QSVT circuit, which uses only one ancilla qubit and no multi-qubit controlled gates. We formulate a simple metric called the quantum unitary evolution score (QUES), which is a scalable quantum benchmark and can be verified without any need for classical computation. Under the globally depolarized noise model, we demonstrate that QUES is directly related to the circuit fidelity, and the potential classical hardness of an associated quantum circuit sampling problem. Under the same assumption, theoretical analysis suggests there exists an ‘optimal’ simulation time t opt  ≈ 4.81, at which even a noisy quantum device may be sufficient to demonstrate the potential classical hardness. 

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