REVIEW 6 cited by
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Efficient LCU block encodings through Dicke states preparation
read the original abstract
With the Quantum Singular Value Transformation (QSVT) emerging as a unifying framework for diverse quantum speedups, the efficient construction of block encodings -- their fundamental input model -- has become increasingly crucial. However, devising explicit block encoding circuits remains a significant challenge. A widely adopted strategy is the Linear Combination of Unitaries (LCU) method. While general, its practical utility is often limited by substantial gate overhead. To address this, we introduce the Fast One-Qubit-Controlled Select LCU (FOQCS-LCU), a compact LCU formulation that requires only a linear number of ancilla qubits and is explicitly decomposed into one- and two-qubit gates. By exploiting the underlying Hamiltonian structure, we design a parametrized family of efficient Dicke state preparation routines, enabling systematic realization of the state preparation oracle at substantially reduced gate cost. The check matrix formalism further yields a constant-depth SELECT oracle, implemented as two fully parallelizable layers of singly controlled Pauli gates. We construct explicit block encoding circuits for representative spin models such as the Heisenberg and spin glass Hamiltonians and provide detailed, non-asymptotic gate counts. Our numerical benchmarks confirm the efficiency of the FOQCS-LCU approach, illustrating over an order-of-magnitude reduction in CNOT count compared to conventional LCU. This framework opens a pathway toward practical, low-depth block encodings for a broad class of structured matrices beyond those considered here.
Forward citations
Cited by 6 Pith papers
-
Qubit Routing for (Almost) Free
Restricting phase-polynomial synthesis to allowed CNOTs on a given architecture reduces routing overhead from O(log n) or worse to a constant factor of at most 4.
-
Quantum Channel Polynomial Processing
QCPP implements polynomial transformations of Hamiltonians via stochastic mixtures of unitary channels, achieving a tunable tradeoff between query and sample complexity.
-
Lowering LCU Circuit Width through Maximum-Weight Birkhoff-von Neumann Decomposition
Bottleneck and greedy largest-weight variants of Birkhoff-von Neumann decomposition reduce permutation count to O(N log(1/ε)) or ~2N for dense matrices, lowering LCU ancilla width and enabling α=1 normalization.
-
Lowering LCU Circuit Width through Maximum-Weight Birkhoff-von Neumann Decomposition
A bottleneck and largest-weight greedy Birkhoff-von Neumann decomposition reduces LCU permutation terms from O(N²) to O(N log(1/ε)) or ~2N, halving ancilla qubits while setting normalization constant α=1.
-
Block-encodings as programming abstractions: The Eclipse Qrisp BlockEncoding Interface
The Eclipse Qrisp BlockEncoding interface provides high-level programming abstractions for block-encodings, enabling easier implementation of quantum algorithms such as QSVT, matrix inversion, and Hamiltonian simulation.
-
TARE: Block Encoding Linear Combinations of Pauli Strings Without Ancilla State Preparation
TARE block-encodes sums of Pauli strings with reduced T-gate count and improved circuit depth versus standard LCU by leveraging mutually anti-commuting Pauli sets and transformations.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.