The key idea is to enlarge the optical system, decompose the resulting transformation into six quadratic shears, and distribute each mode over many submodes, which permits a fixed local occupation cutoff, after which local basis changes and parallel phase gates give the qubit circuit.
Abstract
We show that boson sampling with an arbitrary $m$-mode interferometer and $n\le m$ single-photon inputs can be simulated to inverse-polynomial total-variation error by a logarithmic-depth qubit circuit with polynomially many qubits. The circuit uses Clifford+$T$ gates, arbitrary qubit connectivity, and a single final measurement, and its family is logspace uniform. The key idea is to enlarge the optical system, decompose the resulting transformation into six quadratic shears, and distribute each mode over many submodes. This redistribution permits a fixed local occupation cutoff, after which local basis changes and parallel phase gates give the qubit circuit. Consequently, our result places boson sampling within shallow quantum computation.
The results show that precise Haar-like statistics can emerge from sparse commuting dynamics with remarkably low quantum resources, with applications to randomized characterization, quantum metrology, quantum algorithms, and many-body physics.
Qing-Yue Zhang, Jun-Jie Chen, Zhou You et al.· 0 citations
In this paper, we propose a linear-optical quantum computation scheme that starts from high-dimensionally entangled qudits but performs quantum computation on qubits defined in their subspaces. This approach enables us to increase the success probability of linear-optical fusions from $50\%$ to $1-1/d$ for qudits of di...
Gaussian boson sampling (GBS) seeks quantum advantage by sampling photon-number patterns generated with squeezed inputs and passive linear optics. Many proposed GBS applications instead target function computation by applying functions to mode-resolved photon-number outcomes---a natural form of experimental postprocess...
Ruo-Ting Dou, Hao Zhan, Sheng-Jun Wu et al.· 0 citations
We consider quantum circuits consisting of $d$ layers of nearest-neighbor two-qubit gates acting on $n$ qubits arranged on a line, where every qubit is independently depolarized with a constant probability before each layer. We describe a randomized parallel algorithm which samples from the output distribution of any s...
Drawing on insights from stochastic calculus, geometric functional analysis, and randomized linear algebra, the approach exploits the circuit's response to variations of individual gates and requires no control over convergence to high-order unitary designs.
Mid-circuit measurements with feedforward reduce the optimal worst-case quantum depth for exact $n$-qubit unitary synthesis from $\Theta(n)$ to $O(1)$, using arbitrary one- and two-qubit gates and unrestricted ancillary space. Measurements and resets without feedforward remain subject to the circuit causal-cone bound....
Chen-Feng Cao· 1 citation
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