Manas Patra
In this paper we introduce a projective invarinat measure on the special unitary group. It is directly related to transition probabilities. It has some interesting connection with convex geometry. Applications to approximation of quantum circuits and entanglement are given.
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Dual-unitary circuits have emerged as a minimal model for chaotic quantum many-body dynamics in which the dynamics of correlations and entanglement remains tractable. Simultaneously, there has been intense interest in the effect of measurements on the dynamics of quantum information in many-body systems. In this work we introduce a class of models combining dual-unitary circuits with particular projective measurements that allow the exact computation of dynamical correlations of local observables, entanglement growth, and steady-state entanglement. We identify a symmetry preventing a measureme…
Quantum Computing has been evolving in the last years. Although nowadays quantum algorithms performance has shown superior to their classical counterparts, quantum decoherence and additional auxiliary qubits needed for error tolerance routines have been huge barriers for quantum algorithms efficient use. These restrictions lead us to search for ways to minimize algorithms costs, i.e the number of quantum logical gates and the depth of the circuit. For this, quantum circuit synthesis and quantum circuit optimization techniques are explored. We studied the viability of using Projective Simulatio…
Ultra-Precise Quantum Projective Designs in Constant Depth
该研究提出了一种稀疏对易量子电路系综，可在恒定深度下实现高精度量子投影设计，所需量子资源极低，适用于随机表征、量子计量等多个领域。
A set of gauge invariants are identified for the gauge theory of quantum anholonomies, which comprise both the Berry phase and an exotic anholonomy in eigenspaces. We examine these invariants for hierarchical families of quantum circuits whose qubit size can be arbitrarily large. It is also found that a hierarchical family of quantum circuits generally involves an NP-complete problem.
Topological phase transition induced by spatially-tuned single-site measurement is investigated in a measurement-only circuit, in which three different types of projective measurement operator. Specific spatial setting and combination of commutation relations among three measurement operators generate such a transition. In practice, symmetry protected topological (SPT) phase is recovered on even sublattice by eliminating a projective measurement disturbing the SPT via applying another spatially-tuned projective measurement on odd sublattice. We further investigate the critical properties of th…
Unitary-transformed projective squeezing: applications for circuit-knitting and state-preparation of non-Gaussian states
本文提出了一种基于单元变换的压缩态投影方法，用于模拟更大规模的量子设备并制备高非线性非高斯态，同时抑制光子损失误差的影响。
Quantum Compiling Algorithms decompose (exactly, without approximations) an arbitrary $2^\nb$ unitary matrix acting on $\nb$ qubits, into a sequence of elementary operations (SEO). There are many possible ways of decomposing a unitary matrix into a SEO, and some of these decompositions have shorter length (are more efficient) than others. Finding an optimum (shortest) decomposition is a very hard task, and is not our intention here. A less ambitious, more doable task is to find methods for optimizing small segments of a SEO. Call these methods piecewise optimizations. Piecewise optimizations i…
We study the level-spacing statistics in the entanglement spectrum of output states of random universal quantum circuits where qubits are subject to a finite probability of projection to the computational basis at each time step. We encounter two phase transitions with increasing projection rate: The first is the volume-to-area law transition observed in quantum circuits with projective measurements; The second separates the pure Poisson level statistics phase at large projective measurement rates from a regime of residual level repulsion in the entanglement spectrum within the area-law phase,…
We realize indirect partial measurement of a transmon qubit in circuit quantum electrodynamics by interaction with an ancilla qubit and projective ancilla measurement with a dedicated readout resonator. Accurate control of the interaction and ancilla measurement basis allows tailoring the measurement strength and operator. The tradeoff between measurement strength and qubit back-action is characterized through the distortion of a qubit Rabi oscillation imposed by ancilla measurement in different bases. Combining partial and projective qubit measurements, we provide the solid-state demonstratio…
Harmonic analysis and circuit approximation of Sobolev functions on quantum input spaces
该研究针对代表量子态和量子酉操作的空间上的Sobolev函数，通过调和分析结合Solovay–Kitaev定理，建立了谱截断与量子电路近似的定量误差分离速率。
Projective Measurements: Topological Quantum Computing with an Arbitrary Number of Qubits
针对拓扑量子计算中编织门扩展后无法支撑完整Clifford群的 scaling 难题，提出结合投影测量实现编码切换以恢复通用性的方法，经多体模拟验证在多量子比特系统中保真度超99%且具鲁棒性与可扩展性。
Operator spreading in random unitary circuits with orthogonal/symplectic-invariant gate distributions
研究从正交不变或辛不变系综中抽取门组成的随机量子电路中的算子扩散，揭示了与酉不变情况的关键区别，包括权重三元结构、有限宽度畴壁以及蝴蝶速度的二分性。
This chapter covers the development of feedback control of superconducting qubits using projective measurement and a discrete set of conditional actions, here referred to as digital feedback. We begin with an overview of the applications of digital feedback in quantum computing. We then introduce an implementation of high-fidelity projective measurement of superconducting qubits. This development lays the ground for closed-loop control based on the binary measurement result. A first application of digital feedback control is fast and deterministic qubit reset, allowing the repeated initializat…
We study the effect of projective measurements on the entanglement structure of quantum black holes. It is shown that the entanglement verification in monitored quantum circuits, recently discussed in condensed matter physics, is equivalent to the information recovery from a black hole with projective measurements. This correspondence provides useful predictions about non-perturbative effects on quantum gravity and some insights on the black hole interior as well as the final state proposal.
We study the entanglement behavior of a random unitary circuit punctuated by projective measurements at the measurement-driven phase transition in one spatial dimension. We numerically study the logarithmic entanglement negativity of two disjoint intervals and find that it scales as a power of the cross-ratio. We investigate two systems: (1) Clifford circuits with projective measurements, and (2) Haar random local unitary circuit with projective measurements. Remarkably, we identify a power-law behavior of entanglement negativity at the critical point. Previous results of entanglement entropy …
Bounds in the Projective Unitary Group with Respect to Global Phase Invariant Metric
本文研究了在全局相位不变度量下项目性酉群的界限，推导了Gilbert-Varshamov和Hamming界限，并探讨了码本的最小距离、失真率和覆盖半径等特性。
Reinforced Disentanglers on Random Unitary Circuits
本文使用PPO强化学习算法在随机Clifford电路中寻找最优解纠缠器，通过将投影测量表示为状态并利用比特翻转操作作为动作，发现解纠缠所需测量次数远少于测量诱导相变数值结果，并成功表征了最优解纠缠器的模式。
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