Quantum simulation using noisy unitary circuits and measurements

Abstract

Many-body quantum systems are notoriously hard to study theoretically due to the exponential growth of their Hilbert space. It is also challenging to probe the quantum correlations in many-body states in experiments due to their sensitivity to external noise. Using synthetic quantum matter to simulate quantum systems has opened new ways of probing quantum many-body systems with unprecedented control, and of engineering phases of matter which are otherwise hard to find in nature. Noisy quantum circuits have become an important cornerstone of our understanding of quantum many-body dynamics. In particular, random circuits act as minimally structured toy models for chaotic nonintegrable quantum systems, faithfully reproducing some of their universal properties. Crucially, in contrast to the full microscopic model, random circuits can be analytically tractable under a reasonable set of assumptions, thereby providing invaluable insights into questions which might be out of reach even for state-of-the-art numerical techniques. Here, we give an overview of two classes of dynamics studied using random-circuit models, with a particular focus on the dynamics of quantum entanglement. We will especially pay attention to potential near-term applications of random-circuit models on noisy-intermediate scale quantum (NISQ) devices. In this context, we cover hybrid circuits consisting of unitary gates interspersed with nonunitary projective measurements, hosting an entanglement phase transition from a volume-law to an area-law phase of the steadystate entanglement. Moreover, we consider random-circuit sampling experiments and discuss the usefulness of random quantum states for simulating quantum many-body dynamics on NISQ devices by leveraging the concept of quantum typicality. We highlight how emergent hydrodynamics can be studied by utilizing random quantum states generated by chaotic circuits.

Noisy induced entanglement transition in one-dimensional random quantum circuits

“…Because both the physical noise and projective measurements destroy the quantum coherence of the system, the non-unitary projective measurement model has some similarities to the noisy random quantum circuit. But in the projective measurement driven quantum circuit, the system is always a pure state and the entanglement grows with the circuit depth increases until saturate [14][15][16][17][18][19][20][21][22]. To measure the mixed state entanglement, we have used the logarithmic entanglement negativity, which can be measured experimentally through the PT moments [47].…”

“…In the absence of physical noise, the von Neumann entanglement entropy or Rényi entropy and the corresponding entanglement spectrum are well used to characterize the entanglement properties in quantum circuits [11]. It has been established that the usual non-unitary projective measurement may destroy the quantum entanglement in random quantum circuits, and an entanglement phase transition is induced from an area law phase to a volume law phase when the probability of measurements is decreased [14][15][16][17][18][19][20][21][22]. However, for the random quantum circuit with physical noise, it is a challenge to separate the classical correlation from the quantum entanglement, where the noise can thermalize the system as a mixed state.…”

Transport and entanglement growth in long-range random Clifford circuits

“…In particular, suitable randomcircuit models faithfully capture aspects of generic quantum systems [14][15][16][17], including the flexibility to describe settings with conservation laws and constraints [18,19], as well as dual-unitary [20,21], time-periodic [22,23], or nonunitary dynamics [24,25]. Moreover, random circuits are particularly attractive in the context of today's noisy intermediate-scale quantum devices [26][27][28], where they found applications to achieve a quantum computational advantage [29] and to explore operator entanglement [30].…”