Observation of a dynamical purification phase transition in a trapped-ion quantum computer
Crystal Noel, Duke University
When measurements are interspersed in random quantum circuits, the long-time entanglement of the system exhibits a phase transition with the varying density of measurements. Here, we use a single reference qubit entangled with the larger system to efficiently study these quantum phases. We probe the purification dynamics by sampling hundreds of instances of random circuits using a quantum computer with 13 trapped 171Yb+ ions as the qubits. On the accessible circuit depths and system sizes, we find conclusive evidence of the two phases and show numerically that, with modest increases in circuit depth and system size, critical properties of the purification transition clearly emerge.
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What Limits the Simulation of Quantum Computers?
Miles Stoudenmire, Flatiron Institute
Recent experimental demonstrations of quantum computing hardware and claims of quantum supremacy have motivated debates over the true resources needed to perform classical simulations of quantum circuits. While exactly simulating certain circuits would certainly require exponential classical resources, there have been fewer investigations into approximate simulations. We use matrix product states (MPS) to simulate quantum circuits at a cost linear in the number of qubits N and circuit depth D. The tradeoff is a loss of fidelity (finite error rate) incurred at every step, such that the fidelity decreases exponentially. When studying 1D circuits, we observe that the error rate can be decreased with polynomial effort down to a certain value comparable to very high quality qubits. But going beyond this error rate requires exponential resources, an effect which may be explainable by random matrix theory arguments. By pursuing strategies for simulating 2D random circuits we reach fidelities comparable to recent experiments, though only when using a lower-rank type of two-qubit gate. Future directions include both conceptual questions about classical simulability and pushing two-dimensional simulations further.
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Non-unitary dynamics via spacetime duality
Matteo Ippoliti, Stanford University
I will present recent work on quantum entanglement in an interesting class of non-unitary circuits -- those that are obtained by exchanging the roles of space and time in unitary circuits [1,2]. This "spacetime duality" transformation is useful in multiple ways: theoretically, it allows us to make significant analytical progress by leveraging known results on unitary dynamics; experimentally, it makes it possible to implement these non-unitary dynamics on present-day digital quantum simulators, with a vanishing density of measurements in spacetime. I will show how this class of non-unitary circuits can realize steady states that exhibit a rich variety of behavior in the scaling of their entanglement with subsystem size, from logarithmic to extensive to a novel fractal scaling which is not found in generic many-body unitary dynamics. These scalings are closely related to the possible behaviors of entanglement in time under unitary evolution. The connection is sharpened by an exact mapping to a problem of unitary evolution with edge decoherence, in which information is irreversibly “radiated away” from one edge of the system.
[1] MI, T. Rakovszky, V. Khemani, arxiv:2103.06873
[2] MI, V. Khemani, PRL 126, 060501 (2021)
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Emergent quantum randomness and its application for quantum device benchmarking
Soonwon Choi, UC Berkeley; MIT (starting July 2021)
In this talk, we describe a novel, universal phenomenon that occurs in strongly interacting many-body quantum dynamics beyond the conventional thermalization. The observed universality leads to the development of a novel benchmarking method applicable for a wide variety of near-term quantum devices. More specifically, we point out that a single many-body wavefunction can encode an ensemble of a large number of pure states defined on a subsystem. For a wide class of many-body wavefunctions, we show that the ensembles encoded in them display universal statistical properties by using a notion in quantum information theory, called quantum state k-designs. The special case (k=1) reduces to the conventional quantum thermalization. The universality is corroborated by two theorems, extensive numerical simulations of Hamiltonian dynamics, and recent experimental observations based on a Rydberg quantum simulator. Our results offer a new approach for studying quantum chaos and provide a practical method for sampling pseudorandom quantum states. As an example of practical utility, I will explain how our results allow us to develop a novel sample-efficient benchmarking protocol, which has been already demonstrated in an experiment.