Shadow process tomography of quantum channels

Abstract

Quantum process tomography is a critical capability for building quantum computers, enabling quantum networks, and understanding quantum sensors. Like quantum state tomography, the process tomography of an arbitrary quantum channel requires a number of measurements that scales exponentially in the number of quantum bits affected. However, the recent field of shadow tomography, applied to quantum states, has demonstrated the ability to extract key information about a state with only polynomially many measurements. In this work, we apply the concepts of shadow state tomography to the challenge of characterizing quantum processes. We make use of the Choi isomorphism to directly apply rigorous bounds from shadow state tomography to shadow process tomography, and we find additional bounds on the number of measurements that are unique to process tomography. Our results, which include algorithms for implementing shadow process tomography, enable new techniques including evaluation of channel concatenation and the application of channels to shadows of quantum states. This provides a dramatic improvement for understanding large-scale quantum systems.

Classical shadows with Pauli-invariant unitary ensembles

“…The classical shadow paradigm was recently extended to the shadow tomography of quantum channels 29,30 . In these works, the unitary ensembles considered were the local and global Clifford ensembles.…”

“…Several applications have been proposed 1,[8][9][10][11][12][13][14][15][16][17][18][19][20][21] , ranging from the estimation of properties of quantum states and gates to quantum chaos in quantum evolution. Moreover, several improved versions of this protocol have been developed 1,8,[22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] , such as noise-resilient versions 20,37 .…”

“…Second, we apply our results to the shadow process tomography of quantum channels using the Choi-Jamiołkowski isomorphism, thereby generalizing the results of refs. 29,30 to the broad class of Pauli-invariant unitary ensembles.…”

Gravitoelectric effect in the condensed magnetic sea

“…Further discussion can be found in Ref. [2]. Suppose space H regards time as a constant in the additional space of Earth's gravity and that they can exchange energy; m μ is filled with gravitons or photons.…”

“…Recent cooling, control, and mechanical system measurements have allowed various low-energy quantum gravity models [1]. Quantum process tomography for enabling quantum networks and quantum sensors requires a number of measurements of the quantum bits affected, and the recent algorithms for implementing shadow process tomography have been applied to quantum shadow states [2]. The effects of the quantum noise of gravitons on the motion of point masses can now be considered.…”