Quantum Search-to-Decision Reductions and the State Synthesis Problem

Speaker: Anand Natarajan , CSAIL MIT

Date: Tuesday, May 03, 2022

Time: 4:00 PM to 5:00 PM Note: all times are in the Eastern Time Zone

Public: Yes

Location: 32-124

Event Type: Seminar

Room Description: 32-124

Host: Sam Hopkins, CSAIL MIT

Contact: Nathan Higgins, nhiggins@csail.mit.edu

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Reminders to: seminars@csail.mit.edu, theory-seminars@lists.csail.mit.edu, seminars@lists.csail.mit.edu

Reminder Subject: TALK: Quantum Search-to-Decision Reductions and the State Synthesis Problem

NOTE: This seminar will be held in room 32-124

In this work, we explore search-to-decision reductions for quantum search problems, wherein a quantum algorithm makes queries to a classical decision oracle to output a desired quantum state. In particular, we focus on search-to-decision reductions for QMA, and show that there exists a quantum polynomial-time algorithm that can generate a witness for a QMA problem up to inverse polynomial precision by making one query to a PP decision oracle. We complement this result by showing that QMA-search does not reduce to QMA-decision in polynomial-time, relative to a quantum oracle. We also explore the more general state synthesis problem, in which the goal is to efficiently synthesize a target state by making queries to a classical oracle encoding the state. We prove that there exists a classical oracle with which any quantum state can be synthesized to inverse polynomial precision using only one oracle query and to inverse exponential precision using two oracle queries. This answers an open question of Aaronson from 2016, who presented a state synthesis algorithm that makes O(n) queries to a classical oracle to prepare an n-qubit state, and asked if the query complexity could be made sublinear.

Joint work with Sandy Irani, Chinmay Nirkhe, Sujit Rao, and Henry Yuen, https://arxiv.org/abs/2111.02999

Research Areas:
Algorithms & Theory

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Created by Nathan Higgins Email at Thursday, April 28, 2022 at 2:35 PM.