We study the power of quantum witnesses under perfect completeness. We construct a classical oracle relative to which a language lies in $\mathsf{QMA}_1$ but not in $\mathsf{QCMA}$ when the $\mathsf{QCMA}$ verifier is only allowed polynomially many adaptive rounds and exponentially many parallel queries per round. Additionally, we derandomize the permutation-oracle separation of Fefferman and Kimmel, obtaining an in-place oracle separation between $\mathsf{QMA}_1$ and $\mathsf{QCMA}$ . Furthermore, we focus on $\mathsf{QCMA}$ and $\mathsf{QMA}$ with an exponentially small gap, where we show a separation assuming the gap is fixed, but not when it may be arbitrarily small. Finally, we derive consequences for approximate ground-state preparation from sparse Hamiltonian oracle access, including a bounded-adaptivity frustration-free variant.We study the power of quantum witnesses under perfect completeness. We construct a classical oracle relative to which a language lies in $\mathsf{QMA}_1$ but not in $\mathsf{QCMA}$ when the $\mathsf{QCMA}$ verifier is only allowed polynomially many adaptive rounds and exponentially many parallel queries per round. Additionally, we derandomize the permutation-oracle separation of Fefferman and Kimmel, obtaining an in-place oracle separation between $\mathsf{QMA}_1$ and $\mathsf{QCMA}$. Furthermore, we focus on $\mathsf{QCMA}$ and $\mathsf{QMA}$ with an exponentially small gap, where we show a separation assuming the gap is fixed, but not when it may be arbitrarily small. Finally, we derive consequences for approximate ground-state preparation from sparse Hamiltonian oracle access, including a bounded-adaptivity frustration-free variant.

quant-pharXiv:2604.26921Apr 30, 20260 citations

The Space "Just Above" BQP

Scott Aaronson, Adam Bouland, Joseph F. Fitzsimons +1 more

We explore the space "just above" BQP by defining a complexity class naCQP (non-adaptive Collapse-free Quantum Polynomial time) which is larger than BQP but does not contain NP relative to an oracle. The class is defined by imagining that quantum computers can perform (non-adaptive) measurements that do not collapse the wavefunction. This non-physical model of computation can efficiently solve problems such as Graph Isomorphism and Approximate Shortest Vector which are believed to be intractable for quantum computers. Furthermore, it can search an unstructured N-element list in Õ(N1/3) time, but no faster than Ω(N1/4), and hence cannot solve NP-hard problems in a black box manner. In short, this model of computation is more powerful than standard quantum computation, but only slightly so. This is surprising as most modifications of BQP increase the power of quantum computation to NP or beyond.We explore the space "just above" BQP by defining a complexity class naCQP (non-adaptive Collapse-free Quantum Polynomial time) which is larger than BQP but does not contain NP relative to an oracle. The class is defined by imagining that quantum computers can perform (non-adaptive) measurements that do not collapse the wavefunction. This non-physical model of computation can efficiently solve problems such as Graph Isomorphism and Approximate Shortest Vector which are believed to be intractable for quantum computers. Furthermore, it can search an unstructured N-element list in Õ(N1/3) time, but no faster than Ω(N1/4), and hence cannot solve NP-hard problems in a black box manner. In short, this model of computation is more powerful than standard quantum computation, but only slightly so. This is surprising as most modifications of BQP increase the power of quantum computation to NP or beyond.

Conference on Innovations in Theoretical Computer ScienceJan 5, 201615 citations

Oracle Quantum Algorithms: An Overview

Rafael Pereira da Silva

Jan 1, 20240 citations

Derivatives of Quantum Randomness: Separating Pseudorandom Unitaries from Pseudorandom (Function-like) States

Minki Hhan

Quantum computation gives rise to new pseudorandom primitives for states and unitaries, including pseudorandom state generators (PRSGs), pseudorandom function-like state generators (PRFSGs), and pseudorandom unitaries (PRUs). In this paper, we show a full unitary oracle separation between PRFSGs and PRUs. The separation holds between the strongest state notion and the weakest unitary notion: even adaptively secure, quantum-accessible PRFSGs do not imply non-adaptively secure, forward-only PRUs, even when their implementations are allowed to be non-unitary and use an arbitrary number of ancillary qubits. This reveals a fundamental distinction between pseudorandomness for quantum states and for quantum unitaries. Our main technical idea is to view a candidate PRU construction with access to state generation oracles as a map from the underlying oracle states to implemented unitaries, and to study the derivatives of this map. These derivatives are inherently low rank, and we exploit this low-rank structure to distinguish the resulting unitaries from truly random ones. We believe this differential perspective may be useful for studying other structural questions about quantum states and unitaries.Quantum computation gives rise to new pseudorandom primitives for states and unitaries, including pseudorandom state generators (PRSGs), pseudorandom function-like state generators (PRFSGs), and pseudorandom unitaries (PRUs). In this paper, we show a full unitary oracle separation between PRFSGs and PRUs. The separation holds between the strongest state notion and the weakest unitary notion: even adaptively secure, quantum-accessible PRFSGs do not imply non-adaptively secure, forward-only PRUs, even when their implementations are allowed to be non-unitary and use an arbitrary number of ancillary qubits. This reveals a fundamental distinction between pseudorandomness for quantum states and for quantum unitaries. Our main technical idea is to view a candidate PRU construction with access to state generation oracles as a map from the underlying oracle states to implemented unitaries, and to study the derivatives of this map. These derivatives are inherently low rank, and we exploit this low-rank structure to distinguish the resulting unitaries from truly random ones. We believe this differential perspective may be useful for studying other structural questions about quantum states and unitaries.

quant-pharXiv:2609.14626Sep 15, 20260 citations

We study the power of quantum witnesses under perfect completeness. We construct a classical oracle relative to which a language lies in

\mathsf{QMA}_1

but not in

\mathsf{QCMA}

when the

\mathsf{QCMA}

verifier is only allowed polynomially many adaptive rounds and exponentially many parallel queries per round. Additionally, we derandomize the permutation-oracle separation of Fefferman and Kimmel, obtaining an in-place oracle separation between

\mathsf{QMA}_1

and

\mathsf{QCMA}

. Furthermore, we focus on

\mathsf{QCMA}

and

\mathsf{QMA}

with an exponentially small gap, where we show a separation assuming the gap is fixed, but not when it may be arbitrarily small. Finally, we derive consequences for approximate ground-state preparation from sparse Hamiltonian oracle access, including a bounded-adaptivity frustration-free variant.