Related papers: Quantum Depth in the Random Oracle Model
In the near future, there will likely be special-purpose quantum computers with 40-50 high-quality qubits. This paper lays general theoretical foundations for how to use such devices to demonstrate "quantum supremacy": that is, a clear…
Recent oracle separations [Kretschmer, TQC'21, Kretschmer et. al., STOC'23] have raised the tantalizing possibility of building quantum cryptography from sources of hardness that persist even if the polynomial hierarchy collapses. We…
We exhibit some simple gadgets useful in designing shallow parallel circuits for quantum algorithms. We prove that any quantum circuit composed entirely of controlled-not gates or of diagonal gates can be parallelized to logarithmic depth,…
We explore the space "just above" BQP by defining a complexity class PDQP (Product Dynamical 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…
In the universal blind quantum computation problem, a client wants to make use of a single quantum server to evaluate $C|0\rangle$ where $C$ is an arbitrary quantum circuit while keeping $C$ secret. The client's goal is to use as few…
Decoherence of quantum hardware is currently limiting its practical applications. At the same time, classical algorithms for simulating quantum circuits have progressed substantially. Here, we demonstrate a hybrid framework that integrates…
A proof of quantumness is an efficiently verifiable interactive test that an efficient quantum computer can pass, but all efficient classical computers cannot (under some cryptographic assumption). Such protocols play a crucial role in the…
Extracting information efficiently from quantum systems is a major component of quantum information processing tasks. Randomized measurements, or classical shadows, enable predicting many properties of arbitrary quantum states using few…
We study the computational power of shallow quantum circuits with $O(\log n)$ initialized and $n^{O(1)}$ uninitialized ancillary qubits, where $n$ is the input length and the initial state of the uninitialized ancillary qubits is arbitrary.…
A defining feature in the field of quantum computing is the potential of a quantum device to outperform its classical counterpart for a specific computational task. By now, several proposals exist showing that certain sampling problems can…
We provide an $\Omega(log(n))$ lower bound for the depth of any quantum circuit generating the unique groundstate of Kitaev's spherical code. No circuit-depth lower bound was known before on this code in the general case where the gates can…
We study the quantum-classical polynomial hierarchy, QCPH, which is the class of languages solvable by a constant number of alternating classical quantifiers followed by a quantum verifier. Our main result is that QCPH is infinite relative…
Recently Brakerski, Christiano, Mahadev, Vazirani and Vidick (FOCS 2018) have shown how to construct a test of quantumness based on the learning with errors (LWE) assumption: a test that can be solved efficiently by a quantum computer but…
Motivated by realistic hardware considerations of the pre-fault-tolerant era, we comprehensively study the impact of uncorrected noise on quantum circuits. We first show that any noise `truncates' most quantum circuits to effectively…
Quantum hashing is a widely used technique in quantum computation that allows us to design space-efficient algorithms and protocols. Recently, Vasiliev has shown that the phase form of shallow quantum hashing can be implemented by a circuit…
We show that if a language is recognized within certain error bounds by constant-depth quantum circuits over a finite family of gates, then it is computable in (classical) polynomial time. In particular, our results imply EQNC^0 is…
Achieving reliable performance on early fault-tolerant quantum hardware will depend on protocols that manage noise without incurring prohibitive overhead. We propose a novel framework that integrates quantum computation with the…
The growing prevalence of near-term intermediate-scale quantum (NISQ) systems has brought forth a heightened focus on the issue of circuit reliability. Several quantum computing activities, such as circuit design and multi-qubit mapping,…
Bennett's notion of depth is usually considered to describe the usefulness and internal organization of the information encoded into an object such as an infinite binary sequence. We consider a natural way to relativize the notion of depth…
Noise is one of the main obstacles to realizing quantum devices that achieve a quantum computational advantage. A possible approach to minimize the noise effect is to employ shallow-depth quantum circuits since noise typically accumulates…