REVIEW 9 cited by
Approximation by Quantum Circuits
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
In a recent preprint by Deutsch et al. [1995] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on $n$ qubits by 2-qubit unitary operations. We address that comment by proving strong lower bounds on the approximation capabilities of g-qubit unitary operations for fixed g. We consider approximation of unitary operations on subspaces as well as approximation of states and of density matrices by quantum circuits in several natural metrics. The ability of quantum circuits to probabilistically solve decision problem and guess checkable functions is discussed. We also address exact unitary representation by reducing the upper bound by a factor of n^2 and by formalizing the argument given by Barenco et al. [1995] for the lower bound. The overall conclusion is that almost all problems are hard to solve with quantum circuits.
Forward citations
Cited by 9 Pith papers
-
Practical Tests and Witnesses of Fermionic non-Gaussianity
Introduces practical witnesses of fermionic non-Gaussianity via antiflatness from covariance matrices, with two efficient measurement protocols, a purity-corrected version for mixed states, and experimental results on...
-
Three Hamiltonians are Sufficient for Unitary $k$-Design in Temporal Ensemble
A three-step quench protocol with fixed Hamiltonians and random times forms unitary k-designs for arbitrary k; the two-step protocol cannot.
-
Realizing Unitary $k$-designs with a Single Quench
A single quench between two independent random Hamiltonians at the Thouless time generates unitary k-designs.
-
Efficient High-Dimensional Quantum Circuit Synthesis: From Multi-Controlled Gates to Isometries and Quantum Channels
Multi-controlled single-qudit gates can be synthesized with O(n²) CINC gates (O(n) for special unitaries), enabling improved qudit isometry and channel circuits and, for prime d, equivalent SUM-gate circuits.
-
A Compass on the Quantum State Sphere: The Hopf Ansatz for Arbitrary Pure-State Optimization
The Hopf binary-tree ansatz provides universal state preparation plus an explicit inverse map, diagonal metric, and exact tangent-state gradients, organizing gradient access into O(log N) circuit families.
-
Cartan-Khaneja-Glaser decomposition of $SU(2^n)$ via involutive automorphisms
Reformulation of Cartan-Khaneja-Glaser decomposition for SU(2^n) via involutive automorphisms and symmetric Lie algebra decompositions yields a stable recursive factorization with open-source Python code validated on ...
-
Quantum AIXI: Universal Intelligence via Quantum Information
The paper introduces Quantum AIXI, a channel-based formulation of universal intelligence over quantum environments, and argues that contextuality, measurement back-action, and no-cloning fundamentally limit any such agent.
-
Quantum Monte Carlo algorithm for option pricing and its complexity analysis
A quantum Monte Carlo algorithm solves multidimensional Black-Scholes PDEs for option pricing with polynomial complexity in dimension d and accuracy 1/ε, with rigorous error bounds and a claimed speedup over classical...
-
Statistical and Algorithmic Foundations of Probing Quantum Systems with Compressive Measurements: A Review
A survey of structured quantum state tomography covering compact representations, measurement design, and optimization algorithms, connected to compressive sensing for sample efficiency.
Discussion (0). Continue with ORCID to comment.