arXiv subjects

Oumarou Oumarou

Publications and source records attributed to Oumarou Oumarou.

10 recordsLinked to original sources

arXiv2026

Optimizing and Comparing Quantum Resources of Statistical Phase Estimation and Krylov Subspace Diagonalization

We develop a framework that enables direct and meaningful comparison of two early fault-tolerant methods for the computation of eigenenergies, namely \gls{qksd} and \gls{spe}, within which both methods use expectation values of Chebyshev polynomials of the Hamiltonian as input. For \gls{qksd} we propose methods for optimally distributing shots and ensuring sufficient non-linearity of states spanning the Krylov space. For \gls{spe} we improve rigorous error-bounds, achieving roughly a factor $2/3$ reduction of circuit depth. We provide insights into the scalability of and the practical realization of these methods by computing the maximum Chebyshev degree, linearly related to circuit depth, and the respective number of repetitions required for the simulation of molecules with active spaces up to 54 electrons in 36 orbitals by leveraging \gls{mps}/\gls{dmrg}.

quant-ph↗

arXiv2025

Molecular Properties from Quantum Krylov Subspace Diagonalization

Quantum Krylov subspace diagonalization is a prominent candidate for early fault tolerant quantum simulation of many-body and molecular systems, but so far the focus has been mainly on computing ground-state energies. We go beyond this by deriving analytical first-order derivatives for quantum Krylov methods and show how to obtain relaxed one and two particle reduced density matrices of the Krylov eigenstates. The direct approach to measuring these matrices requires a number of distinct measurement that scales quadratically with the Krylov dimension $D$. Here, we show how to reduce this scaling to a constant. This is done by leveraging quantum signal processing to prepare Krylov eigenstates, including exited states, in depth linear in $D$. We also compare several measurement schemes for efficiently obtaining the expectation value of an operator with states prepared using quantum signal processing. We validate our approach by computing the nuclear gradient of a small molecule and estimating its variance.

quant-ph↗

arXiv2023

Tailored and Externally Corrected Coupled Cluster with Quantum Inputs

We propose to use wavefunction overlaps obtained from a quantum computer as inputs for the classical split-amplitude techniques, tailored and externally corrected coupled cluster, to achieve balanced treatment of static and dynamic correlation effects in molecular electronic structure simulations. By combining insights from statistical properties of matchgate shadows, which are used to measure quantum trial state overlaps, with classical correlation diagnostics, we are able to provide quantum resource estimates well into the classically no longer exactly solvable regime. We find that rather imperfect wavefunctions and remarkably low shot counts are sufficient to cure qualitative failures of plain coupled cluster singles doubles and to obtain chemically precise dynamic correlation energy corrections. We provide insights into which wavefunction preparation schemes have a chance of yielding quantum advantage, and we test our proposed method using overlaps measured on Google's Sycamore device.

quant-ph↗

arXiv2022

Accelerating Quantum Computations of Chemistry Through Regularized Compressed Double Factorization

We propose the regularized compressed double factorization (RC-DF) method to classically compute compressed representations of molecular Hamiltonians that enable efficient simulation with noisy intermediate scale (NISQ) and error corrected quantum algorithms. We find that already for small systems with 12 to 20 qubits, the resulting NISQ measurement scheme reduces the number of measurement bases by roughly a factor of three and the shot count to reach chemical accuracy by a factor of three to six compared to truncated double factorization (DF) and we see order of magnitude improvements over Pauli grouping schemes. We demonstrate the scalability of our approach by performing RC-DF on the CpdI species of cytochrome P450 with 58 orbitals and find that using the resulting compressed Hamiltonian cuts the run time of qubitization and truncated DF based error corrected algorithms almost in half and even outperforms the lambda parameters achievable with tensor hypercontraction (THC) while at the same time reducing the CCSD(T) energy error heuristic by an order of magnitude.

quant-ph↗

arXiv2022

Efficient Quantum Analytic Nuclear Gradients with Double Factorization

Efficient representations of the Hamiltonian such as double factorization drastically reduce circuit depth or number of repetitions in error corrected and noisy intermediate scale quantum (NISQ) algorithms for chemistry. We report a Lagrangian-based approach for evaluating relaxed one- and two-particle reduced density matrices from double factorized Hamiltonians, unlocking efficiency improvements in computing the nuclear gradient and related derivative properties. We demonstrate the accuracy and feasibility of our Lagrangian-based approach to recover all off-diagonal density matrix elements in classically-simulated examples with up to 327 quantum and 18470 total atoms in QM/MM simulations, with modest-sized quantum active spaces. We show this in the context of the variational quantum eigensolver (VQE) in case studies such as transition state optimization, ab initio molecular dynamics simulation and energy minimization of large molecular systems.

quant-ph↗

arXiv2021

Fast quantum circuit simulation using hardware accelerated general purpose libraries

Quantum circuit simulators have a long tradition of exploiting massive hardware parallelism. Most of the times, parallelism has been supported by special purpose libraries tailored specifically for the quantum circuits. Quantum circuit simulators are integral part of quantum software stacks, which are mostly written in Python. Our focus has been on ease of use, implementation and maintainability within the Python ecosystem. We report the performance gains we obtained by using CuPy, a general purpose library (linear algebra) developed specifically for CUDA-based GPUs, to simulate quantum circuits. For supremacy circuits the speedup is around 2x, and for quantum multipliers almost 22x compared to state-of-the-art C++-based simulators.

quant-ph↗

arXiv2021

Halving the width of Toffoli based constant modular addition to n+3 qubits

We present an arithmetic circuit performing constant modular addition having $\mathcal{O}(n)$ depth of Toffoli gates and using a total of $n+3$ qubits. This is an improvement by a factor of two compared to the width of the state-of-the-art Toffoli-based constant modular adder. The advantage of our adder, compared to the ones operating in the Fourier-basis, is that it does not require small angle rotations and their Clifford+T decomposition. Our circuit uses a recursive adder combined with the modular addition scheme proposed by Vedral et. al. The circuit is implemented and verified exhaustively with QUANTIFY, an open-sourced framework. We also report on the Clifford+T cost of the circuit.

quant-ph↗

arXiv2021

On the realistic worst case analysis of quantum arithmetic circuits

We provide evidence that commonly held intuitions when designing quantum circuits can be misleading. In particular we show that: a) reducing the T-count can increase the total depth; b) it may be beneficial to trade CNOTs for measurements in NISQ circuits; c) measurement-based uncomputation of relative phase Toffoli ancillae can make up to 30\% of a circuit's depth; d) area and volume cost metrics can misreport the resource analysis. Our findings assume that qubits are and will remain a very scarce resource. The results are applicable for both NISQ and QECC protected circuits. Our method uses multiple ways of decomposing Toffoli gates into Clifford+T gates. We illustrate our method on addition and multiplication circuits using ripple-carry. As a byproduct result we show systematically that for a practically significant range of circuit widths, ripple-carry addition circuits are more resource efficient than the carry-lookahead addition ones. The methods and circuits were implemented in the open-source QUANTIFY software.

quant-ph↗

arXiv2020

QUANTIFY: A framework for resource analysis and design verification of quantum circuits

Quantum resource analysis is crucial for designing quantum circuits as well as assessing the viability of arbitrary (error-corrected) quantum computations. To this end, we introduce QUANTIFY, which is an open-source framework for the quantitative analysis of quantum circuits. It is based on Google Cirq and is developed with Clifford+T circuits in mind, and it includes the necessary methods to handle Toffoli+H and more generalised controlled quantum gates, too. Key features of QUANTIFY include: (1) analysis and optimisation methods which are compatible with the surface code, (2) choice between different automated (mixed polarity) Toffoli gate decompositions, (3) semi-automatic quantum circuit rewriting and quantum gate insertion methods that take into account known gate commutation rules, and (4) novel optimiser types that can be combined with different verification methods (e.g. truth table or circuit invariants like number of wires). For benchmarking purposes QUANTIFY includes quantum memory and quantum arithmetic circuits. Experimental results show that the framework's performance scales to circuits with thousands of qubits.

quant-ph↗

arXiv2020

Parallelising the Queries in Bucket Brigade Quantum RAM

Quantum algorithms often use quantum RAMs (QRAM) for accessing information stored in a database-like manner. QRAMs have to be fast, resource efficient and fault-tolerant. The latter is often influenced by access speeds, because shorter times introduce less exposure of the stored information to noise. The total execution time of an algorithm depends on the QRAM access time which includes: 1) address translation time, and 2) effective query time. The bucket brigade QRAMs were proposed to achieve faster addressing at the cost of exponentially many ancillae. We illustrate a systematic method to significantly reduce the effective query time by using Clifford+T gate parallelism. The method does not introduce any ancillae qubits. Our parallelisation method is compatible with the surface code quantum error correction. We show that parallelisation is a result of advantageous Toffoli gate decomposition in terms of Clifford+T gates, and after addresses have been translated, we achieve theoretical $\mathcal{O}(1)$ parallelism for the effective queries. We conclude that, in theory: 1) fault-tolerant bucket brigade quantum RAM queries can be performed approximately with the speed of classical RAM; 2) the exponentially many ancillae from the bucket brigade addressing scheme are a trade-off cost for achieving exponential query speedup compared to quantum read-only memories whose queries are sequential by design. The methods to compile, parallelise and analyse the presented QRAM circuits were implemented in software which is available online.

quant-ph↗