<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0609</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2026-10-06</periodOfReport>

    <issuer>
        <issuerCik>0001859690</issuerCik>
        <issuerName>Arqit Quantum Inc.</issuerName>
        <issuerTradingSymbol>ARQQ</issuerTradingSymbol>
        <issuerForeignTradingSymbol></issuerForeignTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001840684</rptOwnerCik>
            <rptOwnerName>Ritchie Garth</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerNonUSAddressFlag>true</rptOwnerNonUSAddressFlag>
            <rptOwnerStreet1>3 ORCHARD PLACE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>LONDON</rptOwnerCity>
            <rptOwnerNonUSStateTerritory></rptOwnerNonUSStateTerritory>
            <rptOwnerCountry>X0</rptOwnerCountry>
            <rptOwnerZipCode>SW1H 0BF</rptOwnerZipCode>
            <rptOwnerStateDescription>UNITED KINGDOM</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2026-10-06</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness></transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>118</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>24.1915</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>105834</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes></footnotes>

    <remarks>Due to the issuer's status as a foreign private issuer pursuant to Rule 3a12-3(b) under the Securities Exchange Act of 1934 (the &quot;Act&quot;), the reporting person's transactions in the issuer's securities are exempt from Sections 16(b) and 16(c) of the Act.</remarks>

    <ownerSignature>
        <signatureName>/s/ Noleen McDonnell, as Attorney-in-Fact</signatureName>
        <signatureDate>2026-10-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
